Decoder an decoding method

[0001] This invention relates to a decoder and a decoding method for decoding a soft-output.

[0002] Research efforts have been made in recent years for reducing symbol error rates by using soft-outputs for decoded outputs of inner codes of concatenated codes and also for outputs of iterative decoding operations using an iterative decoding method. Studies of decoding methods for minimizing symbol error rates are being made extensively. For example, Bahl, Cock, Jelinek and Raviv, “Optimal decoding of linear codes for minimizing symbol error rate” IEEE Trans. Inf. Theory, vol. IT-20, pp. 284–287, March 1974, describes BCJR algorithm as a method for minimizing the symbol error rate when decoding a predetermined code such as a convolutional code. The BCJR algorithm is adapted to output the likelihood of each symbol instead of outputting each symbol as a result of a decoding operation. Such an output is referred to as soft-output. Now, the BCJR algorithm will be summarily described below. In the following description, it is assumed that a piece of digital information is turned into a convolutional code by means of encoder 201 of a transmitter (not shown) and the output of the encoder is input to a receiver (not shown) by way of a memoryless communication channel 202 having noise and decoded by decoder 203 of the receiver for observation.

[0003] Firstly, M states (transition state) representing the contents of the shift register of the encoder 201 are expressed by m (0, 1, . . . , M−1) and the state at clock time t is expressed by S_t. Also, if a k-bit information is input in a single time slot the input at clock time t is expressed by i_t=(i_t1, i_t2, . . . , i_tk) and the input system is expressed by I₁^T=(i₁, i₂, . . . , i_T). If there is a transition from state m′ to state m, the information bit corresponding to the transition is expressed by i(m′, m)=(i₁(m′, m), i₂(m′, m), . . . , i_k(m′, m)). Additionally, if an n-bit code is output in a single time slot, the output at clock time t is expressed by X_t=(x_t1, x_t2, . . . , x_tn) and the output system is expressed by X₁^T=(x₁, x₂, . . . , x_T). If there is a transition from state m′ to state m, the code bit corresponding to the transition is expressed by X(m′, m)=(x₁(m′, m), x₂(m′, m), . . . , x_n(m′, m)).

[0004] The convolutional coding of the encoder 201 starts at state S₀=0 and ends at state S_T=0 after outputting X₁^T. The inter-state transition probability P_t(m|m′) of each state is defined by formula (1) below;
P_t(m|m′)=P_r{S_t=m|S_t−1=m′}  (1),
where Pr{A|B} at the right side represents the conditional probability of occurrence of A under the condition of occurrence of B. This transition probability P_t(m|m′) is equal to the probability Pr{i_t=i} that i_t is i at clock time t when a transition from state m′ to state m occurs in response to input i.
P_t(m|m′)=P_r{i₁=i}  (2)

[0005] The memoryless communication channel 202 having noise receives X₁^T as input and output Y₁^T. If an n-bit value to be received is output in a single time slot, the output at clock time t is expressed by y_t=(y_t1, y_t2, . . . , y_tn) and the expression of Y₁^T=(y₁, y₂, . . . , y_T) is used. Then, the transition probability of the memoryless communication channel 202 having noise is defined by formula (3) below, using the transition probability Pr{y_j|x_j} of all the symbols for all t(1≦t≦T).

[0006] $\begin{array}{cc}\mathrm{Pr}\left\{Y_1^t❘X_1^t\right\}=\prod _{j=1}^t\mathrm{Pr}\left\{y_j❘x_j\right\}& \left(3\right)\end{array}$

[0007] Now, λ_tj is defined by formula (4) below. It will be appreciated that λ_tj of formula (4) below represents the likelihood of the input information at clock time t when Y₁^T is received and hence the soft-output to be obtained.

[0008] $\begin{array}{cc}{\lambda }_{\mathrm{ij}}=\frac{\mathrm{Pr}\left\{i_{\mathrm{ij}}=1❘Y_1^T\right\}}{\mathrm{Pr}\left\{i_{\mathrm{ij}}=0❘Y_1^T\right\}}& \left(4\right)\end{array}$

[0009] With the BCJR algorithm, probabilities α₁, β₁ and γ₁ are defined respectively by formulas (5) through (7) below. Note that Pr{A; B} represents the probability of occurrence of both A and B.
α_t(m)=Pr{S_t=m; Y₁^t}  (5)
β_t(m)=Pr{Y_t+1^T|S_t=m}  (6)
γ_t(m′,m)=Pr{S_t=m; y_t|S_t−1=m′}  (7)

[0010] Now, the probabilities α_t, β_t and γ_t will be specifically described below by referring to FIG. 2 of the accompanying drawings that illustrates a trellis diagram, or a state transition diagram that can be used in the encoder 201. In FIG. 2, α_t−1 corresponds to the passing probability of each state at clock time t−1 that is computed sequentially on a time series basis from state S₀=0 at the coding start time by using the received value and β_t corresponds to the passing probability of each state at clock time 1 that is computed sequentially on an inverse time series basis from state S_T=0 at the coding end time by using the received value, while γ_t corresponds to the reception probability of the output of each branch that is transferred from a state to another at clock time t as computed on the basis of the received value at clock time t and the input probability.

[0011] Then, the soft-output λ_tj can be expressed by formula (8) below, using these probabilities α_t, β_t and γ_t.

[0012] $\begin{array}{cc}{\lambda }_{\mathrm{tj}}=\frac{\sum _{m^{\prime },m{i}_j\left(m^{\prime },m\right)=1}{\alpha }_t\left(m^{\prime }\right){\gamma }_t\left(m^{\prime },m\right){\beta }_t\left(m\right)}{\sum _{m^{\prime },m{i}_j\left(m^{\prime },m\right)=0}{\alpha }_t\left(m^{\prime }\right){\gamma }_t\left(m^{\prime },m\right){\beta }_t\left(m\right)}& \left(8\right)\end{array}$

[0013] Meanwhile, equation (9) below holds true for t=1, 2, . . . , T;

[0014] $\begin{array}{cc}{\alpha }_t\left(m\right)=\sum _{m^{\prime }=0}^{M-1}{\alpha }_{t-1}\left(m^{\prime }\right){\gamma }_t\left(m^{\prime },m\right),& \left(9\right)\end{array}$
where, α₀(0)=1, α₀(m)=0(m≠0)

[0015] Similarly, equation (10) below holds true for t=1, 2, . . . , T.

[0016] $\begin{array}{cc}{\beta }_t\left(m\right)=\sum _{m^{\prime }=0}^{M-1}{\beta }_{t+1}\left(m^{\prime }\right){\gamma }_{t+1}\left(m,m^{\prime }\right)\mathrm{where},\text{}{\beta }_T\left(0\right)=1,{\beta }_T\left(m\right)=0\left(m\ne 0\right)& \left(10\right)\end{array}$

[0017] Likewise, as for y_t, equation (11) below holds true for t=1, 2, . . . , T.

[0018] $\begin{array}{cc}{\gamma }_t\left(m^{\prime },m\right)=\{\begin{array}{c}{P}_t\left(m❘m^{\prime }\right)·\mathrm{Pr}\left\{y_i❘x\left(m^{\prime },m\right)\right\}=\\ \mathrm{Pr}\left\{i_t=i\left(m^{\prime },m\right)\right\}·\mathrm{Pr}\left\{y_i❘x\left(m^{\prime },m\right)\right\}\\ \text{:}{\hspace{0.17em}}^{*}1\\ 0\text{:}{\hspace{0.17em}}^{*}2\end{array}:{\hspace{0.17em}}^{*}1\text{:}\mathrm{for}\mathrm{transition}\mathrm{from}{m}^{\prime }\mathrm{to}m\mathrm{at}\mathrm{input}i:{\hspace{0.17em}}^{*}2\text{:}\mathrm{for}\mathrm{non}\text{-}\mathrm{transition}\mathrm{from}{m}^{\prime }\mathrm{to}m\mathrm{at}\mathrm{input}i& \left(11\right)\end{array}$

[0019] Therefore, the decoder 203 determines soft-output λ_t by following the steps shown in FIG. 3 for soft-output decoding, applying the BCJR algorithm.

[0020] Referring to FIG. 3, firstly in Step S201, the decoder 203 computes the probability α_t(m) and the probability γ_t(m′, m), using the above equations (9) and (11) respectively, each time it receives γ_t.

[0021] Then in Step S202, after receiving all the system Y₁^T, the decoder 203 computes the probability β_t(m) for each state m at all clock times t, using the above equation (10).

[0022] Subsequently in Step S203, the decoder 203 computes the soft-output λ_t at each clock time t, substituting the probabilities α_t, β_t and γ_t obtained respectively in Steps S201 and S202 for the above equation (8).

[0023] Thus, the decoder 203 can decodes the soft-output obtained by applying the BCJR algorithm and following the above processing steps.

[0024] However, the above described BCJR algorithm requires computations to be made by directly holding probability values and the computations involve a large number of operations of multiplication, which by turn entails a problem of a large volume of computing operation. Robertson, Villebrun and Hoeher, “A comparison of optimal and sub-optimal MAP decoding algorithms operating in the domain”, IEEE Int. Conf. On Communications, pp. 1009–1013, June 1995, describes a technique for reducing the volume of computing operation by using a Max-Log-MAP algorithm and a Log-MAP algorithm (to be respectively referred to as Max-Log-BCJR algorithm and Log-BCJR algorithm hereinafter).

[0025] Firstly, the Max-Log-BCJR algorithm will be described. The Max-Log-BCJR algorithm is designed to express the probabilities α_t, β_t and γ_t and the soft-output λ_t in terms of natural logarithm in order to replace the multiplications for computing the probabilities with additions of natural logarithm in a manner as indicated by formula (12) and the additions for the probabilities are approximated by operations for computing maximum values, using formula (13) below. Note that, max (x, y) in formula (13) is a function selecting the larger value of ether x or y.
log(e^x·e^y)=x+y  (12)
log(e^x+e^y)≅max(x,y)  (13)

[0026] Now, for the purpose of simplicity, natural logarithm is denoted by I and the values of α_t, β_t, γ_t and λ_t as expressed in the form of natural logarithm are denoted respectively by Iα_t, Iβ_t, Iγ_t and Iλ_t as shown in formula (14) below.

[0027] $\begin{array}{cc}\{\begin{array}{c}I{\alpha }_t\left(m\right)=\log \left({\alpha }_t\left(m\right)\right)\\ I{\beta }_t\left(m\right)=\log \left({\beta }_t\left(m\right)\right)\\ I{\gamma }_t\left(m\right)=\log \left({\gamma }_t\left(m\right)\right)\\ I{\lambda }_t=\log {\lambda }_t\end{array}& \left(14\right)\end{array}$

[0028] With the Max-Log-BCJR algorithm, the log likelihoods Iα_t, Iβ_t, Iγ_t are approximated by formulas (15) through (17) shown below. Note that maximum value max of the right side of formula (15) in state m′ is determined in state m′ where a transition to state m exists. Similarly, maximum value max of the right side of formula (16) in state m′ is determined in state m′ where a transition from state m exists.

[0029] $\begin{array}{cc}I{\alpha }_t\left(m\right)\cong \underset{m^{\prime }}{\max }\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)\right)& \left(15\right)\\ I{\beta }_t\left(m\right)\cong \underset{m^{\prime }}{\max }\left(I{\beta }_{t+1}\left(m^{\prime }\right)+I{\gamma }_{t+1}\left(m,m^{\prime }\right)\right)& \left(16\right)\end{array}$
Iγ_t(m′,m)=log(Pr{i_t=i(m′,m)})+log(Pr{y_t|x(m′,m)})  (17)

[0030] Additionally, with the Max-Log-BCJR algorithm, the log soft-output Iλ_t is approximated by formula (18) shown below. Note that maximum value max of the first term of the right side in formula (15) is determined in state m′ where a transition to state m exists when the input is equal to “0”.

[0031] $\begin{array}{cc}\begin{array}{c}I{\lambda }_{\mathrm{ij}}\cong \underset{m^{\prime },m{i}_j\left(m^{\prime },m\right)=1}{\max }\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right)-\\ \underset{m^{\prime },m{i}_j\left(m^{\prime },m\right)=0}{\max }\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right)\end{array}& \left(18\right)\end{array}$

[0032] When the decoder 203 decodes the soft-output, applying the Max-Log-BCJR algorithm, it determines the soft-output λ_t on the basis of these relationships, by following the steps shown in FIG. 4.

[0033] Referring to FIG. 4, firstly in Step S211, the decoder 203 computes the log likelihood Iα_t(m) and the log likelihood Iγ_t(m′, m), using the above equations (15) and (17) respectively, each time it receives y_t.

[0034] Then in Step S212, after receiving all the system Y₁^T, the decoder 203 computes the log likelihood Iβ_t(m) for each state m at all clock times t, using the above equation (16).

[0035] Subsequently in Step S213, the decoder 203 computes the log soft-output Iλ_t at each clock time t, substituting the log likelihoods Iα_t, Iβ_t and Iγ_t obtained respectively in Steps S211 and S212 for the above equation (18).

[0036] Thus, the decoder 203 can decodes the soft-output obtained by applying the Max-Log-BCJR algorithm and following the above processing steps.

[0037] Because the Max-Log-BCJR algorithm does not involve multiplications, it can considerably reduce the volume of operation if compared with the BCJR algorithm.

