Soft output viterbi algorithm (SOVA) with error filters

[0002] All of the material in this patent application is subject to copyright protection under the copyright laws of the United States and of other countries. As of the first effective filing date of the present application, this material is protected as unpublished material. However, permission to copy this material is hereby granted to the extent that the copyright owner has no objection to the facsimile reproduction by anyone of the patent documentation or patent disclosure, as it appears in the United States Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.

[0003] Not Applicable

[0004] 1. Field of the Invention

[0005] The invention relates to a Soft Output Viterbi Algorithm. More particularly, the invention is a simplified method and apparatus for more easily computing and providing bit reliabilities in combination with a Viterbi algorithm on a processing unit.

[0006] 2. The Prior Art

[0007] The Viterbi algorithm is used for detecting data possibly corrupted by noise in movement of data through communications or recording systems. The algorithm computes the most likely sequence written on the recording given the received noisy data. The output is consistent with some constraints on the sequences that are allowed to be written.

[0008] a. Ordinary SOVA

[0009] A channel trellis is a diagram defined by states and branches that describes the “ideal” sequence of outputs to a sequence of inputs. For instance, an Inter-Symbol Interference (ISI) channel trellis, determined by a linear channel impulse response such as Partial Response Class 4 (PR4), Extended Partial Response Class 4 (EPR4) or Extended²Partial Response Class 4 (E²PR4) describes the ideal response of such a channel to any possible sequence of binary Non-Return to Zero (NRZ) inputs.

[0010] For simplicity, an assumption is made that the trellis is a possibly “pruned” version of a standard ISI channel trellis diagram with memory v. The states are binary v-tuples, and for u=0 or 1, there is a branch from state (x_−v. . . x₋₁) to (x_−v+1. . . x₋₁u). Each branch has an input label (u) and output label (the ideal channel response to the input sequence (x_−v. . . x₋₁u).

[0011] The “pruning” may be the consequence of a constraint (such as MTR) on the channel inputs designed to improve the performance of the detection process.

[0012] If the channel detector is designed to pass soft information to a code whose codewords are in some domain other than NRZ (e.g., NRZI, PR4), then the approach described here could be modified accordingly.

[0013] Naturally, an assumption is made that the ideal sequence of channel outputs is corrupted by a noise source. The Bahl, Cocke, Jelinek, Raviv (BCJR) algorithm, produces exact a posteriori probabilities (APP) for each bit, assuming that the noise is uncorrelated and data-independent (for instance, Additive White Gaussian Noise (AWGN)). These APP probabilities can be used as soft-decision inputs passed on to other modules in the detection/decoding process, such as a turbo decoder or low density parity check (LDPC) decoder.

[0014] Experimental results on test-stand data show that the BCJR algorithm, in conjunction with low density parity check codes, performs quite well—in spite of the fact that the test-stand noise is typically correlated and data-dependent. But the complexity of the BCJR algorithm may prove too costly for implementation.

[0015] SOVA (soft output Viterbi algorithm) is a method for producing approximate APP's at a lower computational cost than BCJR. The estimates produced by SOVA are based on Viterbi margins (i.e., differences between the metric of a survivor path and its non-surviving path in the Viterbi algorithm). SOVA was introduced by Hagenauer and Hoeher in “A Viterbi Algorithm with Soft Decision Outputs and its Applications”, Proceedings of Globecom, 1989, pp. 1680-1686.

[0016] b. Description of Algorithm

[0017] SOVA begins with an ordinary run of the Viterbi algorithm on a long block (of length N) of data. The branch metrics are ordinarily determined by the received channel sample r_jand the ideal channel output w on the branch: ∥r_j−w∥²; but prior information from previous LDPC iterations may be incorporated in the branch metrics (by adding a term of the form log p where p is the prior probability that the j-th data bit equals the branch input label).

[0018] At each bit position j, in between 1 and N, the Viterbi algorithm computes and outputs a detected data bit x_j. As is well known this requires a delay equal to the so-called path memory, denoted M (typically, N will be much larger than M). SOVA requires an additional delay, denoted Δ, within which one makes use of Viterbi margins.

