Soft output decoder for convolutional codes

[0001] This application is related to U.S. patent applications, Ser. No. 09/500,819 by inventors Desai and Classon, Ser. 09/502,132 No. by inventors Classon, Schaffner, Desai, Baker and Friend, and Ser. No. 09/501,883 by inventors Classon, Schaffner and Desai. The related applications are filed on even date herewith, are assigned to the assignee of the present application, and are hereby incorporated herein in their entirety by this reference thereto.

[0002] This invention relates generally to communication systems, and more particularly to a soft output decoder for use in a receiver of a convolutional code communication system.

[0003] Convolutional codes are often used in digital communication systems to protect transmitted information from error. At the transmitter, an outgoing code vector may be described using a trellis diagram whose complexity is determined by the constraint length of the encoder. Although computational complexity increases with increasing constraint length, the robustness of the coding also increases with constraint length.

[0004] At the receiver, a practical soft-decision decoder, such as a Viterbi decoder as is known in the art, uses a trellis structure to perform an optimum search for the maximum likelihood transmitted code vector. The Viterbi algorithm, however, is computationally complex, and its complexity increases exponentially with increasing constraint length. This essentially means that a Viterbi decoder requires a significant amount of memory and processing power for convolutional codes with large constraint lengths.

[0005] Coders for various communications systems, such as Direct Sequence Code Division Multiple Access (DS-CDMA) standard IS-95 and Global System for Mobile Communications (GSM), have such large constraint lengths. For example, the GSM half-rate constraint length K=7 and the IS-95 constraint length K=9.

[0006] Another disadvantage of Viterbi decoders is that a fixed number of computations must be performed for each code vector, irrespective of the actual number of errors that occurred during transmission. Thus, a Viterbi decoder processes a received signal having few transmission errors or no errors at all using the same number of computations as a received signal having many errors.

[0007] More recently, turbo codes have been developed that outperform conventional coding techniques. Turbo codes are generally composed of two or more convolutional codes and turbo interleavers. Turbo decoding is iterative and uses a soft output decoder to decode the individual convolutional codes. The soft output decoder provides information on each bit position which helps the soft output decoder decode the other convolutional codes. The soft output decoder is usually a MAP (maximum a posteriori) decoder which requires backward and forward decoding to determine the soft output. However, because of memory, processing, and numerical tradeoffs, MAP decoding is usually limited to a sub-optimal approximation. All of these variants require both forward and backward decoding over the block.

[0008] For future standards, such as the 3GPP (third generation partnership project for wireless systems), an 8-state turbo code with a block length of N=5120, needs 40960 words of intermediate storage which may be unacceptable. Future systems (larger frame and greater number of states) will require even more memory. By comparison, a Viterbi decoder that does not produce soft outputs for an N=5120, 8-state trellis requires less than 100 words of intermediate.

[0009] There is a need for a soft output decoder that reduces overall memory and processing requirements for decoding convolutional codes without the degree of limitations imposed by prior art turbo and MAP decoders.

[0022] The present invention greatly reduces the memory requirement from prior art turbo decoders with only a small increase in computation over a Viterbi decoder. In all, this provides for a more efficient decoder. Moreover, the present invention minimizes the limitations of prior art turbo and MAP decoders.

[0023] Typically, block codes, convolutional codes, turbo codes, and others are graphically represented as a trellis as shown in FIG. 1. Maximum a posteriori type decoders (log-MAP, MAP, max-log-MAP, constant-log-MAP, etc.) utilize forward and backward generalized Viterbi recursions on the trellis in order to provide soft outputs, as is known in the art. The MAP decoder minimizes the decoded bit error probability for each information bit based on all received bits. Typical prior art MAP decoders require a memory for use in decoding.

[0024] Because of the Markov nature of the encoded sequence (wherein previous states cannot affect future states or future output branches), the MAP bit probability can be broken into the past (beginning of trellis to the present state), the present state (branch metric for the current value), and the future (end of trellis to current value). More specifically, the MAP decoder performs forward and backward recursions up to a present state wherein the past and future probabilities are used along with the present branch metric to generate an output decision. The principles of providing hard and soft output decisions are known in the art, and several variations of the above described decoding methods exist.