[0038] Now, the Log-BCJR algorithm will be described below. The Log-BCJR algorithm is designed to improve the accuracy of approximation of the Max-Log-BCJR algorithm. More specifically, with the Log-BCJR algorithm, the probability addition of the above formula (13) is modified to produce formula (19) below by adding a correction term to make the sum of the logarithmic addition more accurate. The correction will be referred to as log-sum correction hereinafter.
log(e^x+e^y)=max(x, y)+log(1+e^−|x−y|)  (19)

[0039] The operation of the left side of the above formula (19) is referred to as log-sum operation and, for the sake of convenience, the operator of the log-sum operation is expressed by “#” as shown in formula (20) below by following the numeration system described in S. S. Pietrobon, “Implementation and performance of a turbo/MAP decoder”, Int. J. Satellite Commun., vol. 16, pp. 23–46, January–February 1998 (although “E” is used to denote the operator in the above identified paper). Additionally, the operator of the cumulative addition of log-sum operations is expressed by “#Σ” as shown in formula (21) below (although “E” is used in the above identified paper).
x#y=log(e^x+e^y)  (20)

[0040] $\begin{array}{cc}\#\sum _{i=0}^{M-1}{x}_i=\left(\left(\dots \left(\left(x_0\#x_1\right)\#x_2\right)\dots \right)\#x_{M-1}\right)& \left(21\right)\end{array}$

[0041] The log likelihoods Iα_t and Iβ_t and the log soft-output Iλ_t of the Log-BCJR algorithm are expressed respectively by formulas (22) through (24) below using these operators. Since the expression of (17) is also used for the log likelihood Iγ_t here, it will not be described any further.

[0042] $\begin{array}{cc}I{\alpha }_t\left(m\right)=\#\sum _{m^{\prime }=0}^{M-1}\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)\right)& \left(22\right)\end{array}$

[0043] $\begin{array}{cc}I{\beta }_t\left(m\right)=\#\sum _{m^{\prime }=0}^{M-1}\left(I{\beta }_{t+1}\left(m^{\prime }\right)+I{\gamma }_{t+1}\left(m,m^{\prime }\right)\right)& \left(23\right)\\ \begin{array}{c}I{\lambda }_{\mathrm{tj}}=\#\sum _{m^{\prime },m{i}_j\left(m^{\prime },m\right)=1}\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right)-\\ \#\sum _{m^{\prime },m{i}_j\left(m^{\prime },m\right)=0}\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right)\end{array}& \left(24\right)\end{array}$

[0044] Note that the cumulative addition of log-sum operations in state m′ of the right side of the above formula (22) is conducted in state m′ where a transition to state m exists, whereas the cumulative addition of log-sum operations in state m′ of the right side of the above formula (23) is conducted in state m′ where a transition from state m exists. Furthermore, the cumulative addition of log-sum operations of the first term of the right side in formula (24) is conducted in state m′ where a transition to state m exists when the input is equal to “1”, and the cumulative addition of log-sum operations of the second term is conducted in state m′ where a transition to state m exists when the input is equal to “0”.

[0045] When the decoder 203 decodes the soft-output, applying the Log-BCJR algorithm, it determines the soft-output λ_t on the basis of these relationships, by following the steps shown in FIG. 4.

[0046] Referring to FIG. 4, firstly in Step S211, the decoder 203 computes the log likelihood Iα_t(m) and the log likelihood Iγ_t(m′, m), using the above equations (22) and (17) respectively, each time it receives y_t.

[0047] Then in Step S212, after receiving all the system Y₁^T, the decoder 203 computes the log likelihood Iβ_t(m) for each state m at all clock times t, using the above equation (23).

[0048] Subsequently in Step S213, the decoder 203 computes the log soft-output Iλ_t at each clock time t, substituting the log likelihoods Iα_t, Iβ_t and Iγ_t obtained respectively in Steps S211 and S212 for the above equation (24).

[0049] Thus, the decoder 203 can decodes the soft-output obtained by applying the Log-BCJR algorithm and following the above processing steps. Since the correction term, or the second term, of the right side of the above formula (19) is expressed by means of a linear function of variable |x−y|, it is possible to accurately compute probabilities by storing in advance the values that the term can take in a ROM (not shown).

[0050] While the Log-BCJR algorithm may entail a volume of operation that is greater than the Max-Log-BCJR algorithm, it does not involve any multiplications and its output is exactly the logarithmic value of the soft-output of the BCJR algorithm if the quantization error is eliminated.

[0051] Meanwhile, the above described log likelihood Iγ_t comprises a priori probability information shown in the first term and probability information (to be referred to as channel value hereinafter) obtained from the received value y_t of the second term of the right side of the above equation (17).

[0052] With the Max-Log-BCJR algorithm and the Log-BCJR algorithm, it is also possible to use a log likelihood ratio that is a natural log value of the ratio of two probabilities. Then, the log likelihood Iγ_t can be expressed by formula (25) below. More specifically, the log likelihood Iγ_t can be expressed by using a priori probability information that is the cumulative sum of multiplication products of the natural log values of the log likelihood ratios of probability Pr{i_tj=1} and probability Pr{i_tj=0} and input i_j(m′, m), and a channel value that is the cumulative sum of multiplication products of the natural log values of the log likelihood ratios of probability Pr{y_tj|x_tj=1} and the probability Pr{y_tj|x_tj=0} and output x_j(m′, m).

[0053] $\begin{array}{cc}\begin{array}{c}I{\gamma }_t=\sum _{j=1}^k{i}_j\left(m^{\prime },m\right)·\log \frac{\mathrm{Pr}\left\{i_{\mathrm{tj}}=1\right\}}{\mathrm{Pr}\left\{i_{\mathrm{tj}}=0\right\}}+\\ \sum _{j=1}^n{x}_j\left(m^{\prime },m\right)·\log \frac{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=1\right\}}{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=0\right\}}\end{array}& \left(25\right)\end{array}$

[0054] If it is assumed that additive white Gaussian noise (AWGN) is added to the output x_tj of the encoder 201 by the memoryless communication channel 202, the second term of the above formula (25) can be developed in a manner as shown by formula (26) below. Note that “A” in the formula (26) represents the received value y_tj that maximizes the probability Pr{y_tj|x_tj=1} or, in other words, the average value of the normal distribution that the probability density function using the received value y_tj as variable follows and “σ²” represents the variance of the normal distribution. The received value y_tj that maximizes the probability Pr{y_tj|x_tj=0} is expressed by “−A”. In reality, “A” and “−A” are the transmission amplitudes of the outputs x_tj=1, 0 from the encoder 201.

[0055] $\begin{array}{cc}\begin{array}{c}\log \frac{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=1\right\}}{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=0\right\}}=\log \frac{\frac{1}{\sqrt{2{\mathrm{\pi \sigma }}^2}}{e}^{-\frac{{\left(y_{\mathrm{tj}}-A\right)}^2}{2{\sigma }^2}}}{\frac{1}{\sqrt{2{\mathrm{\pi \sigma }}^2}}{e}^{-\frac{{\left(y_{\mathrm{tj}}+A\right)}^2}{2{\sigma }^2}}}\\ =\log e^{\left(\frac{{\left(y_{\mathrm{tj}}+A\right)}^2}{2{\sigma }^2}-\frac{{\left(y_{\mathrm{tj}}-A\right)}^2}{2{\sigma }^2}\right)}\\ =\frac{{\left(y_{\mathrm{tj}}+A\right)}^2}{2{\sigma }^2}-\frac{{\left(y_{\mathrm{tj}}-A\right)}^2}{2{\sigma }^2}=\frac{2A}{{\sigma }^2}{y}_{\mathrm{tj}}\end{array}& \left(26\right)\end{array}$

[0056] Thus, the decoder 203 can directly obtain the channel value from the received value y_t by knowing the characteristics of the memoryless communication channel 202. More specifically, the Iγ computation circuit for computing the log likelihood Iγ_t of the decoder 203 can be composed of only an adder as shown in FIG. 6. In other words, the decoder 203 can determine the channel value by multiplying the received value y_tj by a predetermined coefficient AMP and then the log likelihood Iγ_t by adding the channel value and a priori probability information (which is denoted by APP in FIG. 6 and will be referred to as a priori probability information APP hereinafter) by means of the Iγ computation circuit. Differently stated, when the decoder 203 needs to multiply the received value y_tj by an appropriate coefficient AMP when it determines the log likelihood Iγ_t.

[0057] However, when a decoder 203 is actually installed as hardware, it is difficult to determine the log likelihood Iγ_t by the arrangement of FIG. 6 because the quantization range is limited.

[0058] More specifically, since the coefficient AMP normally takes a value between 0.5 and 10, the distribution of the channel value obtained by multiplying the received value y_tj by coefficient AMP varies remarkable relative to the dynamic range of a priori probability information APP. If, for example, a range between 0.5 and 8 is selected for coefficient APP, the range of distribution of the channel value obtained by multiplying the received value y_tj by coefficient AMP can be at most 16 times as much as the dynamic range of a priori probability information APP.

[0059] Therefore, the decoder 203 cannot be provided with a dynamic range that is wide enough for satisfactorily expressing information on the received value and hence it is difficult to accurately determine the log likelihood Iγ_t.

[0060] Assume that the encoder 201 is one where a plurality of convolutional encoders are concatenated in parallel or in series with interleavers interposed between them for parallel concatenated convolutional coding (to be referred to as PCCC hereinafter) or serially concatenated convolutional coding (to be referred to as SCCC hereinafter) or one where PCCC or SCCC is combined with multi-valued modulation for turbo trellis coded modulation (to be referred to as TTCM hereinafter) or serial concatinated trellis coded modulation (to be referred to as SCTCM hereinafter), whichever approprate. In this case, the decoder 203 is formed by concatenating a plurality of soft-output decoding circuits designed for maximum a poteriori probability (MAP) decoding with interleavers or deinterleavers interposed between them for the purpose of so-called iterative decoding.

[0061] Extrinsic information that is the difference between the above a posteriori probability information that corresponds to the above described soft-output or log soft-output and the a priori probability information (APP) is used as a priori probability information APP at the time of iterative decoding. In other words, a priori probability information APP is a pile of received values y_tj. When this is taken into consideration, it will not be desirable for the decoder 203 that there are fluctuations in the distribution of the received value y_tj relative to the dynamic range of a priori probability information APP.

[0062] In other words, it will be desirable for the decoder 203 to make the resolution of a priori probability information APP or the quantization slot of a priori probability information APP variable as a function of the signal to noise ratio (S/N), while maintaining the ratio of the dynamic range of a priori probability information APP to the signal point of the received value y_tj to a constant level.

[0063] Such a decoder 203 can be realized substantially by employing a configuration as shown in FIG. 8 for the Iγ computation circuit for computing the log likelihood Iγ_t. Then, the decoder 203 can determine the log likelihood Iγ_t by adding the quotient obtained by dividing the a priori probability information APP by said coefficient AMP to the received value y_tj. With such an arrangement, the decoder 203 can hold the dynamic range of the received value y_tj without relaying on the coefficient AMP.

[0064] However, if “0.5” is selected for the coefficient AMP, the range that can be used for expressing a priori probability information APP extends between −2×Max and 2×Max relative to the upper limit (Max) and the lower limit (−Max) of the quantization range of the received value y_tj, if “8” is selected for the coefficient AMP, the range to be used for expressing a priori probability information APP extends between (−⅛)×Max and (⅛)×Max. In other words, the range that can be used for expressing a priori probability information APP becomes variable. Additionally, the quantization slot of a priori probability information APP also becomes variable. Thus, if a priori probability information APP becomes very fine and goes beyond the allowable range of quantization, it will be no longer possible to express a priori probability information APP.

[0065] In this way, when the resolution of a priori probability information APP is modified, there may arise occasions where a priori probability information APP can no longer be expressed to make it impossible to accurately determine the log likelihood Iγ_t, although a dynamic range can be secured for the received value y_tj.

[0066] In view of the above identified circumstances, it is therefore the object of the present invention to provide a decoder and a decoding method that can select an optimal dynamic range and an optimal quantization slot when the input needs to be made with a fixed number of bits.

[0067] In an aspect of the invention, the above object is achieved by providing a decoder adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, characterized by comprising: a soft-output decoding means for receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, for the purpose of soft-output decoding; said soft-output decoding means generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside of the soft-output decoding means.

[0068] Therefore, a decoder according to the present invention and having the above defined configuration receives the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information by the soft-output decoding means and generates a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient.

[0069] In another aspect of the invention, there is provided a decoding method adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, characterized by comprising: a soft-output decoding step of receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, and generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside for the purpose of soft-output decoding.

[0070] Therefore, a decoding method according to the present invention and having the above described soft-output decoding step is adapted to receive the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information and generate a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient in said soft-output decoding step.

[0071] In still another aspect of the invention, there is provided a decoder for iteratively decoding a code generated by concatenating a plurality of element codes, said decoder being adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, characterized by comprising: a plurality of concatenated soft-output decoding means for receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, for the purpose of soft-output decoding; each of said soft-output decoding means generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside of the soft-output decoding means and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means.

[0072] Therefore, a decoder according to the present invention and having the above defined configuration receives the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information by the soft-output decoding means, generates a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient and outputs the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means.

[0073] In still another aspect of the invention, there is provided a decoding method for iteratively decoding a code generated by concatenating a plurality of element codes, said method being adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, characterized by comprising: a plurality of consecutive soft-output decoding steps of receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding steps for the purpose of soft-output decoding.