[0019] At bit position j, after a delay of Δ+M, the Viterbi detector will have detected data bits in positions up to j+Δ. For each k=j+1, . . . , j+Δ, the detected path up to position k will be a survivor path. As such, it will have at most one non-surviving (runner-up) path ending at the same state (it may have no such paths if the trellis has been pruned). Call this non-surviving path p_k, and let m_kdenote the Viterbi margin (i.e., the difference between the metric of the detected path up to time k and the metric of P_k) The algorithm is concerned only with those p_kthat would result in a different value for the j-th data bit, i.e.

[0020] (p_k)_j≠x_j.

[0021] Such a k is called j-qualified. So, for bit position j, Viterbi margins are computed only for those k that are j-qualified. FIG. 1 illustrates a non-surviving path p_k(100) for a j-qualified k as described in the prior art.

[0022] For the j-th bit position SOVA will output ${\omega }_j={\left(-1\right)}^{X_j}\underset{k}{\min }{m}_k$

[0023] where the minimum runs over all j-qualified k such that j+1≦k≦j+Δ. As shown in J. Hagenauer and E. Offer and L. Papke, “Iterative Decoding of Binary Block and Convolutional Codes”, IEEE Transactions on Information Theory, March, v.42, 1996, pp 429-445, this quantity is an approximation to the true APP log-likelihood: ${\omega }_j\approx \log \left(\frac{P(x_j|r^j)}{P({\stackrel{\_}{x}}_j|r^j)}\right)$

[0024] where r^jdenotes the received sequence of samples up to time j+Δ+M and {overscore (χ_j)}, denotes the binary complement of χ_j.

[0025] c. Access to the non-surviving path p_k

[0026] FIG. 2 illustrates a Soft Output Viterbi Algorithm Decoder (200) as described in the prior art. Signals are input into the decoder (200) from a channel (202). The signals pass through an equalizer (204) and into the primary decoding stages of the SOVA. The non-surviving path p_kcould be obtained from the Viterbi detector with a delay of time M. But then each state s and each i=1, I . . . , M, would require an enormous buffer to store all the non-surviving paths ending at state s at time slot k-i.

[0027] An alternative would be to use a second Viterbi detector (212), V2, operating with delay M (210) with respect to the first Viterbi detector (206), V1. Then V1 (206) would provide the detected data path with delay M (210), and V2 (212) would provide the non-surviving path p_k. This is described as follows.

[0028] First, a buffer is needed, detected buffer (208) DB in FIG. 2, to store the last Δ detected bits: x_k−Δ+1. . . x_k. At time slot k+M, this buffer is updated by shifting one unit to the left and filling in the right-most position with the newly detected bit x_kfrom V1 (206). If Δ≧v (i.e., the look-ahead is at least as large as the channel trellis memory), then the ending state s_kof the detected path can be read directly from DB (208) and fed to V2 (212). The differences between the Viterbi detectors V1 (206) and V2 (212) are:

[0029] 1—V2 (212) has path memory Δ instead of M.

[0030] 2—At time slot k+M, V2 (212) computes all survivor paths ending at bit position k instead of k+M.

[0031] In all other respects, V2 (212) operates exactly the same as V1 (206).

[0032] In the trellis, state s_khas at most two incoming branches. The initial states of these branches are called s and s′. As usual, V2 (212) will add the branch metrics to the current state metrics of s and s′ in order to determine the survivor path at state s_k. One of these will be the detected path, and the other will be the non-surviving path p_k. Of course, V2 (212) will have access to DB (208) and therefore to the identity of state s_kas shown in FIG. 2.

[0033] Then V2 (212) will pass the margin m_k, at state s_k, as well as the last Δ bits of the non-surviving path, (p_k)_j, j=k−Δ+1, . . . , k, to the qualification/minimization (QM 214) module, which also requires access to the buffer DB (208) of detected bits and an accumulated minimum margin buffer (AMMB 216). At any given time instant k, this module finds the bit positions j for which k is j-qualified and iteratively computes the margins m_k, the minimum margin ω and ultimately the soft outputs.