[0025] Most of the soft input-soft output SISO decoders considered for turbo codes are based on the prior art MAP algorithm in a paper by L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv entitled “Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate”, IEEE Transactions on Information Theory, Vol. IT-20, March 1974, pp. 284-7 (BCJR algorithm). FIG. 1 shows a trellis diagram for this algorithm for an 8-state convolutional code, which can be used in a turbo code. As should be recognized, turbo coders are constructed with interleavers and constituent codes which are usually systematic convolutional codes, but can be block codes also. MAP algorithms not only minimize the probability of error for an information bit given the received sequence, they also provide the probability that the information bit is either a 1 or 0 given the received sequence. The BCJR algorithm provides a soft output decision for each bit position (trellis section) wherein the influence of the soft inputs within the block is broken into contributions from the past (earlier soft inputs), the present soft input, and the future (later soft inputs). This decoder algorithm requires a forward and a backward generalized Viterbi recursion on the trellis to arrive at an optimal soft output for each trellis section (stage). These a posterior probabilities, or more commonly the log-likelihood ratio (LLR) of the probabilities, are passed between SISO decoding steps in iterative turbo decoding. The LLR for information bit u_t is $\begin{array}{cc}{\Lambda }_t=\log \frac{\sum _{\left(m,n\right)\in B^1}{\alpha }_{t-1}\left(n\right){\gamma }_t\left(n,m\right){\beta }_t\left(m\right)}{\sum _{\left(m,n\right)\in B^0}{\alpha }_{t-1}\left(n\right){\gamma }_t\left(n,m\right){\beta }_t\left(m\right)},& \left(1\right)\end{array}$
for all bits in the decoded sequence (t=1 to N). In equation (1), the probability that the decoded bit is equal to 1 (or 0) in the trellis given the received sequence is composed of a product of terms due to the Markov property of the code. The Markov property states that the past and the future are independent given the present. The present, γ_t(n,m), is the probability of being in state m at time t and generating the symbol y_t when the previous state at time t−1 was n. The present plays the function of a branch metric. The past, α_t(m), is the probability of being in state m at time t with the received sequence {y₁, . . . , y_t}, and the future, β_t(m), is probability of generating the received sequence {y₁₊₁, . . . y_N} from state m at time t. The probability α₁(m) can be expressed as function of α_t−1(m) and γ_t(n,m) and is called the forward recursion $\begin{array}{cc}{\alpha }_t\left(m\right)=\sum _{n=0}^{M-1}{\alpha }_{t-1}\left(n\right){\gamma }_t\left(n,m\right),m=0,\dots ,M-1,& \left(2\right)\end{array}$
where M is the number of states. The reverse or backward recursion for computing the probability β₁(n) from β_t+1(n) and γ₁(n,m) is $\begin{array}{cc}{\beta }_t\left(n\right)=\sum _{m=0}^{M-1}{\beta }_{t+1}\left(m\right){\gamma }_t\left(n,m\right),n=0,\dots ,M-1.& \left(3\right)\end{array}$
The overall a posteriori probabilities in equation (1) are computed by summing over the branches in the trellis B¹ (B⁰) that correspond to u_t=1 (or 0).

[0026] The LLR in equation (1) requires both the forward and reverse recursions to be available at time t. The BCJR method for meeting this requirement is to compute and store the entire reverse recursion, and recursively compute α_t(m) and A, from t=1 to t=N using α_t−1 and β₁.

[0027] The disadvantage of this decoder is that the entire block of N stages must first be stored in memory before processing. Not only does this requires a large memory (N sections x M states x number of bits per state), this also causes a signal delay of length N before any information can possibly be output. In a W-CDMA system (N˜5000, M=8, 13 bits) the memory required is about 0.5 Mbits. In a cdma2000 system, N is approximately 20000 which requires a memory of about 2 Mbits. For small sequence lengths, memory utilization is generally not an issue. However, for the large N where turbo codes perform the best, memory utilization is significant.

[0028] In terms of complexity, the BCJR method requires NM state updates for the reverse recursion (M state updates per trellis section, N trellis sections in the code) and provides optimal performance. In practice, a backward recursion is performed by a processor across the entire block (as shown in FIG. 1) and stored in memory. Then a forward recursion is performed by the processor and the result is used with the present state and stored future state to arrive at a soft output decision for each stage. In this case the processor operates on each state twice, once to store the backward recursion states, and once during forward recursion processing (throughput of ½).