[0074] Therefore, a decoding method according to the present invention and having the above described soft-output decoding step is adapted to receive the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information, generate a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means in said soft-output decoding step.

[0075] Thus, a decoder according to the first aspect of the invention and adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood is characterized by comprising: a soft-output decoding means for receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, for the purpose of soft-output decoding; said soft-output decoding means generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using the first additive coefficient, the second additive coefficient, and a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside of the soft-output decoding means.

[0076] Therefore, a decoder according to the present invention and having the above defined configuration receives the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information by the soft-output decoding means and generates a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient so that it can selects an optimal quantization slot necessary for the internal arithmetic operations of the soft-output decoding means that are conducted to optimally generate a dynamic range and a quantization slot relative to the information input to the soft-output decoding that requires inputs of a fixed number of bits and also extrinsic information.

[0077] Thus, a decoding method according to the second aspect of the invention and adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood is characterized by comprising: a soft-output decoding step of receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, and generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using the first additive coefficient, the second additive coefficient, and a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside for the purpose of soft-output decoding.

[0078] Therefore, a decoding method according to the present invention and having the above described soft-output decoding step is adapted to receive the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information and generate a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient in said soft-output decoding step so that it can selects an optimal quantization slot necessary for the internal arithmetic operations in the soft-output decoding steps that are conducted to optimally generate a dynamic range and a quantization slot relative to the information input to the soft-output decoding that requires inputs of a fixed number of bits and also extrinsic information.

[0079] Thus, a decoder for iteratively decoding a code generated by concatenating a plurality of element codes according to the third aspect of the invention, said decoder being adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, is characterized by comprising: a plurality of concatenated soft-output decoding means for receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, for the purpose of soft-output decoding; each of said soft-output decoding means generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside of the soft-output decoding means and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means.

[0080] Therefore, a decoder according to the present invention and having the above defined configuration receives the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information by the soft-output decoding means, generates a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient and outputs the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means so that it can selects an optimal quantization slot necessary for the internal arithmetic operations of the soft-output decoding means that are conducted to optimally generate a dynamic range and a quantization slot relative to the information input to the soft-output decoding means that requires inputs of a fixed number of bits and also extrinsic information.

[0081] Thus, a decoding method for iteratively decoding a code generated by concatenating a plurality of element codes according to the fourth aspect of the invention, said method being adapted to determine a log likelihood expressing the probability of passing a state in the form of log ratio on the basis of the received value as soft-input for decoding by using the log likelihood, is characterized by comprising: a plurality of consecutive soft-output decoding steps of receiving as input first probability information obtained by dividing the channel value by a first additive coefficient for regulating the amplitude of the received value, said channel value being produced by multiplying the received value by a predetermined coefficient, said first additive coefficient being adapted to be used for multiplying only the received value, and second probability information obtained by multiplying a priori probability information by the reciprocal of a second additive coefficient, said second additive coefficient being adapted to regulate the amplitude of the a priori probability information by multiplying only the a priori probability information, generating a log soft-output describing the soft-output at each clock time in a logarithmic form and/or extrinsic information by using the first additive coefficient, the second additive coefficient, and a third additive coefficient for regulating the amplitude at the time of arithmetic operation in the inside and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding steps for the purpose of soft-output decoding.

[0082] Therefore, a decoding method according to the present invention and having the above described soft-output decoding step is adapted to receive the first probability information obtained by regulating the amplitude of the received value and the second probability information obtained by regulating the amplitude of the a priori probability information, generate a log soft-output and/or extrinsic information by using the first additive coefficient, the second additive coefficient and the third additive coefficient and outputting the generated extrinsic information as a priori probability information of the immediately succeeding soft-output decoding means in said soft-output decoding step so that it can selects an optimal quantization slot necessary for the internal arithmetic operations in the soft-output decoding steps that are conducted to optimally generate a dynamic range and a quantization slot relative to the information input to the soft-output decoding that requires inputs of a fixed number of bits and also extrinsic information.

[0112] Now, the present invention will be described in greater detail by referring to the accompanying drawings that illustrate a preferred embodiment of the invention.

[0113] Referring firstly to FIG. 10, this embodiment is applied to a data transmission/reception system, in which having encoder 1 of a transmitter (not shown) encodes digital information and transmits it to a receiver (not shown) by way of a memoryless communication path 2 having noise so that the transmitted code is decoded by decoder 3 of the receiver.

[0114] Of the data transmission/reception system, the decoding operation of the decoder 3 for decoding the code encoded by the encoder 1 is a maximum a posteriori probability (to be referred to as MAP hereinafter) decoding operation that is conducted on the basis of the Max-Log-MAP algorithm or the Log-MAP algorithm (to be referred to as Max-Log-BCJR algorithm or Log-BCJR algorithm, whichever appropriate, hereinafter) as described in Robertson, Villebrun and Hoeher, “A comparison of optimal and sub-optimal MAP decoding algorithms operating in the domain”, IEEE Int. Conf. On Communications, pp. 1009–1013, June 1995. In other words, it is adapted to determine probabilities α_t, β_t, γ_t and soft-output λ_t respectively as log likelihoods Iα_t, Iβ_t, Iγ_t that are expressed in the form of log likelihood by using natural logarithm and log soft-output Iλ_t that corresponds to so-called a posteriori probability information. Particularly, the decoder 3 is adapted to optimally select a dynamic range and a quantization slot for the received value that needs to be input with a fixed number of bits and so-called a priori probability information and also a quantization slot necessary for internal arithmetic operations in order to generate extrinsic information.

[0115] Note that, in the following description, the decoder 3 decodes codes on the basis of the Log-BCJR algorithm. Also the following assumptions are made. M states (transition state) representing the contents of the shift register of the encoder 11 are expressed by m (0, 1, . . . , M−1) and the state at clock time t is expressed by S_t. Also, if a k-bit information is input in a single time slot the input at clock time t is expressed by i_t=(i_t1, i_t2, . . . , i_tk) and the input system is expressed by I₁^T=(i₁, i₂, . . . , i_T). If there is a transition from state m′ to state m, the information bit corresponding to the transition is expressed by i(m′, m)=(i₁(m′, m), i₂(m′, m), . . . , i_k(m′, m)). Additionally, if an n-bit code is output in a single time slot, the output at clock time t is expressed by X_t=(x_t1, x_t2, . . . , x_tn) and the output system is expressed by X₁^T=(x₁, x₂, . . . , x_T). If there is a transition from state m′ to state m, the code bit corresponding to the transition is expressed by X(m′, m)=(x₁(m′, m), x₂(m′, m), . . . , x_n(m′, m)). The memoryless communication channel 2 receives X₁^T as input and produces Y₁^T as output. if an n-bit received value is output in a single time slot, the output at clock time t is expressed by Y_t=(y_t1, y_t2, . . . , y_tn) and Y₁^T=(y₁, y₂, . . . , y_T) is used.

[0116] The encoder 1 is designed to modulate a code such as a convolutional code, a parallel concatenated convolutional code (to be referred to as PCCC hereinafter) or a serially concatenated convolutional code (to be referred to as SCCC hereinafter) by means of a modulation method of arranging the signal points that can provide a distribution of the received value for each bit such as the binary phase shift keying (to be referred to as BPSK hereinafter) modulation method whose signal points are illustrated in FIG. 11 or the quadrature phase shift keying (to be referred to as QPSK hereinafter) modulation method whose signal points are illustrated in FIG. 12. Alternatively, the encoder 1 may be designed to modulate a convolutional code by a modulation method of arranging the signal points that can not provide a distribution of the received value for each bit such as the 8-phase shift keying (to be referred to as 8PSK hereinafter) modulation method as shown in FIG. 13 for the purpose of trellis coded modulation (to be referred to as TCM hereinafter) that can accommodate both the arrangement of signal points and the decoding characteristics of error correction codes in an integrated manner. It is also possible to make the encoder 1 to be adapted to turbo trellis coded modulation (to be referred to as TTCM hereinafter) or serial concatenated trellis code modulation (to be referred to as SCTCM hereinafter). All these coding methods are know as turbo coding methods.

[0117] For the purpose of simplicity, in the following description, it is assumed for the time being that an encoder 1′ as shown in FIG. 14 is used. The encoder 1′ comprises three exclusive-OR circuits 11, 13, 15 and two shift registers 12, 14 and is designed to perform convolutional coding operations with a constraint length of “3”. It is also assumed that the encoder 1′ does not discriminate the modulation methods of modulators (not shown).

[0118] The exclusive-OR circuit 11 performs an exclusive-OR operation, using a 1-bit input data i_t1 and the data supplied from the exclusive-OR circuit 13 and supplies the outcome of the operation to the shift register 12 and the exclusive-OR circuit 15.

[0119] The shift register 12 keeps on supplying the 1-bit data it holds to the exclusive-OR circuit 13 and the shift register 14. Then, the shift register 12 newly holds the 1-bit data fed from the exclusive-OR circuit 11 in synchronism with the clock and supplies the data to the exclusive-OR circuit 13 and the shift register 14.

[0120] The exclusive-OR circuit 13 performs an exclusive-OR operation, using the data fed from the shift registers 12, 14 and supplies the outcome of the operation to the exclusive-OR circuit 11.

[0121] The shift register 14 keeps on supplying the 1-bit data it holds to the exclusive-OR circuits 13, 15. Then, the shift register 14 newly holds the 1-bit data fed from the shift register 12 in synchronism with the clock and supplies the data to the exclusive-OR circuits 13, 15.

[0122] The exclusive-OR circuit 15 performs an exclusive-OR operation, using the data fed form the exclusive-OR circuit 11 and the data fed from the shift register 14 and outputs the outcome of the operation as 1-bit output data x_t2 out of 2-bit output data X_t.

[0123] Upon receiving a 1-bit input data i_t1 as input, the encoder 1′ externally outputs the input data without modifying it as systematic component 1-bit output data x_t1 of 2-bit output data X_t and, at the same time, performs a recursive convolutional coding operation on the input data i_t1. Then, it externally outputs the outcome of the operation as the other 1-bit output data x_t2 out of 2-bit output data X_t. In other words, the encoder 1′ performs a recursive convolutional coding operation with a coding ratio of “1/2” and externally outputs the output data X_t.

[0124] FIG. 15 schematically illustrates the trellis of the encoder 1′. In FIG. 15, the paths indicated by broken lines are for an input data i_t1 that is equal to “0” whereas the paths indicated by solid lines are for an input data i_t1 that is equal to “1”. The label put to each path indicates 2-bit output data X_t. In FIG. 15, states are produced by sequentially arranging the contents of the shift register 12 and those of the shift register 14 and state numbers “00”, “10”, “01”, “11” are expressed respectively by “0”, “1”, “2”, “3”. Thus, the number of states M of the encoder 1′ is equal to 4 and two paths are used for transition from a state to the next state.

[0125] The output data X_t coded by the encoder 1′ is modulated by a modulator (not shown) by means of a predetermined modulation method and output to a receiver by way of the memoryless communication channel 2.

[0126] On the other hand, FIG. 16 shows a decoder 3′ adapted to decode the code encoded by the encoder 1′. Referring to FIG. 16, the decoder 3′ comprises two multipliers 21, 22 and a soft-output decoding circuit 23 operating as soft-output decoding means. The decoder 3′ is adapted to estimate the input data i_t1 of the encoder 1′ by determining the log soft-output Iλ_t from the received value y_t that is reduced as soft-input under the influence of the noise generated on the memoryless communication channel 2.

[0127] If it is assumed that additive white Gaussian noise (to be referred to as AWGN hereinafter) is added by the memoryless communication channel 2, the multiplier 21 multiplies the value AMP/C_R obtained by dividing the predetermined coefficient AMP by the first additive coefficient C_R by which only the received value y_t is multiplied to regulate the amplitude of the received value y_t by the received value y_t. In other words, the multiplier 21 generates probability information AMP/C_R×y_t that is the first probability information obtained by dividing the probability information (to be referred to as channel value hereinafter) AMP×y_tj, which is acquired from the received value y_tj by multiplying the received value y_t by the coefficient AMP, by the first additive coefficient C_R. Then, the multiplier 21 supplies the probability information AMP/C_R×y_t obtained as a result of the multiplication to the soft-output decoding circuit 23.

[0128] The multiplier 22 multiplies the a priori probability information APP_t by 1/C_A, which is the reciprocal of the second additive coefficient C_A to be used as multiplier for multiplying only the a priori probability information APP_t in order to regulate the amplitude of the a priori probability information APP_t. Then, the multiplier 22 supplies the second probability information 1/C_A×APP_t to the soft-output decoding circuit 23. The a priori probability information APP_t is given as the log likelihood ratio that is a natural log value expressing the ratio of the probability Pr{i_t1=1} that the input data i_t1 is equal to “1” to the probability Pr{i_t1=0} that the input data i_t1 is equal to “0”. The a priori probability information APP_t is give as probability Pr{i_t1=1} or probability Pr{i_t1=0}. Because the sum of the probability Pr{i_t1=1} and the probability Pr{i_t1=0} is equal to “1”, the a priori probability information APP_t may be determined as the difference of the natural log value of the probability Pr{i_t1=1} and the natural log value Pr{i_t1=0}.