[0034] c. Pseudo-Code for Computation of Soft-Output

[0035] Fork=1, . . . , N,{

[0036] obtain detected bit x_kfrom Viterbi detector;

[0037] μ_k=1000;

[0038] d. Complexity

[0039] The overhead required by SOVA, above and beyond that required by the Viterbi detector V1, comprises the following:

[0040] 1—A second Viterbi detector V2 with path memory Δ.

[0041] 2—A detection buffer (DB) to hold the detected bits x_k−Δ+1. . . x_k.

[0042] 3—Δ−1 comparisons per bit in the qualification/minimization module.

[0043] 4—An accumulated minimum margin buffer (AMMB) to hold the accumulated minimum margins μ_k−Δ+1. . . μ_k.

[0044] For a 64-state channel trellis, with M=Δ=64, the number of additions and multiplications for SOVA will be double that of ordinary Viterbi detection and the number of comparisons with be triple that of Viterbi detection. Also, the additional buffers will make the storage requirements somewhat more than double that of Viterbi detection. In addition, SOVA will produce soft outputs with double the latency that the Viterbi algorithm produces hard decisions.

[0045] e. Other Prior Art

[0046] Further, other related prior art includes Hagenauer's paper, a patent application filed on Oct. 27, 1999, Attorney Docket No. CH19990112, “Method and Apparatus for Encoding and Detection/Decoding of MTR/Parity Codes”, by Cideciyan et al., and U.S. Pat. No. 5,949,831, “Method and Apparatus for Data Detection for PRML Data Channels”, by Coker et al., filed May 21, 1997, issued Sep. 7, 1999. These references use error filters to determine if the output reliability crosses some threshold or if parity is violated in a transmission or recording. Here, each filter corresponds to a most likely error which is corrected using an error correction scheme applied to a sequence of symbols or bits.

[0047] Also, H. Sawaguchi and S. Mita describe a method for decoding using concatenated error correction in “Soft-output decoding for concatenated error correction in high-order PRML channels,” ICC, 1999, pp. 1632-1637.

[0048] Accordingly, what is needed is an improved system and method that is not as complex as a BCJR or the ordinary SOVA algorithm and yet accurately produces bit reliabilities. The present invention addresses such a need.

[0049] This invention is not a variation of a Viterbi Algorithm itself, rather, the invention is a Viterbi algorithm combined with the use of error filter outputs to produce bit reliabilities.

[0050] Thus, the present invention is a SOVA-like method using error filters to reduce the complexity of bit reliability determination further than that of the ordinary SOVA method.

[0051] Error patterns corresponding to each of a handful of dominant i.e., most common error patterns, are determined from experimental data. Error filters determine likelihoods of each postulated error pattern. The filters, typically six or seven of them, resolve most of the errors thereby simplifying computation dramatically. The filters do not do general error correction, rather, the error filters compute likelihoods of the most likely error-causing events and are combined to provide bit reliability estimates.

[0052] The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features and advantages of the invention will be apparent from the following detailed description taken in conjunction with the accompanying drawings.

[0053] FIG. 1 illustrates a non-surviving path p_kfor a j-qualified k as described in the prior art.

[0054] FIG. 2 illustrates a Soft Output Viterbi Algorithm Decoder as described in the prior art.

[0055] FIG. 3 illustrates an Error Event which is the difference between two sequences that differ in only finitely many places.

[0056] FIG. 4 illustrates a Modified Soft Output Viterbi Algorithm with Error Filters as practiced in this invention.

[0057] It is important to note that these embodiments are only examples of the many advantageous uses of the innovative teachings herein. In general, statements made in the specification of the present application do not necessarily limit any of the various claimed inventions. Moreover, some statements may apply to some inventive features but not to others. In general, unless otherwise indicated, singular elements may be in the plural and vice versa with no loss of generality.

[0058] In the drawing like numerals refer to like parts through several views.