[0029] To address the memory utilization problem, a sliding window method and similar variations were developed. In the sliding window technique, described in a paper by S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, entitled “Algorithm for continuous decoding of turbo codes,” Electronics Letters, Vol. 32, Feb. 15, 1996, pp. 314-5, as represented in FIG. 2 (in the figures that follow a solid arrow represents an output provided with recursion but no storage, a dotted arrow represents a learning period with no output and no storage, and a hollow arrow represents a stored recursion with no output, with the direction of the arrows indicating forward or backward recursions). An assumption that all states at time t+P are equally probable (or unknown) is used for the reverse recursion. To use this assumption, the learning period P must be several constraint lengths of the constituent code in order to provide near-optimal performance. Making the learning period too small can introduce noticeable performance degradation, similar to the effects of ‘finite’ traceback in the conventional Viterbi algorithm.

[0030] The sliding window technique does not require any memory, but is computationally complex. Specifically, instead of an entire backward recursion being performed and stored, only a partial backward recursion is performed (and not stored) to determined each state. For each present state, the algorithm initializes the future recursion at a learning period of P away from the present state with the initial state unknown. The future probabilities are calculated backward from the unknown future point, not from the known end of the trellis. The length P (learning period) is set such that by the time the partial backward recursion reaches the present state, the future probabilities are most likely correct. P depends on the rate and constraint length of the code and the expected channel conditions. For example, given an 8-state decoder with a ½ rate convolutional code, P is typically between 16 to 32, wherein P is some multiple of constraint lengths. The disadvantage of this decoder is that the partial backward recursion is started with equally likely (unknown states) and is allowed to iterate until it reaches the present window. This is a sub-optimal algorithm as the sliding window causes degradation from true MAP performance, similar to the effects of finite traceback in a conventional Viterbi algorithm, increasing the probability of decoded bit error. Also, the processor operates on each state P times (throughput of 1/P) and has a output delay of P. Moreover, this algorithm requires P times the complexity which can only be reduced by adding more processing.

[0031] The sliding window method can be summarized as, for t=1 to N, compute the reverse recursion starting at time t+P to time t, and compute α_t(m) and A, from α_t−1(m) and β_t. The sliding window method reduces the memory requirement from NM as needed in the BCJR method down to an insignificant amount of memory needed for a recursion. Assuming double buffering, the amount of memory is only 2M, and can be safely ignored in the analysis.

[0032] However, to achieve this memory saving, the computational complexity for the backward recursion increases by a factor of P. The sliding window method is also sub-optimal due to the ‘finite’ window size.

[0033] Another prior art decoder, described in U.S. Pat. No. 5,933,462 to Viterbi et al. (and similarly in a paper of S. Pietrobon and S. Barbulescu, “A Simplification of the Modified Bahl et al. Decoding Algorithm for Systematic Convolutional Codes,” Int. Symp. On Inform. Theory and its Applications, Sydney, Australia, pp. 1073-7, November 1994, revised Jan. 4, 1996 and S. Pietrobon, “Efficient Implementation of Continuous MAP Decoders and a Synchronisation Technique for Turbo Decoders,” Int. Symp. On Inform. Theory and its Applications, Victoria, B.C., Canada, pp. 586-9, September 1996) describes another sliding window technique, as represented in FIG. 3.

[0034] The Viterbi sliding window method reduces the large increase in computational complexity of the prior art sliding window method by performing processing in blocks. The reverse recursion is started at time t+2L, and the reverse recursion values are stored from time t+L to time t. The forward recursion and output likelihood computation are then performed over the block of time t to time t+L. Memory is reduced from NM down to LM, while only doubling the computational complexity. The key observation of starting the recursion in an unknown state is the same as for the sliding window technique.

[0035] This technique requires some memory and is still computationally complex. The decoder differs from the previously described sliding window technique by providing a window that slides forward in blocks rather than a symbol at a time. Specifically, a sliding window is defined having a length L which is equal to the previously described learning period P. Also, L is some multiple of the total trellis length, N, and the window slides from the beginning to the end of the trellis in steps of length L. In this way, the memory required in prior art decoders, where the entire trellis was stored, has been reduced from N to NIL (typically 3 kbits for cdma2000 and W-CDMA systems where L=32).