[0129] $\begin{array}{cc}{\mathrm{APP}}_t=\log \frac{\mathrm{Pr}\left\{i_{\mathrm{t1}}=1\right\}}{\mathrm{Pr}\left\{i_{\mathrm{t1}}=0\right\}}& \left(27\right)\end{array}$

[0130] The soft-output decoding circuit 23 is formed as a large scale integerated circuit (to be referred to as LSI hereinafter) by arranging integrally all the components on a single semiconductor substrate. The soft-output decoding circuit 23 comprises a controller 24, an Iγ computation/storage circuit 25 operating as first probability computing means for computing and storing the first log likelihood Iγ, an Iα computation/storage circuit 26 operating as second probability computing means for computing and storing the second log likelihood Iα, an Iβ computation/storage circuit 27 operating as third probability computing means for computing and storing the third log likelihood Iβ, a soft-output computation circuit 28 operating as soft-output computing means for computing the log soft-output Iλ_t and an external information computation circuit 29 operating as external information computing means for computing external information EX_t.

[0131] The controller 24 supplies control signals SCγ, SCα and SCβ respectively to the Iγ computation/storage circuit 25, Iα computation/storage circuit 26 and the Iβ computation/storage circuit 27 to control the operation of each of these circuits.

[0132] The Iγ computation/storage circuit 25 performs under the control of the control signal SCγ fed from the controller 24 an arithmetic operation of formula (28) for each received value y_t, using the probability information AMP/C_R×y_tj fed from the multiplier 21, the probability information 1/C_A×APP_t fed from the multiplier 22, the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I by which both the received value y_t and the a priori probability information APP_t are multiplied to regulate the amplitude of arithmetic operation in the inside of the soft-output decoding circuit 23 and computes the log likelihood C_I×Iγ_t whose amplitude is regulated at each clock time t. It then stores the computed log likelihood C_I×Iγ_t. In other words, the Iγ computation/storage circuit 25 computes the log likelihood C_I×Iγ_t whose amplitude is regulated, wherein the log likelihood C_I×Iγ_t being the logarithmic expression of the probability γ that is determined for each received value γ_t from the output pattern of code and the received value.

[0133] $\begin{array}{cc}\begin{array}{c}{C}_I\times I{\gamma }_t\left(m^{\prime },m\right)=C_I\times (\sum _{j=1}^k{i}_j\left(m^{\prime },m\right)·\log \frac{\mathrm{Pr}\left\{i_{\mathrm{t1}}=1\right\}}{\mathrm{Pr}\left\{i_{\mathrm{t1}}=0\right\}}+\\ \sum _{j=1}^m{x}_j\left(m^{\prime },m\right)·\log \frac{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=1\right\}}{\mathrm{Pr}\left\{y_{\mathrm{tj}}❘x_{\mathrm{tj}}=0\right\}})\\ =C_I\times \left({\mathrm{APP}}_t+\mathrm{AMP}\times y_{\mathrm{tj}}\right)\end{array}& \left(28\right)\end{array}$

[0134] More specifically, as shown in FIG. 17, the Iγ computation/storage circuit 25 comprises as substantive components two multipliers 31, 32, or first and second multiplying means, and an adder 33, or an adding means.

[0135] The Iγ computation/storage circuit 25 multiplies the probability information AMP/C_R×y_tj fed from the multiplier 21 by the product of multiplication of the first additive coefficient C_R and the third additive coefficient C_I by means of the multiplier 31 and supplies the adder 33 with the obtained result. At the same time, the Iγ computation/storage circuit 25 multiplies the probability information 1/C_A×APP_t fed from the multiplier 22 by the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I by means of the multiplier 32 and supplies the adder 33 with the obtained result. Additionally, the Iγ computation/storage circuit 25 adds the values fed from the multipliers 31, 32 by means of the adder 33 to computational determines the log likelihood C_I×Iγ_t. In other words, the Iγ computation/storage circuit 25 computationally determines the log likelihood C_I×Iγ_t that is also expressed as C_I×(APP_t+AMP×y_tj). Then, the Iγ computation/storage circuit 25 stores the obtained log likelihood C_I×Iγ_t in a storage section. Although not shown, the Iγ computation/storage circuit 25 in reality comprises as many adders as the number of states. Therefore, in the case of the above instance, it comprises four adders 33.

[0136] Then, the Iγ computation/storage circuit 25 supplies the Iα computation/storage circuit 26, the Iβ computation/storage circuit 27 and the soft-output computation circuit 28 with the log likelihood C_I×Iγ_t it stores. At this time, the Iγ computation/storage circuit 25 supplies the log likelihood Iγ_t to the Iα computation/storage circuit 26, the Iβ computation/storage circuit 27 and the soft-output computation circuit 28 sequentially in an order suitable for the processing operations of the circuits. In the following description, the log likelihood C_I×Iγ_t fed from the Iγ computation/storage circuit 25 to the Iα computation/storage circuit 26 is expressed by C_I×Iγ(α) and the log likelihood C_I×Iγ_t fed from the Iγ computation/storage circuit 25 to the Iβ computation/storage circuit 27 is expressed by C_I×Iγ(α1), C_I×Iγ(β2), while the log likelihood C_I×Iγ_t fed from the Iγ computation/storage circuit 25 to the soft-output computation circuit 28 is expressed by C_I×Iγ(λ).

[0137] The Iα computation/storage circuit 26 performs under the control of the control signal SCα fed from the controller 24 an arithmetic operation of formula (29), using the log likelihood C_I×Iγ(α) fed from the Iγ computation/storage circuit 25 to determine the log likelihood C_I×Iα_t at each clock time and stores it in itself. Note that the operator “#” in the formula (29) indicates a so-called log-sum operation of the log likelihood of transition from state m′ to state m for input “0” and also the log likelihood of transition from state m″ to state m for input “1”. More specifically, the Iα computation/storage circuit 26 computationally determines the log likelihood C_I×Iα_t at each clock time t by performing an arithmetic operation of formula (30) below. In other words, the Iα computation/storage circuit 26 computationally determines the log likelihood C_I×Iα_t whose amplitude is regulated by performing an arithmetic operation of formula (30) below on the basis of the log likelihood C_I×Iγ at each clock time t, wherein the log likelihood C_I×Iα_t is a logarithmic expression of the probability α of transition from the state at the coding start time to each state on a time series bases for each received value y_t. Then, the Iα computation/storage circuit 26 supplies the soft-output computation circuit 28 with the log likelihood C_I×Iα_t it stores. At this time, it supplies the log likelihood C_I×Iα_t in an order suitable for the processing operation of the soft-output computation circuit 28. In the following description, the log likelihood C_I×Iα_t supplied from the Iα computation/storage circuit 26 to the soft-output computation circuit 28 is expressed by C_I×Iα(λ).

[0138] $\begin{array}{cc}\begin{array}{c}{C}_I\times I{\alpha }_t\left(m\right)=C_I\times (\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)\right)\#\\ \left(I{\alpha }_{t-1}\left(m^{″}\right)+I{\gamma }_t\left(m^{″},m\right)\right))\end{array}& \left(29\right)\\ \begin{array}{c}{C}_I\times I{\alpha }_t\left(m\right)=C_I\times (\max (I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right),I{\alpha }_{t-1}\left(m^{″}\right)+\\ I{\gamma }_t\left(m^{\prime },m\right))+\\ \log \left(1+e^{-\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)\right)-\left(I{\alpha }_{t-1}\left(m^{″}\right)+I{\gamma }_t\left(m^{″},m\right)\right)}\right))\end{array}& \left(30\right)\end{array}$

[0139] The Iβ computation/storage circuit 27 performs under the control of the control signal SCβ fed from the controller 24 an arithmetic operation of formula (31), using the log likelihoods C_I×Iγ(β1) and C_I×Iγ(β2) fed from the Iγ computation/storage circuit 25 to determine the log likelihoods C_I×Iβ_t of two systems at each clock time in parallel and stores them in itself. Note that, as described above, the operator “#” in the formula (31) indicates a so-called log-sum operation of the log likelihood of transition from state m′ to state m for input “0” and also the log likelihood of transition from state m″ to state m for input “1”. More specifically, the Iβ computation/storage circuit 27 computationally determines the log likelihood C_I×Iβ_t at each clock time t by performing an arithmetic operation of formula (32) below. In other words, the Iβ computation/storage circuit 27 computationally determines the log likelihood C_I×Iβ_t whose amplitude is regulated by performing an arithmetic operation of formula (30) below on the basis of the log likelihood C_I×Iγ at each clock time t, wherein the log likelihood C_I×Iβ_t is a logarithmic expression of the probability β of transition from the state at the coding end time to each state on an inverted time series bases for each received value y_t. Then, the Iβ computation/storage circuit 27 supplies the soft-output computation circuit 28 with the log likelihood C_I×Iβ_t of one of the two systems it stores. At this time, it supplies the log likelihood C_I×Iβ_t in an order suitable for the processing operation of the soft-output computation circuit 28. In the following description, the log likelihood C_I×Iβ_t supplied from the Iβ computation/storage circuit 27 to the soft-output computation circuit 28 is expressed by C_I×Iβ(λ).

[0140] $\begin{array}{cc}\begin{array}{c}{C}_I\times I{\beta }_t\left(m\right)=C_I\times (\left(I{\beta }_{t+1}\left(m^{\prime }\right)+I{\gamma }_{t+1}\left(m^{\prime }\right)\right)\#\\ \left(I{\beta }_{t+1}\left(m^{″}\right)+I{\gamma }_{t+1}\left(m,m^{″}\right)\right))\end{array}& \left(31\right)\\ \begin{array}{c}{C}_I\times I{\beta }_t\left(m\right)=C_I\times (\max (I{\beta }_{t+1}\left(m^{\prime }\right)+\\ I{\gamma }_{t+1}\left(m,m^{\prime }\right),I{\beta }_{t+1}\left(m^{″}\right)+I{\gamma }_{t+1}\left(m,m^{″}\right))+\\ \log \left(1+e^{-\left(I{\beta }_{t+1}\left(m^{\prime }\right)+I{\gamma }_{t+1}\left(m,m^{\prime }\right)\right)-\left(I{\beta }_{t+1}\left(m^{″}\right)+I{\gamma }_{t+1}\left(m,m^{″}\right)\right)}\right))\end{array}& \left(32\right)\end{array}$

[0141] The soft-output computation circuit 28 performs an arithmetic operation of formula (33), using the log likelihoods C_I×Iγ(λ) fed from the Iγ computation/storage circuit 25, the log likelihood C_I×Iα(λ) fed from the Iα computation/storage circuit 26 and the log likelihood C_I×Iβ(λ) fed from the Iβ computation/storage circuit 27 to determine the log likelihoods C_I×Iλ_t at each clock time, whose amplitude is regulated, and stores it in itself. At this time, if necessary, the soft-output computation circuit 28 also computationally determines the log soft-output C_I×Iλ_It corresponding to the a posteriori probability information for information bits and the log soft-output C_I×Iλ_Ct corresponding to the a posteriori probability information for code bits and stores them in itself. Then, after rearranging the log soft-outputs C_I×Iλ_It and/or the log soft-output C_I×Iλ_Ct on a time series basis, the soft-output computation circuit 28 supplies them to the external information computation circuit 29 or externally output them. Note that the operator “#Σ” in formula (33) below indicates an cumulative addition for log-sum operations expressed by “#” as described above.

[0142] $\begin{array}{cc}\begin{array}{c}{C}_I\times I{\lambda }_t=C_I\times (\#\sum _{m^{\prime },mi\left(m^{\prime },m\right)=1}\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right)-\\ \#\sum _{m^{\prime },mi\left(m^{\prime },m\right)=0}\left(I{\alpha }_{t-1}\left(m^{\prime }\right)+I{\gamma }_t\left(m^{\prime },m\right)+I{\beta }_t\left(m\right)\right))\end{array}& \left(33\right)\end{array}$

[0143] The external information computation circuit 29 computationally determines the external information 1/C_A×EX_t, using log soft-output C_I×Iλ_t fed from the soft-output computation circuit 28, the probability information 1/C_A×APP_t fed from the multiplier 22, the second additive coefficient C_A and the third additive coefficient C_I. At this time, if necessary, the external information computation circuit 29 also computationally determines the external information 1/C_A×EX_It for information bits and the external information 1/C_A×EX_Ct for code bits.

[0144] More specifically, as shown in FIG. 18, the external information computation circuit 29 comprises an adder 34 that operates as three multiplying means and a differentiator 35 operating as differentiating means.

[0145] The external information computation circuit 29 multiplies the log soft-output C_I×Iλ_t fed from the soft-output computation circuit 28 by the reciprocal of the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or 1/(C_A×C_I), by means of the multiplier 34 and supplies the obtained product to the differentiator 35. Then, the external information computation circuit 29 computes the difference of the information 1/C_A×Iλ_t fed from the multiplier 34 and the probability information 1/C_A×APP_t fed from the multiplier 22 by means of the differentiator 35 and externally outputs the difference as external information 1/C_A×EX_t obtained by regulating the amplitude of the external information EX_t. Although not shown, the external information computation circuit 29 in reality comprises a differentiator 35, the number of which corresponds to the number of bits of the external information 1/C_A×EX_It relative to information bits, and two differentiators 35, the number of which corresponds to the number of bits of the external information 1/C_A×EX_Ct for code bits.