[0059] 1. Exemplary Embodiment

[0060] a. Modified SOVA: SOVA with Error Filters

[0061] An error event is the difference between two sequences which differ in only finitely many places. If the sequences are binary (such as NRZ), then an error event can be considered to be a finite word over the alphabet {+1,0,−1}, often abbreviated as {+,0,−}. For a given channel impulse response, a finite set E of error events is fixed. These should be chosen to be the most likely error events for a given channel impulse response, such as E={+,+−+} for PR4.

[0062] Just as in ordinary SOVA, the ordinary Viterbi algorithm is applied to a block of data, possibly incorporating prior information from a previous LDPC iteration, with some specified path memory M. But instead of using the minimum Viterbi margin over a range of some size, the modified SOVA uses the minimum Viterbi margin with respect to only the error events in E. This sub-optimal scheme will generally have much lower complexity than ordinary SOVA.

[0063] Typically, an assumption is made that the block size N is substantially larger than the path memory M which in turn is substantially larger than the maximal length, L, of an error event in E.

[0064] b. Description of Algorithm

[0065] Let h₀, h₁, . . . , h_vdenote the coefficients of the channel impulse response h so v+1 is the length of the response. For any k, at time k+M the Viterbi detector will have detected candidate symbols or data bits in positions up to k:

[0066] x=x₁. . . x_k.

[0067] For any error event e=e₁. . . e_Iin E where I=I(e) is the length of e, let y be the sequence obtained from x by e positioned so that it ends at bit position k−v as in FIG. 3. It is convenient to represent this translate of e as a sequence, s_k(e), of length k:

[0068] s_k(e)=0 . . . 0 e₁. . . e_I0 . . . 0

[0069] where in this expression there are k−I−v 0's at the beginning and v 0's at the end. Then:

[0070] y=x+s_k(e).

[0071] Note that while the error event (in NRZ) ends at bit position k−v, the effect of the error event in the channel trellis does not end until bit position k (in order to flush out the channel memory).

[0072] Of course, in order for the error event to be plausible, y must be a binary sequence. For instance, one cannot simultaneously have x_I=1 and (s_k(e))_I=+. Also, the only error events that need to be considered are those that would have resulted in a different detected decision. So, given j, for the j-th bit position Viterbi margins are computed only over those pairs (k, e) that qualify under the following two conditions:

[0073] Q1: for i=k−I−v+1, . . . k−v

[0074] if (s_k(e))_I=+, then x_I=0 and

[0075] if (s_k(e))_I=−, then x_I=1

[0076] Q2: (s_k(e))_j≠0

[0077] Such a pair (k,e) is called j-qualified.

[0078] Let {circumflex over (χ)}, ŷ denote the channel responses to the input sequences x,y:

[0079] {circumflex over (χ)}=h*χ  (1)

[0080] ŷ{circumflex over ( )}=h*y  (2)

[0081] where * denotes convolution. The channel error response to the error event e is then:

[0082] 𝑓=ŷ−{circumflex over (χ)}=h*s_k(e)  (3)

[0083] Define the (k,e)-margin to be: $\begin{array}{cc}\begin{array}{c}{m}_{k,e}={\Vert r-\hat{y}\Vert }^2-{\Vert r-\hat{x}\Vert }^2\\ ={\Vert \left(r-\hat{x}\right)-f\Vert }^2-{\Vert r-\hat{x}\Vert }^2\\ =-2ϵ·f+{\Vert f\Vert }^2\end{array}& \left(4\right)\end{array}$

[0084] where r denotes the sequence of received channel samples up to time k and

[0085] εr−{circumflex over (χ)}

[0086] the alleged error sequence.

[0087] The (k,e)-margin is computed as follows. The dot product in equation 4 above can be rewritten: $\begin{array}{c}ϵ·f=ϵ·\left(h*s_k\left(e\right)\right)\\ =\left(ϵ*h^R\right)·s_k\left(e\right)\end{array}$

[0088] where h^Ris the filter matched to h, i.e., the time reversal of h.