[0036] This decoder also uses a learning period starting from an unknown future state and is therefore sub-optimal as described previously. Specifically, a forward recursion is performed by the processor starting from a known state at the beginning of a first window L and over the length (L) of the first window. These forward recursion states are stored. The processor then performs a backward recursion from an unknown state starting at a point that is 2L away from where the forward recursion started so as to define a known state at the end of the first window. Then the processor performs a second backward recursion starting from the known state at the end of the first window to the present state wherein information from the backward recursion and the stored forward recursion are used to generate the soft output. Once all the outputs of the first window are determined the window slides forward an amount L and the process is repeated starting from the state that was determined at the end of the first window.

[0037] The disadvantage of this decoder is that the first backward recursion over the learning period, L, is started with equally likely (unknown states) and is allowed to iterate over the length L which is sub-optimal as previously described. Also, the processor operates on each state three times although a forward and backward processor can be run concurrently such that the throughput of ½ is obtained. The decoder produces an output delay of 2L. Moreover, the backward recursion requires twice the complexity which can only be reduced (or the throughput increased) by adding more processing. Further, this decoder produces soft outputs in reverse order which would need to be buffered in a supplementary memory before being output.

[0038] FIG. 4 shows an expanded diagram of the graph of FIG. 3 with a time component added. In operation, at time 0 a forward processor performs a forward recursion over a first window from position 0 to L and stores the information while over the same time period a backward processor performs a backward recursion from position 2L to L to define a known state at the end of the first window at position L at time L. Thereafter, a second backward recursion operates from time L to 2L over position L to 0 to define the soft outputs over the first window. At this time, the soft decisions can now be reversed and output in order (which clearly occurs after a delay of 2L), the memory is cleared, the window position slides forward a length of L, and the process repeats. Alternatively, with an additional backward recursion processor and memory, throughput can be increased.

[0039] FIG. 5 shows an alternative result for the graph of FIG. 3 using an additional backward processor. In operation, at time 0 the forward processor performs a forward recursion over a first window from position 0 to L and stores the information while over the same time period the backward processor performs a backward recursion from position 2L to L to define a known state at the end of the first window at position L at time L. Thereafter, a second backward recursion operates from time L to 2L over position L to 0 to define the soft outputs over the first window. At the same time, the forward and additional backward processor start a second cycle by beginning to process information the second window (from position L to 2L). At time 2L, the soft decisions for the first window are output while the forward recursion and backward learning period for the second window have already been completed. Then a second backward recursion for the second window is performed to obtain the soft outputs for the second window. As can be seen, this technique doubles the throughput. Twice the memory is needed as the information of the forward recursion for the first window is being used while the forward recursion for the second window is being stored.

[0040] The above decoders (specifically of FIGS. 4 and 5) suffer from the problem of the soft outputs being produced out of order requiring their reversed before being output. This requires additional buffer memory and produces an additional delay to reverse the outputs.

[0041] The present invention solves this problem in a novel way. FIG. 6 shows a trellis diagram utilizing convolutional decoding in accordance with the present invention. The trellis code is obtained from a convolutionally coded sequence of signals represented by a trellis of length N in a communication system, as simplified in FIG. 7. In a radiotelephone 100, a signal travels through an antenna 102 to a receiver 104 and demodulator 106, as is known in the art. The signal is loaded into a frame buffer 106. A forward recursion processor 110 and backward recursion processor 112 operate on the block.

[0042] The present invention differs from the previously described sliding window technique of FIGS. 3-5 by providing a full backward recursion stored over a specified window, L, followed by a forward recursion such that the soft outputs are generated in order and can be output immediately without waiting for the entire window to be traversed. Although the window sizes are not required to be equal throughout the trellis, it is assumed that they are equal for purposes of explanation. In particular, a sliding window is defined having a length L such that some multiple of L equals the total trellis length, N, and the window slides from the beginning to the end of the trellis in steps of length L. This present invention uses a learning period, P, starting from an unknown future state and is therefore sub-optimal as described previously. The learning periods are assumed to be equal for purposes of explanation, but the learning periods are not required to be all equal. For example, in those cases where the code is punctured more at one end of a trellis than the other, this will likely require a longer learning period for equal performance.