[0146] In response to the input of the received value y_t of the soft-input received by the receiver, the decoder 3′ computes the log likelihood C_I×Iγ_t (m′, m) by means of the Iγ computation/storage circuit 25 of the soft-output decoding circuit 23 each time it receives the received value y_t and also the log likelihood C_I×Iα_t (m) by means of the Iα computation/storage circuit 26 each time it receives the received value y_t. Subsequently, upon receiving all the received values y_t, it computes the log likelihood C_I×Iβ_t (m) for each state m at all clock times t. Then, the decoder 3′ computes the log soft-output C_I×Iλ_t at each clock time t by means of the soft-output computation circuit 28, using the obtained log likelihoods C_I×Iα_t, C_I×Iβ_t and C_I×Iγ_t and externally outputs the log soft-output C_I×Iλ_t or supplies it to the external information circuit 29. Additionally, the decoder 3′ computes the external information 1/C_A×EX_t at each clock time t by means of the external information computation circuit 29. In this way, the decoder 3′ can perform a soft-output decoding operation by applying the Log-BCJR algorithm.

[0147] Particularly, the decoder 3′ can regulate the amplitude of the channel value AMP×y_tj and that of the a priori probability information APP_t input to the soft-output decoding circuit 23 by defining the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I so that it can optimally define an dynamic range and a quantization slot to be used for the inputs to the soft-output circuit 23 along with a quantization slot necessary for internal arithmetic operations of the soft-output decoding circuit 23 that are to be conducted to generate the log soft-output Iλ_t and/or the external information EX_t.

[0148] As an example, assume an input of channel value AMP×y_tj expressed with a gradation between −255 and +255 when the number of bits that can be entered to the soft-output decoding circuit 23 as input is not greater than seven bits and hence it is only possible to input with a gradation between −127 and +127.

[0149] Then, the decoder 3′ selects “2” for both the first additive coefficient C_R and the second additive coefficient C_A and, at the same time, selects “½” for the third additive coefficient C_I. In other words, the decoder 3′ halves the channel value AMP×y_tj and the a priori probability information APP_t input to the soft-output decoding circuit 23. Thus, the decoder 3′ can express the channel value AMP×y_tj and the a priori probability information APP_t input to the soft output decoding circuit 23 with a gradation between −127 and +127 so that it can inputs the channel value AMP×y_tj and the a priori probability information APP_t to the soft-output decoding circuit 23 without inadvertently clipping them.

[0150] In this way, the decoder 3′ can optimally define a dynamic range and a quantization slot for the channel value AMP×y_tj and the a priori probability information APP_t to be input to the soft-output decoding circuit 23 that requires its inputs to be made with a fixed number of bits as a function of the coefficient AMP by which the received value y_tj is multiplied by selecting the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. Thus, it can optimally define the quantization slot necessary for the internal arithmetic operations in the soft-output decoding circuit 23.

[0151] At this time, the decoder 3′ can operate for multiplications by means of bit shifts without actually using the above described multipliers 22, 31, 32, 34 by selecting values that can be expressed by power exponents of 2 respectively for the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I to realize high speed processing operations and a reduced circuit size.

[0152] Note that predetermined constant values may be selected respectively for the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. Particularly, when the Log-BCJR algorithm is applied, the regulating operation for computing the correction term necessary when computing log-sums for determining the log likelihoods Iα_t, Iβ_t, or the second term of the right side of each of the above formulas (30) and (32), can be eliminated by using a predetermined constant value for the third additive coefficient C_I.

[0153] It is possible to make the quantization slot of information for internal arithmetic operations finer relative to the quantization slot of information outside the soft-output decoding circuit 23 by selecting a value greater than “1” for the third additive coefficient C_I. With such an arrangement, it is possible to improve the performance of the decoder 3′ as evidenced by simulations.

[0154] The decoder 3′ may be made to comprise only the soft-output decoding circuit 23. If such is the case, the above described multipliers 21, 22 are arranged in another decoder arranged upstream. Also, the decoder 3′ may be made to externally output not the log soft-output C_I×Iλ_t but the log soft-output Iλ_t obtained by multiplying the log soft-output C_I×Iλ_t by the reciprocal of the third additive coefficient C_I. Then, the operation of multiplying the log soft-output C_I×Iλ_t by the reciprocal of the third additive coefficient C_I may be conducted in the inside of the soft-output decoding circuit 23 or at the outside thereof. Furthermore, if the decoder 3′ is not applied to iterative decoding as will be described hereinafter, it does not need to be provided with the external information computation circuit 29 nor compute the log soft-output C_I×Iλ_Ct that corresponds to the a priori probability information for code bits.

[0155] Now, a decoder 3 adapted to iterative decoding will be described. Then, the decoder 3 is realized by applying the above described decoder 3′.

[0156] As discussed above, it is possible to make the encoder 1 adapted to modulate not only convolutional codes but also PCCCs and SCCCs by means of a modulation method such as the BPSK modulation method, the QPSK modulation method, the TTCM method or the SCTCM method. If such is the case, the decoder 3 is so configured that it performs an iterative decoding operation by concatenating a plurality of soft-output decoding circuits adapted to do MAP decoding on the basis of any of the above described algorithms by way of an interleaver or deinterleaver. Here, an encoder 1″ and a decoder 3″ adapted to respectively perform coding and decoding operations by means of PCCCs as shown in FIGS. 19 and 20 and an encoder 1′″ and a decoder 3′″ adapted to respectively perform coding and decoding operations by means of SCCCs as shown in FIGS. 21 and 22 will be described.

[0157] Firstly, an encoder 1″ adapted to perform coding operations by means of PCCCs and a decoder 3″ adapted to decode the codes encoded by the encoder 1″ will be discussed.

[0158] The encoder 1″ may comprise a delay circuit 41 for delaying the input data, two convolutional coding circuits 42, 44 for convolutional coding operations and an interleaver 43 for rearranging the sequence of data. The encoder 1″ performs a parallel concatenated convolutional coding operation with a coding ratio of “1/3” on a 1-bit input data i_t1, generates 3-bit output data x_t1, x_t2 and x_t3 and outputs the data to the outside by way of a modulator (not shown) adapted to use e.g., a BPSK modulation method or a QPSK modulation method.

[0159] The delay circuit 41 is provided to make the timings of outputting the 3-bit output data x_t1, x_t2 and x_t3 match each other. Upon receiving a 1-bit input data i_t1, the delay circuit 41 delays the input data i_t1, by a time period equal to the time required for the processing operation of the interleaver 43. The delay circuit 41 externally outputs the delayed data obtained as a result of the delay as 1-bit output data x_t1 out of 3-bit output data X_t and also supplies it to the downstream convolutional coding circuit 42.

[0160] Upon receiving the delayed 1-bit data from the delay circuit 41, the convolutional coding circuit 42 performs a convolutional coding operation on the delayed data and externally outputs the outcome of the operation as 1-bit output data x_t2 out of the 3-bit output data X_t.

[0161] The interleaver 43 receives the input data i_t1 of a series of bits, rearrange the order of arrangement of the bits of the input data i_t1 and supplies the generated interleave data to the downstream convolutional coding circuit 44.

[0162] Upon receiving the 1-bit interleave data supplied from the interleaver 43, the convolutional coding circuit 44 performs a convolutional coding operation on the interleave data and externally outputs the outcome of the operation as 1-bit output data x_t3 of the 3-bit output data X_t.

[0163] Thus, upon receiving a 1-bit input data i_t1, the encoder 1″ as a whole performs a parallel concatenated convolutional coding operation with a coding ratio of “1/3” by outputting the input data i_t1 as systematic component output data x_t1 by way of the delay circuit 41 and also by externally outputting the output data x_t2 obtained as a result of the convolutional coding operation conducted on the delayed data by means of the convolutional coding circuit 42 and the output data x_t3 obtained as a result of the convolutional coding operation conducted on the interleave data by means of the convolutional coding circuit 44. The data encoded by the encoder 1″ are mapped for the signal points by a modulator (not shown) on the basis of a predetermined modulation method and output to the receiver by way of the memoryless communication channel 2.

[0164] On the other hand, as shown in FIG. 20, the decoder 3″ for decoding the code encoded by the encoder 1″ comprises two multipliers 51, 52 and 2×M processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2, which perform decoding operations corresponding to the coding operations of the convolutional coding circuits 42, 44 that are element coding circuits of the encoder 1″, the number of the processing circuits being equal to the product of multiplication of the number of element codes and the number of times M of repetition of iterative decoding operation. The decoder 3″ is adapted to estimate the input data i_t1 by obtaining decoded data DEC_t from the received value y_t that is reduced as soft-input under the influence of the noise generated on the memoryless communication channel 2 by means of an iterative decoding operation.

[0165] Like the multiplier 21 of the above described decoder 3′, the multiplier 51 multiplies the received value y_t by AMP/C_R, which is obtained by dividing the coefficient AMP by the first additive coefficient C_R. Then, the multiplier 51 supplies the obtained probability information AMP/C_R×y_t that is the product of multiplication to the processing circuit 53₁₁.

[0166] Then, like the multiplier 22 of the decoder 3′, the multiplier 52 multiplies the a priori probability information APP_t by the reciprocal 1/C_A of the second additive coefficient C_A. Thereafter, the multiplier 52 supplies the obtained probability information 1/C_A×APP_t to the processing circuit 53₁₁.

[0167] The processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 are substantially identical LSIs and each of them is formed by arranging integrally all the components on a single semiconductor substrate. Of the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2, those expressed by 53_i1 are provided in correspondence to the convolutional coding circuit 42 of the encoder 1″ and adapted to iteratively perform the i-th decoding operation, whereas those expressed by 53_i2 are provided in correspondence to the convolutional coding circuit 44 of the encoder 1″ and adapted to iteratively perform the i-th decoding operation.

[0168] More specifically, the processing circuit 53₁₁ comprises a delay circuit 54₁₁ that is a delay means for delaying the input data, a soft-output decoding circuit 55₁₁ and an interleaver 56₁₁ that is an interleaving means for rearranging the order of arrangement of the input data.

[0169] The delay circuit 54₁₁ is provided to make the timing of outputting the probability information 1/C_A×APP_t12 supplied from the interleaver 56₁₁ match that of inputting the probability information AMP/C_R×y_t to the next step processing circuit 53₁₂. Upon receiving the probability information AMP/C_R×y_t supplied from the multiplier 51, the delay circuit 54₁₁ delays the probability information AMP/C_R×y_t by the time period equal to the time period required for the processing operation of the soft-output circuit 55₁₁ and the interleaves 56₁₁. Then, the delay circuit 54₁₁ supplies the delayed probability information AMP/C_R×y_t to the next step processing circuit 53₁₂.

[0170] The soft-output decoding circuit 55₁₁ is provided in correspondence to the convolutional coding circuit 42 of the encoder 1″ and, although not shown, has a configuration similar to that of the soft-output decoding circuit 23 of the above described decoder 3′. Like the soft-output decoding circuit 23, the soft-output decoding circuit 55₁₁ performs a soft-output decoding operation, using the probability information AMP/C_R×y_t fed from the multiplier 51, the probability information 1/C_A×APP_t fed from the multiplier 52, the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. The soft-output decoding circuit 55₁₁ computationally determines the external information 1/C_A×EX_t11, for information bits required by the constraining condition of code and supplies the external information 1/C_A×EX_t11 to the downstream interleaver 56₁₁ as soft-output. However, note that, unlike the above described soft-output decoding circuit 23, the soft-output decoding circuit 55₁₁ does not need to output a log soft-output for information bits nor computationally determine the log soft-output and external information for code bits.

[0171] The interleaver 56₁₁ inverleaves the external information 1/C_A×EX_t11 for information bits, which is the soft-input from the soft-output decoding circuit 55₁₁, on the basis of the information on the position of substitution that is identical with the corresponding information of the interleaver 43. The interleaver 56₁₁ supplies the external information obtained as a result of the interleaving operation to the processing circuit 53₁₂ of the next step as probability information 1/C_A×APP_t12 that is obtained by regulating the amplitude of the a priori probability information for information bits for the next step processing circuit 53₁₂.

[0172] The processing circuit 53₁₂ comprises a delay circuit 54₁₂ that is a delay means for delaying the input data, a soft-output decoding circuit 55₁₂ that is a soft-output decoding means for soft-output decoding and a deinterleaver 56₁₂ that is a deinterleaving means for restoring the original order of arrangement of the input data.

[0173] The delay circuit 54₁₂ is provided to make the timing of outputting the probability information 1/C_A×APP_t21 supplied from the deinterleaver 56₁₂ match that of inputting the probability information AMP/C_R×y_t to the next step processing circuit 53₂₁. Upon receiving the probability information AMP/C_R×y_t supplied from the processing circuit 53₁₁, the delay circuit 54₁₂ delays the probability information AMP/C_R×y_t by the time period equal to the time period required for the processing operation of the soft-output circuit 55₁₂ and the deinterleaver 56₁₂. Then, the delay circuit 54₁₂ supplies the delayed probability information AMP/C_R×y_t to the next step processing circuit 53₂₁.

[0174] The soft-output decoding circuit 55₁₂ is provided in correspondence to the convolutional coding circuit 44 of the encoder 1″ and, although not shown, has a configuration similar to that of the soft-output decoding circuit 23 of the above described decoder 3′. The soft-output decoding circuit 55₁₂ performs a soft-output decoding operation, using the probability information AMP/C_R×y_t and 1/C_A×APP_t12 fed from the processing circuit 53₁₁, the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. The soft-output decoding circuit 55₁₂ computationally determines the external information 1/C_A×EX_t12 for information bits required by the constraining condition of code and supplies the external information 1/C_A×EX_t12 to the downstream deinterleaver 56₁₂ as soft-output. However, note that, unlike the above described soft-output decoding circuit 23, the soft-output decoding circuit 55₁₂ does not need to output a log soft-output for information bits nor computationally determine the log soft-output and external information for code bits.