[0089] FIG. 4 illustrates a Modified Soft Output Viterbi Algorithm with Error Filters (400) as practiced in this invention. The Modified SOVA Decoder (400) comprises a channel (402) for reception of symbols, bits or numbers, an equalizer (404), a viterbi detector (406) a detected buffer (408) a delay M (410), accumulated minimum margin buffers (416, 418), qualification/minimization modules (412, 414) and a minimization function (420). To begin with, the alleged error sequence ε is convolved with h^R, a filter (*h^R) as shown in FIG. 4, and the result is passed through a bank of error filters with taps given by the error events e (see the filters (·eⁱ) in FIG. 4). The output of each error filter is then added to the term ∥f∥²which is a constant energy term using a summation unit. Each such f depends on e and can be retrieved from a look-up table. The first convolution involves multiplications and additions, but the bank of error filters involves only additions since the entries of e are {+1, 0, −1}. Then, a qualification and combining process is performed on the margins m_k,ein the QMs (412, 414). The specific operational conduct of the qualification and combining process is found below. The combining process is a process utilizing a combining unit, in this example a QM, so that the combining process is a minimization process. Next, the m_k,ethat are j-qualified are buffered in the AMMBs (416, 418). Finally, a minimization function is performed by the minimizer (420). The minimizer (420) computes a minimization over all m_k,ethat are j-qualified and produces μ_k−v−L+1, which is multiplied by a sign value (−1)^Xk−v−L+1to produce a soft output ω_j.

[0090] The soft output is defined as: ${\omega }_j={\left(-1\right)}^{x_j}\underset{\left(k,e\right)}{\min }{m}_{k,e}$

[0091] where the minimum ranges over all j-qualified pairs (k,e). Alternatively, instead of generating a final soft output reliability using a minimization function, an averaging function can be used instead in the combining unit. Returning to the analysis of the soft output, ω_jgives an approximation to the log-likelihood: $\log \left(\frac{P(r\left|x_j\right)}{P(r\left|{\stackrel{\_}{x}}_j\right)}\right),$

[0092] which agrees with the APP log-likelihood: $\log \left(\frac{P(x_j\left|r\right)}{P({\stackrel{\_}{x}}_j\left|r\right)}\right)$

[0093] provided that 0's and 1's are equally likely. Otherwise, the computation of m_k,eis adjusted using prior information p(x_I=1): namely, by adding to m_k,ethe following quantity: $\sum _{i=k-l-v+1}^{k-v}{v}_i$

[0094] where

[0095] v_I=0 if (s_k(e))_I=0

[0096] v_I=log(p(x_i=1)/p(x_I=0)) if (s_k(e))_I=+

[0097] v_I=log(p(x_i=0)/p(x_I=1)) if (s_k(e))_I=−

[0098] The pseudo-code in the next section describes the operations of the filters and the qualification/minimization QM′ (412, 414) modules in FIG. 4. The qualification/minimization modules represent a plurality of modules though only two are shown in FIG. 4. Likewise, there are a plurality of AMMB′ present although only two are shown in FIG. 4.

[0099] Within a QM module, the error event is tested for plausibility, i.e., condition Q1 above, and then the set of j=k−I(e) −v+1, . . . , k−v for which (k,e) is j-qualified (condition Q2 above) is determined. (If the error event is not plausible, then the set of such j is empty.) For each such j, the margin is updated by comparison with m_k,e. The QM′ modules (412, 414) require access to an accumulated minimum margin buffer AMMB′ (416, 418) and a detected buffer (420). For each error event, e, the corresponding QM module computes the minimum of m_k,eover all j-qualified (k,e). These are then passed on to the minimization function (420) which computes on overall minimum over all error patterns, e. Alternatively, the minimization operation in the QM modules as well as the minimization function (420) can be replaced by averaging operations.