[0043] Specifically, a backward learning recursion is performed by the backward processor 112 starting from an unknown state that is length P (in the simplest embodiment P=L) beyond the end of a first window backward to the end of the first window to approximate and define a known state at the end of that window. Then a second backward recursion is performed by the backward processor 112, starting at the known state at the end of the first window back to the beginning of the window and stored in a memory 114. The forward recursion processor 110 then performs a forward recursion from the known state at the beginning of the window throughout the length of the window. At the same time the decoder 116 outputs the soft output decisions as they are generated using the known backward recursion in the memory 114 and the information from the forward recursion processor 110 using the present branch metrics.

[0044] At the end of the first window, the window slides forward an amount L and the process is repeated. In a preferred embodiment, an additional backward processor 118 is used in parallel with the backward processor 112 such that when the backward recursion processor 112 operates within the window the additional backward recursion processor 118 operates to decode a portion of the trellis using a learning backward recursion from a next point P that is after the end of the next window back to the end of the next window. Also, when the forward recursion processor 110 operates within the window the additional backward recursion processor 118 decodes the portion of the trellis within the next window using backward recursion from the known state at the end of the next window back to the beginning of the next window to define a set of known backward recursion state metrics within the next window which is stored in the memory 114 as the memory is cleared by the forward recursion processors 10, leaving the forward recursion processor 110 available to begin decoding the next window immediately after the present window is processed. The forward, backward and additional backward processor operate concurrently until all of the windows within the block are decoded. Alternatively, the two backward recursion processors can be used to first operate within the learning periods for two windows and then within the windows themselves. This can be accomplished concurrently or not.

[0045] The advantage of the present invention is that the outputs are provided in order and can be outputted as they are generated without the need of a supplementary buffer memory. The output decoder of the present invention provides a throughput of ½ with an output delay of 2L. However, with the addition of an additional backward processor the throughput is increased to 1 without the need for any more memory as is needed in the prior art.

[0046] FIG. 8 shows an expanded diagram of the graph of FIG. 6 with a time component added and using an additional backward processor (as shown in FIG. 7). In this embodiment, the learning period P is set equal to L for the sake of simplicity but this is not necessary. In operation, at time 0 a backward processor performs a backward learning recursion from position 2L to L to define a known state at the end of the first window at position L at time L. From time L to 2L, a second backward recursion is performed over the first window from position L to 0 and stores the information, while over the same time period the additional backward processor performs a backward learning recursion from position 3L to 2L to define the state at the end of the next window. From time 2L to 3L, a forward recursion operates from an initial known state at time 0 to L to generate and outputs the soft outputs over the first window utilizing the forward recursion values, the stored backward recursion values, and the current branch metric. During this same time (from 2L to 3L), separate backward recursions are also being performed on positions 2L to L and 4L to 3L to be used in subsequent windows repeating the above. The present invention computes each soft output in accordance with known turbo coding techniques, such as those represented in the Bahl et al. paper (BCJR algorithm) cited above.

[0047] The advantage of the present invention is that the soft outputs are being output as they are being generated, freeing up memory as they are being output. Also, as memory clears, new information from the backward recursion for the next window can be circulated into the memory. Therefore, the present invention not only eliminates buffer memory for reversing outputs as is need in the prior art, but also cuts in half the memory requirement. Alternatively, a doubled buffer memory can be used to hold each of the backward recursion soft outputs eliminating the need for circular buffering. Further, the present invention saves time by not having to reorder any soft outputs as would be generated in the prior art.

[0048] The present invention provides further differences over the prior art in that the learning period of the first backward recursion is not required to be equal to the window length, although it can be. Further, although it is preferred that the learning period is equal to at least some multiple of constraint lengths, the window length need not be.