[0175] The deinterleaver 56₁₂ deinverleaves the external information 1/C_A×EX_t12 for information bits, which is the soft-output from the soft-output decoding circuit 55₁₁, so as to restore the bit arrangement of the original input data i_t1 that has been interleaved by the interleaver 43 of the encoder 1″. The deinterleaver 56₁₂ supplies the external information obtained as a result of the deinterleaving operation to the processing circuit 53₂₁ of the next step as probability information 1/C_A×APP_t12 that is obtained by regulating the amplitude of the a priori probability information for information bits for the next step processing circuit 53₂₁.

[0176] Like the processing circuit 53₁₁, the processing circuit 53_M1 comprises a delay circuit 54_M1 that is a delay means for delaying the input data, a soft-output decoding circuit 55_M1 that is a soft-output decoding means and an interleaver 56_M1 that is an interleaving means for rearranging the order of arrangement of the input data. Like the processing circuit 53₁₁, the processing circuit 53_M1 performs a soft-output decoding operation, using the probability information AMP/C_R×y_t, and 1/C_A×APP_tM1 fed from the multiplier processing 53_M−11, the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I and supplies the obtained external information to the processing circuit 53_M2 of the final step as probability information 1/C_A×APP_tM2 that is obtained by regulating the amplitude of the a priori probability information for information bits for the next step processing circuit 53_M2. Like the processing circuit 53₁₂, the processing circuit 53_M2 of the final step comprises a delay circuit 54_M2 that is a delay means for delaying the input data, a soft-output decoding circuit 55_M2 that is a soft-output decoding means and a deinterleaver 56_M2 that is a deinterleaving means for restoring the original order of arrangement of the input data along with two adders 57_M2 for adding data. The processing circuit 53_M2 does not output the probability information AMP/C_R×y_t supplied from the processing circuit 53_M1 and delayed by the delay circuit 54_M2 nor allow the probability information AMP/C_R×y_t fed from the processing circuit 53_M1 to be input to the delay circuit 54_M2. The processing circuit 53_M2 outputs the decoded data 1/C_A+DEC_t obtained by regulating the amplitude of the decoded data DEC_t which is obtained by adding the external information 1/C_A×EX_tM2 that is obtained by regulating the amplitude of the a priori probability information for information bits as a result of a processing operation similar to that of the soft-output decoding circuit 55₁₂ of the processing circuit 53₁₂ and the probability information 1/C_A×APP_tM2 fed from the processing circuit 53_M1 as a priori probability information for information bits obtained by regulating the amplitude by means of the adder 57_M2 and deinterleaving the sum by means of the deinterleaver 56_M2.

[0177] Thus, since the decoder 3″ comprises the soft-output decoding circuits 55_i1, 55_i2 that correspond to the convolutional coding circuits 42, 44 of the encoder 1″, it can decompose a code requiring a highly complex decoding operation into elements that are less complex to successively improve its performance through the interaction of the soft-output decoding circuits 55_i1, 55_i2. Upon receiving the received value y_t, the decoder 3″ performs an iterative decoding operation for a number of times of M by means of the 2×M processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 and outputs the decoded data 1/C_A+DEC_t obtained on the basis of the external information 1/C_A×EX_tM2 of the soft-output obtained as a result of the decoding operation. Like the decoder 3′, the decoder 3″ can regulate the amplitude of the channel value AMP×y_t and that of the a priori probability information APP_t input to each of the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 by selecting the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I so that it can optimally select the dynamic range and the quantization slot to be used for inputting data to the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 and also the quantization slot necessary for the internal arithmetic operations of the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2.

[0178] The decoder 3″ may be so arranged that it externally outputs the decoded data DEC_t obtained by multiplying the decoded data 1/C_A×DEC_t by the second additive coefficient C_A instead of outputting the decoded data 1/C_A×DEC_t. The multiplication of the decoded data 1/C_A×DEC_t by the second additive coefficient C_A may be conducted either in the inside or at the outside of the processing circuit 53_M2. The processing circuits 53₁₁, 53₁₂, . . . , 53_{M1, 53M2} of the decoder 3″ may have a same and identical configuration. If such is the case, the processing circuits 53₁₁, 53₁₂, . . . , 53_M1 are made to comprise respective adders like the processing circuit 53_M2. Then, the adders need to be controlled by a control signal so that any unnecessary adders may not be operated.

[0179] Now, an encoder 1′″ adapted to perform coding operations by means of SCCCs and a decoder 3′″ adapted to decode the codes encoded by the encoder 1′″ will be discussed.

[0180] As shown in FIG. 21, the encoder 1′″ may comprise a convolutional coding circuit 61 for coding a code referred to as outer code, an interleaver 62 for rearranging the sequence of input data and a convolutional coding circuit 63 for coding a code referred to as inner code. The encoder 1′″ performs a serially concatenated convolutional coding operation with a coding ratio of “1/3” on a 1-bit input data i_t1, generates 3-bit output data x_t1, x_t2 and x_t3 and outputs the data to the outside by way of a modulator (not shown) adapted to use e.g., a BPSK modulation method or a QPSK modulation method.

[0181] Upon receiving a 1-bit input data i_t1, the convolutional coding circuit 61 performs a convolutional coding operation on the input data i_t1 and supplies the outcome of the operation as 2-bit coded data to the downstream interleaver 62. In other words, the convolutional coding circuit 61 performs a convolutional coding operation with a coding ratio of “1/2” for coding an outer code and supplies the coded data to the downstream interleaves 62.

[0182] The interleaver 62 receives the coded data of two series of bits fed from the convolutional coding circuit 61, rearrange the order of arrangement of the bits of the input data and supplies the generated interleave data of two series of bits to the downstream convolutional coding circuit 63.

[0183] Upon receiving the 2-bit interleave data fed from the interleaver 62, the convolutional coding circuit 63 performs a convolutional coding operation on the interleave data and externally outputs the outcome of the operation as output data x_t1, x_t2 and x_t3. In other words, the convolutional coding circuit 63 performs a convolutional coding operation with a coding ratio of “2/3” for coding an inner code and externally outputs output data x_t.

[0184] The encoder 1′″ performs a convolutional coding operation of encoding an outer code by means of the convolutional coding circuit 61 with a coding ratio of “1/2” and a convolutional coding operation of encoding an inner code by means of the convolutional coding circuit 63 with a coding ratio of “2/3” so as to realize a serially concatenated convolutional coding with a coding ratio of “(1/2)×(2/3)=1/3” as a whole. Then, the data encoded by the encoder 1′″ are mapped for the signal points by a modulator (not shown) on the basis of a predetermined modulation method and output to the receiver by way of the memoryless communication channel 2.

[0185] On the other hand, as shown in FIG. 22, the decoder 3′″ for decoding the code encoded by the encoder 1′″ comprises two multipliers 71, 72 and 2×M processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2, which perform decoding operations corresponding to the coding operations of the convolutional coding circuits 61, 63 that are element coding circuits of the encoder 1′″, the number of the processing circuits being equal to the product of multiplication of the number of element codes and the number of times of repetition of iterative decoding operation. The decoder 3′″ is adapted to estimate the input data i_t1 by obtaining decoded data DEC_t from the received value y_t that is reduced as soft-input under the influence of the noise generated on the memoryless communication channel 2 by means of an iterative decoding operation.

[0186] Like the multiplier 21 of the above described decoder 3′, the multiplier 71 multiplies the received value y_t by AMP/C_R, which is obtained by dividing the coefficient AMP by the first additive coefficient C_R. Then, the multiplier 71 supplies the obtained probability information AMP/C_R×y_t that is the product of multiplication to the processing circuit 73₁₁.

[0187] Then, like the multiplier 22 of the decoder 3′, the multiplier 72 multiplies the a priori probability information APP_t by the reciprocal of the second additive coefficient C_A. Thereafter, the multiplier 72 supplies the obtained probability information 1/C_A×APP_t to the processing circuit 73₁₁.

[0188] The processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2 are substantially identical LSIs and each of them is formed by arranging integrally all the components on a single semiconductor substrate. Of the processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2, those expressed by 73_i1 are provided in correspondence to the convolutional coding circuit 63 for inner code of the encoder 1′″ and adapted to iteratively perform the i-th decoding operation, whereas those expressed by 73_i2 are provided in correspondence to the convolutional coding circuit 61 for outer code of the encoder 1′″ and adapted to iteratively perform the i-th decoding operation.

[0189] More specifically, the processing circuit 73₁₁ comprises a delay circuit 74₁₁ that is a delay means for delaying the input data, a soft-output decoding circuit 75₁₁ that is a soft-output decoding means and an deinterleaver 76₁₁ that is a deinterleaving means for restoring the original order of arrangement of the input data.

[0190] The delay circuit 74₁₁ is provided to make the timing of outputting the probability information 1/C_A×APP_t12 supplied from the deinterleaver 76₁₁ match that of inputting the probability information AMP/C_R×y_t to the next step processing circuit 73₁₂. Upon receiving the probability information AMP/C_R×y_t supplied from the multiplier 71, the delay circuit 74₁₁ delays the probability information AMP/C_R×y_t by the time period equal to the time period required for the processing operation of the soft-output circuit 75₁₁ and the deinterleaver 76₁₁. Then, the delay circuit 74₁₁ supplies the delayed probability information AMP/C_R×y_t to the next step processing circuit 73₁₂.

[0191] The soft-output decoding circuit 75₁₁ is provided in correspondence to the convolutional coding circuit 63 of the encoder 1′″ and, although not shown, has a configuration similar to that of the soft-output decoding circuit 23 of the above described decoder 3′. Like the soft-output decoding circuit 23, the soft-output decoding circuit 75₁₁ performs a soft-output decoding operation, using the probability information AMP/C_R×y_t fed from the multiplier 71, the probability information 1/C_A×APP_t fed from the multiplier 72, the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. The soft-output decoding circuit 75₁₁ computationally determines the external information 1/C_A×EX_t11, for information bits required by the constraining condition of code and supplies the external information 1/C_A×EX_t11 to the downstream deinterleaver 76₁₁ as soft-output. The external information 1/C_A×EX_t11 corresponds to the interleave data interleaved by the interleaver 62 of the encoder 1′″. However, note that, unlike the above described soft-output decoding circuit 23, the soft-output decoding circuit 75₁₁ does not need to output a log soft-output for information bits nor computationally determine the log soft-output and external information for code bits.

[0192] The deinterleaver 76₁₁ deinverleaves the external information 1/C_A×EX_t11 for information bits, which is the soft-output from the soft-output decoding circuit 75₁₁, so as to restore the original bit array of the input data i_t1 from the bit array of the data interleaved by the interleaver 62 of the encoder 1′″. Then, the deinterleaver 76₁₁ supplies the external information obtained as a result of the deinterleaving operation to the processing circuit 73₁₂ of the next step as probability information 1/C_A×APP_t12 that is obtained by regulating the amplitude of the a priori probability information for information bits for the next step processing circuit 73₁₂.

[0193] The processing circuit 73₁₂ comprises a delay circuit 74₁₂ that is a delay means for delaying the input data, a soft-output decoding circuit 75₁₂ and an interleaver 76₁₂ that is an interleaving means for rearranging the order of arrangement of the input data.

[0194] The delay circuit 74₁₂ is provided to make the timing of outputting the probability information 1/C_A×APP_t21 supplied from the interleaver 76₁₂ match that of inputting the probability information AMP/C_R×y_t to the next step processing circuit 73₂₁. Upon receiving the probability information AMP/C_R×y_t supplied from the processing circuit 73₁₁, the delay circuit 74₁₂ delays the probability information AMP/C_R×y_t by the time period equal to the time period required for the processing operation of the soft-output circuit 75₁₂ and the interleaver 76₁₂. Then, the delay circuit 74₁₂ supplies the delayed probability information AMP/C_R×y_t to the next step processing circuit 73₂₁.

[0195] The soft-output decoding circuit 75₁₂ is provided in correspondence to the convolutional coding circuit 61 of the encoder 1′″ and, although not shown, has a configuration similar to that of the soft-output decoding circuit 23 of the above described decoder 3′. Like the soft-output decoding circuit 23, the soft-output decoding circuit 75₁₂ performs a soft-output decoding operation on the external code, using the probability information AMP/C_R×y_t fed from the processing circuit 73₁₁, the a priori probability information for information bits having a value of “0”, an arbitrary coefficient C, the second additive coefficient C_A and the third additive coefficient C_I. Note that a coefficient identical with the second coefficient C_A applied to the soft-output decoding circuit 75₁₁ is input to the terminal of the soft-output decoding circuit 75₁₂ that is supposed to receive the first coefficient C_R and the coefficient C having an arbitrarily selected value is applied to the terminal that is supposed to receive the second coefficient C_A. The coefficient C having an arbitrarily selected value is input to the terminal that is supposed to receive the second coefficient C_A because the value of the a priori probability information for information bits that is multiplied by the coefficient C is equal to “0”. The soft-output decoding circuit 75₁₂ computationally determines the external information 1/C_A×EX_t12 for code bits required by the constraining condition of code and supplies the external information 1/C_A×EX_t12 to the downstream interleaver 76₁₂ as soft-output. However, note that, unlike the above described soft-output decoding circuit 23, the soft-output decoding circuit 75₁₂ does not need to output a log soft-output for information bits nor computationally determine the log soft-output and external information for code bits.

