1. Introduction. 2. Communication Theory Basics. 3. Trellis Coded Modulation. 4. Convolutional Codes. 5. Link to Block Codes. 6. Performance Bounds. 7. Decoding Strategies. 8. Factor Graphs. 9. Low-Density Parity Check Codes. 10. Parallel Concatenation (Turbo Codes). 11. Serial Concatenation. 12. Turbo Coded Modulation.

http://www.ece.ualberta.ca/~hcdc/Library/ErrorContrClass/Chap5new.pdf

Trellis and turbo coding

Sequential decoding is characterized as a sequential search for the shortest path through a trellis. An easily analyzed algorithm closely related to the stack and Fano algorithms is described. Martingale techniques are used to find the distribution of computation on totally symmetric channels. For general channels, our universal bounding technique yields the well-known Pareto distribution of computation, as well as a bound on error probability that is asymptotically optimum in the high-rate range. The performance-complexity relation is shown to be asymptotically Pareto for both sequential and maximum-likelihood (Viterbi) decoding, with the same exponent in either case. A semisequential list-of-L Viterbi algorithm is introduced to extend the analogies below Rcomp.

Convolutional codes III. Sequential decoding

Comparisons are made of a genie-aided sequential algorithm due to D. Haccoun and M.J. Ferguson (1975), the Viterbi algorithm, the M-algorithm, and the Fano algorithm for rate-1/2 and rate-2/3 trellis modulation codes on rectangular signal sets. The effects of signal-to-noise ratio and decoding-delay constraints on the choice of decoding algorithms for framed data are examined by computer simulation. Additionally, the genie-aided algorithm is used as a tool in estimating the asymptotic behavior of the M-algorithm. In general, the results conform closely to experience with convolutional codes due to the similar distance structure of the codes. The Fano algorithm produces good error performance with a low average number of computations when long decoding delay is permissible. The M-algorithm provides a savings in computation compared to the Viterbi algorithm if a small decoding delay is required. >

A comparison of reduced complexity decoding algorithms for trellis codes

One of the anomalies of coding theory has been that while block parity-check codes form the subject for the overwhelming majority of theoretical studies, convolutional codes have been used in the majority of practical applications of “error-correcting codes.” There are many reasons for this, not the least being the elegant algebraic characterizations that have been formulated for block codes. But while we may for aesthetic reasons prefer to speculate about linear block codes rather than convolutional codes, it seems to me that an information-theorist can no longer be inculpably ignorant of non-block codes. It is the purpose of these lectures to provide a reasonably complete and self-contained treatment of non-block codes for a reader having some general familiarity with block codes.

Error Bounds for Tree Codes, Trellis Codes, and Convolutional Codes with Encoding and Decoding Procedures

This article surveys many variants of sequential decoding in literature. Rather than introducing them chronologically, this article first presents the Algorithm A, a general sequential search algorithm. The stack algorithm and the Fano algorithm are then described in details. Next, trellis variants of sequential decoding, including the recently proposed maximum-likelihood sequential decoding algorithm, are discussed. Additionally, decoding complexity and error performance of sequential decoding are investigated, followed by a discussion on the implementation of sequential decoding from various practical aspects. Moreover, classes of convolutional codes that are particularly appropriate for sequential decoding are outlined.


Keywords:

coding;
decoding;
convolutional codes;
convolutional coding;
sequential decoding;
maximum-likelihood decoding

Sequential Decoding of Convolutional Codes

The results of comparison of the conventional Fano algorithm and a new stack algorithm proposed by Zigangirov and Jelinek, by computer simulation of two sequential decoding algorithms are reported. The results indicate that for rates near R comp the stack algorithm offers a considerable improvement in decoder speed over the Fano algorithm, provided that fairly large storage capacity is available for use by the decoder.

J. Geist

Papers

An Empirical Comparison of Two Sequential Decoding Algorithms