[0049] FIG. 9 shows a flow chart representing a method 200 of decoding a received convolutionally coded sequence of signals represented by a trellis of block length N, in accordance with the present invention (also see FIG. 6). Trellis diagrams are well known in the art. A first step 202 is dividing the trellis into windows of length L. A next step 204 is selecting a window of the trellis. A next step 206 is decoding a portion of the trellis using backward recursion from a point P that is after the end of the window back to the end of the window, wherein P is chosen at a sufficient distance from the end of the window such that backward recursion determines a known state metric at the end of the window. In general, the state metric at point P will be unknown and the backward recursion using a generalized Viterbi algorithm will converge to a known state at the end of the window with a high probability. P is some function of the constraint length of the convolutional code. P can be greater than or less than the length L, but in a preferred embodiment, P is set equal to L. A next step 208 is decoding the portion of the trellis within the window using backward recursion from the known state at the end of the window defined in the above decoding step back to the beginning of the window to define a set of known backward recursion state metrics within the window, and storing the set of known backward recursion state metrics in a memory. A next step 210 is decoding the portion of the trellis within the window using forward recursion starting from a known state at the beginning of the window and moving forward. A next step 212 is calculating a soft output at each stage of the forward recursion process using the forward recursion state metrics, the branch metrics, and the stored backward recursion state metrics, and outputting the soft output for that stage. Preferably, the recursion updates and soft outputs are calculated using a MAP algorithm or one of the MAP derivatives (i.e., log-MAP, max-log-MAP, constant-log-MAP, etc.).

[0050] Once a window is completely decoded, the window can be “slided” forward a distance L where the beginning of the new window starts at the end of the last window so as to start at a previously determined known state. The above steps can then be repeated for the new window. This process continues until all of the windows in the block are processed. The first and last windows are a special case in that the beginning and ends of the block are usually at known states for the convolutional code. Therefore, when processing the first window, the forward recursion starts at the known first state of the block, and when processing the last window it is not necessary to perform the first backward learning recursion as the end state of the window is the known end state of the block.

[0051] In a preferred embodiment, a further step is included where an additional backward learning recursion is performed two windows ahead of the present window and concurrently with the stored backward recursion of the present window so as to define the end state of the next window. In other words, the processing for the next window begins while the first window is being processed. In particular, the further step includes repeating the above steps, wherein the repeated selecting step includes selecting a next window starting at the end of the presently selected window, and wherein the repeated steps decoding and calculating steps for the next window occur one step out of sequence and concurrently with the processing of the present window. This additional step saves processing time since outputs can be provided continuously. No additional memory is required. More preferably, while the forward recursion for the first window is being performed the stored memory is being cleared, and the backward recursion of the next window can stored, or circulated, into the cleared portions of the memory, although this is not required.

[0052] Table 1 summarizes approximately the memory, throughput, and computational requirements of the three prior art methods along with the method of the present invention. Entries in parentheses use an additional backward processor.

[0053]

TABLE 1
Comparison of the four methods for backward recursion.
			Computational
Method	Memory Needed	Throughput	Complexity
BCJR	NM words	1/2	NM state updates
Sliding Window	0 words	1/P	PNM state updates
Viterbi Sliding	ML (2ML) words	½ (1)	2NM state updates
Window
Present Invention	ML (ML) words	½ (1)	2NM state updates

To illustrate the differences among the methods, Table 2 presents the results when typical values of sequence length (N=5000), number of states (M=8), window size (L=32) are used.

[0054]

TABLE 2
Comparison among the methods for typical values of N, M and L.
		Through-	Computational
Method	Memory Needed	put	Complexity
BCJR	40,000 words	1/2	40,000 state updates
Sliding	0 words	1/32	1,280,000 state updates
Window
Viterbi Sliding	256 (512) words	½ (1)	80,000 state updates
Window
Present	256 (256) words	½ (1)	80,000 state updates
Invention

As Table 2 shows, the memory requirements of the present invention are well within a reasonable range and more than an order of magnitude less than the BCJR method, while only requiring twice as many state updates. Finally, note that in the example, the block length and window size was chosen to be identical to simplify the comparisons. However, while P must be set for performance, L can be chosen to provide the desired memory/computation complexity tradeoff. In some cases, the memory required by the present invention is less than that required by the Viterbi Sliding Window method.

[0055] In an alternate embodiment of the present invention, as represented in FIG. 10, the situation is reversed from that of FIG. 8. This is advantageous for those cases utilizing a last-in first-out (LIFO) decoding scheme. In this instance, a forward recursion is stored over a specified window, L, followed by a backward recursion such that the soft outputs are generated in a LIFO order and can be output immediately without waiting for the entire window to be traversed. Although the window sizes are not required to be equal throughout the trellis, for simplicity of discussion, it is assumed that they are equal. In particular, a sliding window is defined having a length L such that some multiple of L equals the total trellis length, N, and the window slides from a known state at the end of the trellis back to the beginning of the trellis in steps of length L. A learning period, P, starts from an unknown past state such that the decoding in the present invention is sub-optimal as described previously. The learning periods are not required to be all equal as described above.