[0196] The interleaver 76₁₂ inverleaves the external information 1/C_A×EX_t12 for code bits, which is the soft-output from the soft-output decoding circuit 75₁₂, on the basis of the information on the position of substitution that is identical with the corresponding information of the interleaver 62 of the encoder 1′″. The interleaver 76₁₂ supplies the external information obtained as a result of the interleaving operation to the processing circuit 73₂₁ of the next step as probability information 1/C_A×APP_t21 that is obtained by regulating the amplitude of the a priori probability information for information bits for the next step processing circuit 73₂₁ (not shown).

[0197] Like the processing circuit 73₁₁, the processing circuit 73_M1 comprises a delay circuit 74_M1 that is a delay means for delaying the input data, a soft-output decoding circuit 75_M1 that is a soft-output decoding means and a deinterleaver 76_M1 that is a deinterleaving means for restoring the original order of arrangement of the input data. Like the processing circuit 73₁₁, the processing circuit 73_M1 performs a processing operation, using the probability information AMP/C_R×y_t, and 1/C_A×APP_tM1 fed from the processing circuit 73_M−11 (not shown), the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I and supplies the obtained external information to the processing circuit 73_M2 of the final step as probability information 1/C_A×APP_tM2 that is obtained by regulating the amplitude of the a priori probability information for code bits for the next step processing circuit 73_M2. Note that the processing circuit 73_M1 does not output the probability information AMP/C_R×y_t supplied from the processing circuit 73_M−11 (not shown) and delayed by the delay circuit 74_M1 nor allow the probability information AMP/C_R×y_t fed from the processing circuit 73_M−11 to be input to the delay circuit 74_M1.

[0198] Like the processing circuit 73₁₂, the processing circuit 73_M2 of the final step comprises a delay circuit 74_M2 that is a delay means for delaying the input data, a soft-output decoding circuit 75_M2 that is a soft-output decoding means and an interleaver 76_M2 that is an interleaving means for rearranging the order of arrangement of the input data. The processing circuit 73_M2 does not output the probability information AMP/C_R×y_t supplied from the processing circuit 73_M1 and delayed by the delay circuit 74_M2 nor allow the probability information AMP/C_R×y_t fed from the processing circuit 73_M1 to be input to the delay circuit 74_M2. Unlike the soft-output decoding circuit 75₁₂ of the processing circuit 73₁₂, the processing circuit 73_M2 does not need to computationally determine nor outputs the external information for code bits. Note that a coefficient identical with the second coefficient C_A applied to the soft-output decoding circuit 75_M1 is input to the terminal of the soft-output decoding circuit 75_M2 that is supposed to receive the first coefficient C_R and the coefficient C having an arbitrarily selected value is applied to the terminal that is supposed to receive the second coefficient C_A. The coefficient C having an arbitrarily selected value is input to the terminal that is supposed to receive the second coefficient C_A because the value of the a priori probability information for information bits that is multiplied by the coefficient C is equal to “0”. The processing circuit 73_M2 computationally determines the external information 1/C_A×EX_tM2 by regulating the amplitude of the external information EX_tM2 for information bits and supplies the external information 1/C_A×EX_tM2 to the outside decoded data 1/C_A×DEC_t obtained by regulating the amplitude of the decoded data DEC_t.

[0199] Thus, like the above described decoder 3″, since the decoder 3′″ comprises the soft-output decoding circuits 75_i1, 75_i2 that correspond to the convolutional coding circuits 63, 61 of the encoder 1′″, it can decompose a code requiring a highly complex decoding operation into elements that are less complex to successively improve its performance through the interaction of the soft-output decoding circuits 75_i1, 75_i2. Upon receiving the received value y_t, the decoder 3′″ performs an iterative decoding operation for a number of times of M by means of the 2×M processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2 and outputs the decoded data 1/C_A+DEC_t obtained on the basis of the external information 1/C_A+EX_tM2 of the soft-output obtained as a result of the decoding operation. Like the decoders 3′, 3″, the decoder 3′″ can regulate the amplitude of the channel value AMP×y_t and that of the a priori probability information APP_t input to each of the processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2 by selecting the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I so that it can optimally select the dynamic range and the quantization slot to be used for inputting data to the processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2 and also the quantization slot necessary for the internal arithmetic operations of the processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2.

[0200] The decoder 3′ may be so arranged that it externally outputs the decoded data DEC_t obtained by multiplying the decoded data 1/C_A×DEC_t by the second additive coefficient C_A instead of outputting the decoded data 1/C_A×DEC_t. The multiplication of the decoded data 1/C_A×DEC_t by the second additive coefficient C_A may be conducted either in the inside or at the outside of the processing circuit 53_M2. Since the external information EX_tM2 for information bits is identical with the log soft-output Iλ_tM2 for information bits, the decoder 3′″, may be so arranged as to output the log soft-output C_I×Iλ_tM2 as decoded data C_I×DEC_t instead of outputting the external information 1/C_A×EX_tM2 as decoded data 1/C_A×DEC_t.

[0201] Additionally, a decoder for decoding codes by means of the TTCM method may be made to have a configuration similar to that of the above described decoder 3″ so that symbols of common components and those of orthogonal components may be input directly as received value y_t. Still additionally, a decoder for decoding codes by means of the SCTCM method may be made to have a configuration similar to that of the above described decoder 3′″ so that symbols of common components and those of orthogonal components may be input directly as received value y_t.

[0202] Now, methods for selecting specific values for the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I will be discussed below.

[0203] Firstly, a method for selecting a value for the first additive coefficient C_R will be described when the encoder 1 is adapted to do modulations, using a modulation method of arranging the signal points so as to provide a distribution of the received value for each bit such as the BPSK modulation method of the QPSK modulation method.

[0204] The coding loss that arises in a decoding operation was determined by simulation by varying the received value of each of different types of code and the dynamic range of the channel value as expressed by the product of the received value and the coefficient AMP. A sufficiently large value of “32” was selected for the dynamic range of the external information to be generated in the simulation. For codes, PCCCs with coding ratios of “1/6” and “1/3” recommended as turbo codes by the CCSDS (Consultative Committee for Space Data Systems), PCCCs with a coding ratio of “3/4” generated by puncturing on the basis of turbo codes recommended by the CCSDS, and SCCCs with a coding ratio of “1/3” were used and modulated by the BPSK modulation method. As a result of the simulation, it was confirmed that the dynamic range where no coding loss arises varies depending on the used codes in terms of both received value and channel value. Additionally, it was also confirmed that the dynamic range where no coding loss arises differs between the received value and the channel value.

[0205] The value of the coefficient AMP for signal to noise power ratio (to be referred to as E_b/N_o hereinafter) per bit is determined for each code. Table 1 shows the obtained values.

[0206]

TABLE 1
Coefficient AMP
	code	Eb/No (dB)	AMP
	PCCC (1/6)	−0.5	0.594167
	PCCC (1/3)	0.0	1.33333
	PCCC (3/4)	2.0	4.75468
	SCCC (1/3)	0.5	1.49602

[0207] FIG. 23 and FIG. 24 respectively show the relationship between the dynamic range of received value and the coding loss and the relationship between the dynamic range of channel value and the coding loss. In FIGS. 23 and 24, curves C₁, C₂ and C₃ indicate PCCCs with coding ratios of “1/6”, “1/3” and “3/4” respectively, whereas curve C₄ indicates SCCCs with a coding ratio of “1/3”.

[0208] As seen from FIG. 23, the dynamic range of received value where the coding loss is equal to “0” is located close to “4” for PCCCs with a coding ratio of “1/6” and close to “3” for PCCCs with a coding ratio of “1/3”, while the dynamic range of received value where the coding loss is equal to “0” is located close to “1.5” for PCCCs with a coding ratio of “3/4” and close to “2.5” for SCCCs with a coding ratio of “1/3”.

[0209] As seen from FIG. 24, the dynamic range of channel value where the coding loss is equal to “0” is located close to “2.5” for PCCCs with a coding ratio of “1/6” and close to “3.5” for PCCCs with a coding ratio of “1/3”, while the dynamic range of received value where the coding loss is equal to “0” is located close to “7” for PCCCs with a coding ratio of “3/4”.

[0210] Since AWGN is added by the memoryless communication channel, both the received value and the channel value show a normal distribution and a distribution equivalent to the normal distribution can be generated by varying the variance and the average value. More specifically, as shown in FIG. 25, if the average value is “±1” and the variance is “σ²” for the distribution of received value or channel value, the distribution can be normalized by making the average value equal to “±1/σ”.

[0211] Then, optimum quantization for Viterbi decoding is applied to the post-normalization distribution obtained after normalizing the distribution of received value or channel value. With Viterbi decoding, it is known that uniform quantization using a quantization slot of “0.3” provides a good performance relative to the distribution of received value with variance of “1” when quantizing the received value to 4-bit. Then, the average value of the normalized distribution is about “2.1”. It is also known that this does not depend on the type of code. The dynamic ranges indicated on the horizontal axes of FIGS. 23 and 24 are those where the average values are between “±2 to ±2.5” for the received value and the channel value respectively.

[0212] More specifically, the average of the received value is between “±2 to ±2.5” when the dynamic range of the received value is between “about 3.7 and about 4.5” for PCCCs with a coding ratio of “1/6”, between “about 2.4 and about 3.1” for PCCCs with a cording ratio of “1/3”, between “about 1.3 and about 1.7” for PCCCs with a coding ratio of “3/4” and between “about 2.3 and about 2.9” for SCCCs with a coding ratio of “1/3”.

[0213] On the other hand, the average of the channel value is between “±2 to ±2.5” when the dynamic range of the channel value is between “about 2.2 and about 2.7” for PCCCs with a coding ratio of “1/6”, between “about 3.3 and about 4.2” for PCCCs with a cording ratio of “1/3”, between “about 6.2 and about 7.7” for PCCCs with a coding ratio of “3/4” and between “about 3.5 and about 4.5” for SCCCs with a coding ratio of “1/3”.

[0214] From the above, it will be safe to say that the decoding accuracy is improved when the average of the received value or the channel value in the post-normalization distribution obtained after normalizing the distribution of received value or channel value is made between “±2 to ±2.5” because the coding loss is close to “0”.

[0215] FIG. 26 shows the relationship between the dynamic range of the received value in the post-normalization distribution obtained after normalizing the distribution of received value and the coding loss obtained as a result of a simulation conducted under the above described condition. It was confirmed that the dynamic range of the received value is found between “2 and 2.5” for any type of code when the coding loss is equal to “0”.

[0216] Thus, as for the decoder 3, a value that makes the dynamic range of the probability information AMP/C_R (=(2/σ²)×(1/C_R)) input to the LSI to be found between “±2 to ±2.5” in the post-normalization distribution obtained after normalizing the distribution of the probability information will be selected for the first additive coefficient C_R. In the case of the above described decoders 3′, 3″ and 3′″, for example, a value that makes the dynamic range of the probability information AMP/C_R (=(2/σ²)×(1/C_R)) output from the respective multipliers 21, 51, 71 to be found between “±2 to ±2.5” in the post-normalization distribution obtained after normalizing the distribution of the probability information will be selected for the first additive coefficient C_R. Ideally, as for the decoder 3, a value of “2/σ” needs to be selected for the first additive coefficient C_R in order to make the value of AMP/C_R by which the received value y_t is multiplied equal to “1/σ”.

[0217] Table 2 below shows the ratio of the received value, or the clip range, where the average of the received value is found within “±2.5” in the post-normalization distribution obtained after normalizing the distribution of the received value. Note that the actual received value for each E_b/N_o is also shown in Table 2.

[0218]

TABLE 2
Ratio of the received value
	code	Eb/No (dB)	Range	Ratio (%)
	PCCC (1/6)	−0.3	±4.48	97.4
	PCCC (1/3)	0.0	±3.06	95.6
	PCCC (3/4)	2.0	±1.62	85.9
	SCCC (1/3)	0.5	±2.89	92.8

[0219] As shown in the table above, the ratio of the received value found within the clip range is “about 97.4%” for PCCCs with a coding ratio of “1/6”, “about 95.6%” for PCCCs with a coding ratio of “1/3”, “about 85.9%” for PCCCs with a coding ratio of “3/4” and “about 92.8%” for SCCCs with a coding ratio of “1/3”.

[0220] From these results, it will be seen that the performance shows little degradation when E_b/N_o shows a large value if the ratio of the received value is found beyond the clip range.

[0221] Thus, as for the decoder 3, if the encoder 1 is adapted to do modulations, using a modulation method of arranging the signal points so as to provide a distribution of the received value for each bit, it is possible to optimally select a dynamic range and a quantization slot for the channel value AMP×y_tj input to the LSI by selecting a value that makes the average of the probability information input to the LSI is found within “±2 to ±2.5” in the post-normalization distribution obtained after normalizing the distribution of the probability information for the first additive coefficient C_R.

[0222] Note that, while the above simulation is described in terms of the BPSK modulation method, it has been proved that similar result can be obtained when the QPSK modulation method is used.

[0223] Now, a method for selecting a value for the first additive coefficient C_R will be described for a situation where the encoder 1 is adapted to do modulations for TCM, using a modulation method of arranging the signal points that can not provide a distribution of the received value for each bit such as the 8PSK modulation method.