[0100] c. Pseudo-Code for Computation of Soft-output

[0101] For (k=1; k<=N; k++), {

[0102] obtain detected bit x_kfrom Viterbi detector;

[0103] obtain alleged error ε_k;

[0104] obtain c_k=(ε*h^R)_k; //convolve alleged error with h^R//

[0105] μ_k=1000;

[0106] For (i=1; i<=n; i++) {//for each error event e in E; executed in parallel//

[0107] d. Complexity

[0108] Convolution of the alleged error ε with the matched filter h^Rrequires v+1 multiplications and v additions per bit while recalling that v+1 is the length of the channel impulse response. The error filter corresponding to error event e involves I(e) −1 additions and no multiplications per bit. Thus, the total overhead required by a Modified SOVA above that required by the Viterbi detector is:

[0109] v+Σ_eεE(I(e) −1) additions per bit;

[0110] v+1 multiplications per bit;

[0111] Σ_eεEI(e) comparisons per bit;

[0112] a detected buffer (DB 408) to store the last L+v detected bits;

[0113] n accumulated minimum margin buffers (AMMB¹, . . . , AMMBⁿ416, 418) where n is the number of error events in E;

[0114] look-up tables to hold the contents of ∥f∥²for each error event e.

[0115] Modified SOVA also requires a latency of L+v beyond the Viterbi detector latency.

[0116] Assuming a 64-state channel trellis (so v=6), M=64, and 5 error events of average length 4 and maximal length L=6, the extra overhead required by modified SOVA would be:

[0117] 6+15=21 additions per bit;

[0118] 7 multiplications per bit;

[0119] 20 comparisons per bit;

[0120] a buffer to store the last 12 detected bits;

[0121] 5 buffers each containing at most 6 analog entries and;

[0122] a look-up table containing 5 analog entries.

[0123] Thus, the buffer and look-up table overhead are insignificant and the number of additions, multiplications and comparisons per bit increase by (roughly) 15%, 5% and 30% respectively. Also, the latency would increase marginally from 64 to 76.

[0124] Note that the multiplications required here are all required by the Viterbi algorithm anyway. So, in principle these extra multiplications could be eliminated but this would come at the price of an additional huge buffer.

[0125] 2. Conclusion

[0126] Therefore, a more efficient method, apparatus and product has been described that is not as complex as a BCJR or the ordinary SOVA algorithms and yet accurately represents bit reliabilities. Such a method is needed in order to produce bit reliabilities, in a simple and efficient manner, to be passed on to an outer error-correction decoder.

[0127] 3. Discussion of Hardware and Software Implementation Options

[0128] The present invention, as would be known to one of ordinary skill in the art could be produced in hardware or software, or in a combination of hardware and software. The system, or method, according to the inventive principles as disclosed in connection with the preferred embodiment, may be produced in a single computer system having separate elements or means for performing the individual functions or steps described or claimed or one or more elements or means combining the performance of any of the functions or steps disclosed or claimed, or may be arranged in a distributed computer system, interconnected by any suitable means as would be known by one of ordinary skill in art.

[0129] According to the inventive principles as disclosed in connection with the preferred embodiment, the invention and the inventive principles are not limited to any particular kind of computer system but may be used with any general purpose computer, as would be known to one of ordinary skill in the art, arranged to perform the functions described and the method steps described. The operations of such a computer, as described above, may be according to a computer program contained on a medium for use in the operation or control of the computer, as would be known to one of ordinary skill in the art. The computer medium which may be used to hold or contain the computer program product, may be a fixture of the computer such as an embedded memory or may be on a transportable medium such as a disk, as would be known to one of ordinary skill in the art.

[0130] The invention is not limited to any particular computer program or logic or language, or instruction but may be practiced with any such suitable program, logic or language, or instructions as would be known to one of ordinary skill in the art. Without limiting the principles of the disclosed invention any such computing system can include, inter alia, at least a computer readable medium allowing a computer to read data, instructions, messages or message packets, and other computer readable information from the computer readable medium. The computer readable medium may include non-volatile memory, such as ROM, Flash memory, floppy disk, Disk drive memory, CD-ROM, and other permanent storage. Additionally, a computer readable medium may include, for example, volatile storage such as RAM, buffers, cache memory, and network circuits.

[0131] Furthermore, the computer readable medium may include computer readable information in a transitory state medium such as a network link and/or a network interface, including a wired network or a wireless network, that allow a computer to read such computer readable information.