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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

The Optimal Sectionalized Trellises for the Generalized Version of Viterbi Algorithm of Linear Block Codes and Its Application to Reed-Muller Codes

Yuansheng Tang, Toru Fujiwara, Tadao Kasami

Published Nov 25, 2000• 1 citation
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Abstract A general framework, based on ideas of Tanner, for the description of codes and iterative decoding (“turbo coding”) is developed. Just like trellis‐based code descriptions are naturally matched to Viterbi decoding, code descriptions based on Tanner graphs (which may be viewed as generalized trellises) are naturally matched to iterative decoding. Two basic iterative decoding algorithms (which are versions of the algorithms of Berrou et al. and of Hagenauer, respectively) are shown to be natural generalizations of the forward‐backward algorithm (Bahl et al.) and the Viterbi algorithm, respectively, to arbitrary Tanner graphs. The careful derivation of these algorithms clarifies, in particular, which a priori probabilities are admissible and how they are properly dealt with. For cycle codes (a class of binary linear block codes), a complete characterization is given of the error patterns that are corrected by the generalized Viterbi algorithm after infinitely many iterations.