[0056] Referring to FIGS. 10 and 11, in operating on the frame buffer 108 a forward learning recursion is performed by a forward recursion processor 110 starting from an unknown state that is length P (in the simplest embodiment P=L) before the beginning of a first window forward to the beginning of the first window to define a known state at the beginning of that window. Then a second forward recursion is performed by the forward processor 110, starting at the known state at the beginning of the first window up to the end of the window and stored in a memory 114. The backward recursion processor 112 then performs a backward recursion from the known state at the end of the window back through the length of the window. At the same time the decoder 116 outputs the soft output decisions as they are generated, in LIFO format, using the known forward recursion in the memory 114 and the information from the backward recursion processor 112 using the present branch metrics.

[0057] At the end of the first window, the window slides backward an amount L and the process is repeated. In a preferred embodiment, an addition forward processor 120 is used in parallel with the forward processor 110 such that when the forward recursion processor 110 operates within the window the additional forward recursion processor 120 operates to decode a portion of the trellis using a learning forward recursion from a next point P that is before the beginning of the next window up to the beginning of the next window. Also, when the backward recursion processor 112 operates within the window the additional forward recursion processor 120 decodes the portion of the trellis within the next window using forward recursion from the known state at the beginning of the next window up to the end of the next window to define a set of known forward recursion state metrics within the next window which is stored in the memory 114 as the memory is cleared by the backward recursion processor 112, leaving the backward recursion processor 112 available to begin decoding the next window immediately after the present window is processed. The forward, backward and additional forward processor operate concurrently until all of the windows within the block are decoded. Alternatively, the two forward recursion processors can be used to first operate within the learning periods for two windows and then within the windows themselves. This can be accomplished concurrently or not.

[0058] The advantage of the present invention is that the outputs are provided in order (where required by a LIFO format) and can be outputted as they are generated without the need of a supplementary buffer memory. The output decoder of the present invention provides a throughput of ½ with an output delay of 2L. However, with the addition of an additional forward processor the throughput is 1 without the need for any more memory as is needed in the prior art.

[0059] In operation, the learning period P is set equal to L for the sake of simplicity but this is not necessary. At time 0 a forward processor performs a forward learning recursion from the position (from the end of the trellis) 2L to L to define a known state at the beginning of the first window at position L at time L. From time L to 2L, a second forward recursion is performed over the first window from position L to 0 and stores the information, while over the same time period the additional forward processor performs a forward learning recursion from position 3L to 2L to define the state at the beginning of the next window. From time 2L to 3L, a backward recursion operates from an initial known state at position 0 to L to generate the soft outputs over the first window utilizing the backward recursion values, the stored forward recursion values, and the current branch metric. During this same time (from 2L to 3L), separate forward recursions are also being performed on positions 2L to L and 4L to 3L to be used in subsequent windows repeating the above. The present invention computes each soft output in accordance with known turbo coding techniques, such as those represented in the Bahl et al. paper (BCJR algorithm) cited above.

[0060] The advantage of the present invention is that the soft outputs are being output as they are being generated, freeing up memory as they are being output. Also, as memory clears, new information from the forward recursion for the next window can be circulated into the memory. Therefore, the present invention not only eliminates buffer memory for reversing outputs as is need in the prior art, but also cuts in half the memory requirement. Alternatively, a doubled buffer memory can be used to hold each of the backward recursion soft outputs eliminating the need for circular buffering. Further, the present invention saves time by not having to reorder any soft outputs as would be generated in the prior art.

[0061] The present invention provides further differences over the prior art in that the learning period of the first forward recursion is not required to be equal to the window length, although it can be. Further, although it is preferred that the learning period is equal to at least some multiple of constraint lengths, the window length need not be.