[0224] When the encoder 1 operates for TCM, the decoder 3 determines the Euclidean distance on the I/Q plane by computing the inner product of the input probability information by means of a circuit for computing and storing the log likelihood such as the Iγ computation/storage circuit 25 of the above described decoder 3′ and uses the Euclidean distance as likelihood. However, the problem as described below arises if the quantization range at the upstream of the means for computing the inner product is smaller than the range of signal points.

[0225] When the encoder do modulations by means of the 8PSK modulation method, the decoder clips the probability information obtained from the received value for both the I axis and the Q axis for quantization so that the probability information is two-dimensionally clipped as indicated by “∘s” in FIG. 27. Thus, the range of quantization is normally smaller than that of signal points. Assume that the signal point indicated by “Δ” in FIG. 27 are quantized. The signal point is located closest to the signal point whose phase is “0°” on the I/Q plane. In such a case, the signal point is quantized in a manner as indicated by “x” so that it is erroneously regarded to be closest to the signal point whose phase is “45°” on the I/Q plane.

[0226] Therefore, the decoder 3 selects a value that provides a quantization range that contains the range of signal points for the first additive coefficient C_R as shown in FIG. 28. Specifically, it is desirable to select a value that makes the quantization range about twice as large as the transmission amplitude of the encoder 1 for the first additive coefficient C_R. It has been proved by simulations that the best decoding accuracy is obtained when such a value is selected.

[0227] Then, the decoder 3 computes the inner product of the probability information AMP/C_R×y_tj that is input to the LSI by means of the circuit for computing and storing the log likelihood Iγ and subsequently computes the multiplication of the first additive coefficient C_R and the third additive coefficient C_I, or C_R×C_I. In the case of the above described decoder 3, for example, it computes the inner product of the probability information AMP/C_R×y_tj that is input to the soft-output decoding circuit 23 by means of the Iγ computation/storage circuit 25 and, after computing the inner product, computes the multiplication of the first additive coefficient C_R and the third additive coefficient C_I, or C_R×C_I, by means of the multiplier 31.

[0228] When the decoder 3 carries out an operation of normalization for correcting the biassed distribution of the computed inner products, it is desirable for the decoder 3 to compute the multiplication of the first additive coefficient C_R and the third additive coefficient C_I, or C_R×C_I, after the normalization in order to improve the performance.

[0229] Taking the above described factors into consideration, the circuit for computing and storing the log likelihood Iγ may be designed in a manner as described below.

[0230] In the case of the decoder 3, for example, the Iγ computation/storage circuit 25 is made to comprise two multipliers 31, 32 that are the first and second multiplication means and an adder 33 that is an addition means as well as an inner product computation circuit 36 for computing inner products, a normalization circuit 37 that is a normalization means for normalizing the inner product computed by the inner product computation circuit 36 and a clip circuit 38 that is a clip means for obtaining a predetermined dynamic range by clipping.

[0231] Thus, the Iγ computation/storage circuit 25 computes the inner product of the probability information AMP/C_R×y_tj that is supplied from the multiplier 21 by means of the inner product computation circuit 36 and supplies the obtained metric to the normalization circuit 37. Subsequently, the Iγ computation/storage circuit 25 corrects the biassed distribution of the metric by normalization that typically makes the smallest value of the metric equal to “0” by means of the normalization circuit 37 and then computes the multiplication of the the first additive coefficient C_R and the third additive coefficient C_I, or C_R×C_I, for the normalized metric by means of the multiplier 31. Them, it clips the obtained result by means of the clip circuit 38 and supplies the adder 33 with the outcome. At the same time, the Iγ computation/storage circuit 25 multiplies the probability information AMP/C_R×y_tj supplied from the multiplier 22 by the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or C_R×C_I, by means of the multiplier 32 and supplies the obtained product to the adder 33. Then, the Iγ computation/storage circuit 25 adds the outcomes of computation supplied from both the multiplier 32 and the clip circuit 38 by means of the adder 33 to obtain the log likelihood C_I×Iγ_t and stores the obtained log likelihood C_I×Iγ_t in a storage section (not shown).

[0232] Thus, when the decoder 3 needs to accommodate a situation where the encoder 1 is adapted to do modulations for TCM, using a modulation method of arranging the signal points that can not provide a distribution of the received value for each bit, it selects a value that makes the quantization range contain the range of signal points for the first additive coefficient C_R and uses the obtained first additive coefficient C_R for multiplication after computing the inner product in the inside of the LSI. With this arrangement, it is possible to optimally select both a dynamic range and a quantization range for the channel value AMP×y_tj input to the LSI and accurately carry out the decoding operation. Additionally, when the decoder 3 normalizes the computed inner products, the decoder 3 can carry out the decoding operation more accurately by performing the multiplication using the obtained first additive coefficient C_R after the normalization.

[0233] Now, a method for optimally selecting values respectively for the second additive coefficient C_A and the third additive coefficient C_I will be discussed.

[0234] The decoder 3 selects such values respectively for the second additive coefficient C_A and the third additive coefficient C_I that makes the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or C_A×C_I, by which the probability information 1/C_A×APP_t input to the LSI is multiplied, not less than “2”. In other words, the decoder 3 selects such values respectively for the second additive coefficient C_A and the third additive coefficient C_I that allow the inner arithmetic operations of the LSI to be performed with a quantization slot smaller than the quantization slot to be used for expressing the generated external information 1/C_A×EX_t. In the case of the decoder 3′, for example, values that make the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or C_A×C_I, not smaller than “2” will be selected respectively for the the second additive coefficient C_A and the third additive coefficient C_I.

[0235] With this arrangement, the decoder 3 can reduce the number of bits necessary for expressing the external information 1/C_A×EX_t and hence its circuit dimensions without degrading its performance. In other words, no degradation of performance occurs to the decoder 3 if the quantization slot to be used for expressing the external information 1/C_A×EX_t is made rather large provided that the inner arithmetic operations of the LSI are performed with a fine quantization slot. This has also been proved by simulations.

[0236] In this way, it is possible to reduce the circuit dimensions and improve the accuracy of decoding operation of the decoder 3 by selecting values respectively for the second additive coefficient C_A and the third additive coefficient C_I that make the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or C_A×C_I, not smaller than “2”.

[0237] It will be appreciated that the above described method of selecting values for the first, second and third additive coefficients is equally applicable to the above described decoders 3″, 3′″ and decodes adapted to do decoding operations by using the TTCM method or the SCTCM method.

[0238] While methods for optimally selecting values respectively for the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I are described above, the first additive coefficient C_R can be used as convergence acceleration coefficient for iterative decoding.

[0239] When the first additive coefficient C_R is used as convergence acceleration coefficient for iterative decoding, a value less than “1” is selected as the first additive coefficient C_R for the decoding operations that comes after a predetermined number of times of decoding operations out of the total number of times M of iterative operations typically in initial stages of convergence.

[0240] This will be described more specifically below by referring to decoders 3″ and 3′″.

[0241] Assume that C_R11, C_R12, . . . , C_RM1, C_RM2 are used for the first additive coefficient C_R and input respectively to the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 of the decoder 3″. Then, the decoder 3″ selects “C_R11=C_R12= . . . =C_Ri2≧1” for the 2×i-th C_Ri2, i being an arbitrarily selected number, and also selects “C_Ri+11=C_Ri+12= . . . =C_RM2<1” as the first additive coefficients C_Ri+11, C_Ri+12, . . . , C_RM2 that are to be input to the processing circuit 53_i+11 that is immediately next to the processing circuit 53_i2 through the last processing circuit 53M₂ respectively.

[0242] On the other hand, in the decoder 3′″, the processing circuits to which the first additive coefficient C_R is input are limited to those that decodes the inner codes produced by the encoder 1′″. Therefore, if C_R11, C_R21, . . . , C_RM−11, C_RM1 are input respectively to processing circuits 73₁₁, 73₂₁, . . . , 73_M−11, 73_M1 of the decoder 3′″, the decoder 3′″ selects “C_R11=C_R21= . . . =C_Ri1≧1” for the first additive coefficients C_R11, C_R21, . . . , C_Ri1 that are to be input to the 2×i−1-th processing circuit 53_i1, i being an arbitrarily selected number, and also selects “C_Ri+11=C_Ri+21= . . . =C_RM1<1” for the first additive coefficients C_Ri+11, C_Ri+21, . . . , C_RM1 that are to be input from the processing circuit 53_i+11 that is immediately next to the processing circuit 53_i2 to the processing circuit 53_M1.

[0243] Thus, for an iterative decoding operation, the decoder 3 selects a value less than “1” for the first additive coefficient C_R that is input to each of the processing circuits, to whose soft-output decoding circuit the probability information AMP/C_R×y_tj is input and that are located downstream relative to a predetermined number of processing circuits out of the plurality of processing circuits, and performs the decoding operation by varying the first additive coefficient C_R and thereby modifying the relationship between the first additive coefficient C_R and the second additive coefficient C_A.

[0244] With this arrangement, it is possible to reduce the influence of the received value on the external information generated by each decoding operation in the case of an iterative decoding operation using the decoder 3. Then, the decoder 3 can accelerates the convergence and reduce the number of repeated operations.

[0245] In this way, it is possible for the decoder 3 to improve the processing speed by using the first additive coefficient C_R not for optimally selecting a dynamic range and a quantization slot for the channel value AMP×y_tj input to the LSI but as convergence acceleration coefficient for an iterative decoding operation.

[0246] Thus, when conducting an iterative decoding operation by means of the TTCM method, an appropriate value is selected for the first additive coefficient C_R as in the case of the decoder 3″. On the other hand, when conducting an iterative code decoding operation by means of the SCTCM method, an appropriate value is selected for the first additive coefficient C_R as in the case of the decoder 3′″.

[0247] As described above in detail, in a data transmission/reception system comprising an encoder 1 and a decoder 3, the decoder 3 can optimally select a dynamic range and a quantization slot for the channel value AMP×y_tj and the a priori probability information APP_t to be input to an LSI that requires its inputs to be made with a fixed number of bits depending on the coefficient AMP by which the received value y_tj is multiplied by selecting appropriate values for the first additive coefficient C_R, the second additive coefficient C_A and the third additive coefficient C_I. Therefore, it is possible to optimally selects an quantization slot that is necessary for inner arithmetic operations of the LSI.

[0248] More specifically, if the encoder 1 is adapted to do modulations, using a modulation method of arranging the signal points that can provide a distribution of the received value for each bit, the decoder 3 selects a value that makes the average of the probability information input to the LSI is found within “±2 to ±2.5” in the post-normalization distribution obtained after normalizing the distribution of the probability information for the first additive coefficient C_R. If, on the other hand, if the encoder 1 is adapted to do modulations for TCM, using a modulation method of arranging the signal points that can not provide a distribution of the received value for each bit, the decoder 3 selects a value that makes the quantization range contain the range of signal points for the first additive coefficient C_R and, if it normalizes the computed inner product, and uses the obtained first additive coefficient C_R for multiplication after the normalization. With this arrangement for selecting an appropriate value for the first additive coefficient C_R, it is possible to optimally select a dynamic range and a quantization slot for the channel value AMP×y_tj to be input to the LSI and realize a highly accurate decoding operation.

[0249] Additionally, the decoder 3 selects such values respectively for the second additive coefficient C_A and the third additive coefficient C_I that makes the product of multiplication of the second additive coefficient C_A and the third additive coefficient C_I, or C_A×C_I, not less than “2”. With this arrangement, it is possible to reduce the circuit dimensions of the decoder 3 and realize a highly accurate decoding operation.

[0250] Furthermore, it is possible to use the first additive coefficient C_R as convergence acceleration coefficient for an iterative decoding operation in order to raise the processing speed.

[0251] Thus, a data transmission/reception system comprising such an encoder 1 and a decoder 3 can perform decoding operations highly efficiently at high speed with reduced circuit dimensions to provide the user with an enhanced degree of reliability and convenience.

[0252] The present invention is by no means limited to the above described embodiment. For instance, the encoder may not be adapted to perform convolutional operations and may be adapted to encode with any coding ratio.

[0253] The above embodiment is so described above that each of the processing circuits 53₁₁, 53₁₂, . . . , 53_M1, 53_M2 for decoding PCCCs in the decoder 3″ and the processing circuits 73₁₁, 73₁₂, . . . , 73_M1, 73_M2 for decoding SCCCs in the decoder 3′″ comprise a soft-output decoding circuit and an interleaver or a deinterleaver along with one or more than one adders, however, and it can be applied to iterative decoding operations if at least the soft-output decoding circuit is realized as LSI.

[0254] Additionally, while decoder of the above described embodiment is adapted to do MAP decoding on the basis of the Log-BCJR algorithm, the present invention is also applicable to a decoder adapted to do MAP decoding on the basis of the Max-Log-BCJR algorithm.

[0255] Finally, while an encoder and a decoder are applied respectively to a transmitter and a receiver of a data transmission/reception system in the above description, the embodiment of the present invention can be applied to a recording and/or reproduction apparatus for recording signals onto and/or reproducing signals from a magnetic, optical or magneto-optical disc such as CD-ROM or MO (magneto-optical) disc. If such is the case, the data encoded by the encoder are stored in a recording medium that is equivalent to the above described memoryless communication channel and decoded and reproduced by the decoder.

[0256] The above described embodiment can be modified and/or altered without departing from the spirit and scope of the present invention.