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  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.11   pp.2329-2340
Publication Date: 2000/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
linear block code,  sectionalization,  minimal sectionalized trellis,  generalized Viterbi algorithm,  computational complexity,  

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Summary: 
An algorithm for finding the optimal sectionalization for sectionalized trellises with respect to distinct optimality criterions was presented by Lafourcade and Vardy. In this paper, for linear block codes, we give a direct method for finding the optimal sectionalization when the optimality criterion is chosen as the total number |E| of the edges, the expansion index |E|-|V|+1, or the quantity 2|E|-|V|+1, only using the dimensions of the past and future sub-codes. A more concrete method for determining the optimal sectionalization is given for the Reed-Muller codes with the natural lexicographic coordinate ordering.