[0062] FIG. 12 shows a flow chart representing a method 300 of decoding a received convolutionally coded sequence of signals represented by a trellis of block length N, in accordance with a LIFO format of the present invention. A first step 302 is dividing the trellis into windows of length L. A next step 304 is selecting a window of the trellis. A next step 306 is decoding a portion of the trellis using forward recursion from a point P that is before the beginning of the window up to the beginning of the window, wherein P is chosen at a sufficient distance from the beginning of the window such that forward recursion determines a known state metric at the beginning of the window. In general, the state metric at point P will be unknown and the forward recursion using a generalized Viterbi algorithm will converge to a known state at the beginning of the window with a high probability. P is some function of the constraint length of the convolutional code. P can be less than the length L, but in a preferred embodiment, P is set equal to L. A next step 308 is decoding the portion of the trellis within the window using forward recursion from the known state at the beginning of the window defined in the above decoding step up to the end of the window to define a set of known forward recursion state metrics within the window, and storing the set of known forward recursion state metrics in a memory. A next step 310 is decoding the portion of the trellis within the window using backward recursion starting from a known state at the end of the window and moving backward through the window. A next step 312 is calculating a soft output at each stage of the forward recursion process using the forward recursion state metrics, the branch metrics, and the stored backward recursion state metrics, and outputting the soft output at that stage. Preferably, the recursion updates and soft outputs are calculated using a MAP algorithm or one of the MAP derivatives (i.e., log-MAP, max-log-MAP, constant-log-MAP, etc.).

[0063] Once a window is completely decoded, the window can be “slided” backward a distance L where the end of the new window starts at the beginning of the last window so as to start at a previously determined known state. The above steps can then be repeated for the new window. This process continues until all of the windows in the block are processed. The first and last windows are a special case in that the beginning and ends of the block are usually at known states for the convolutional code. Therefore, when processing the first window, the forward recursion starts at the known end state of the block, and when processing the last window it is not necessary to perform the first forward learning recursion as the start state of the window is the known first state of the block.

[0064] In a preferred embodiment, a further step is included where an additional forward learning recursion is performed two windows ahead of the present window and concurrently with the stored forward recursion of the present window so as to define the beginning state of the next window. In other words, the processing for the next window begins while the first window is being processed. In particular, the further step includes repeating the above steps, wherein the repeated selecting step includes selecting a next window ending at the beginning of the presently selected window, and wherein the repeated steps decoding and calculating steps for the next window occur one step out of sequence and concurrently with the processing of the present window. This additional step saves processing time since no additional memory is required. More preferably, while the backward recursion for the first window is being performed the stored memory is being cleared, and the forward recursion of the next window can stored, or circulated, into the cleared portions of the memory, although this is not required.

[0065] In a preferred embodiment, the embodiments of FIGS. 8 and 10 (and FIGS. 9 and 11) are combined such that the trellis is decoded from both ends in a bidirectional manner. This requires doubling the memory and processors but results in a doubling of the throughput.

[0066] Table 3 summarizes approximately the memory, throughput, and computational requirements of the three prior art methods along with the preferred bidirectional method of the present invention. Entries in parentheses use an additional backward processor. Computational complexity includes both forward and backward processing.

[0067]

TABLE 3
Comparison of the four methods for soft output decoding.
			Computational
Method	Memory Needed	Throughput	Complexity
BCJR	NM words	1/2	2NM state updates
Sliding Window	0 words	1/P	(L + 1)NM state
			updates
Viterbi Sliding	ML (2ML) words	½ (1)	3NM state updates
Window
Present Invention	2ML words	2	6NM state updates

To illustrate the differences among the methods, Table 4 presents the results when typical values of sequence length (N=5000), number of states (M=8), window size (L=32) are used.

[0068]

TABLE 4
Comparison among the methods for typical values of N, M and L.
		Through-	Computational
Method	Memory Needed	put	Complexity
BCJR	40,000 words	1/2	80,000 state updates
Sliding	0 words	1/32	1,320,000 state updates
Window
Viterbi Sliding	256 (512) words	½ (1)	120,000 state updates
Window
Present	512 words	2	240,000 state updates
Invention

As Table 4 shows, the memory requirements of the present invention are well within a reasonable range and more than an order of magnitude less than the BCJR method. The sliding window methods have similar memory requirements, but have lower throughput than the present invention. Finally, note that in the example, the block length and window size was chosen to be identical to simplify the comparisons.

[0069] The present invention increases throughput and greatly reduces the memory required for a turbo decoder with only a small increase in complexity. For the turbo code within the 3GPP standard, the 40960 words of intermediate storage can be easily reduced to about 500 words.

[0070] While specific components and functions of the soft output decoder for convolutional codes are described above, fewer or additional functions could be employed by one skilled in the art within the broad scope of the present invention. The invention should be limited only by the appended claims.