On Branch Labels of Parallel Components of the L-Section Minimal Trellis Diagrams for Binary Linear Block Codes

Tadao KASAMI  Toru FUJIWARA  Yoshihisa DESAKI  Shu LIN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.6   pp.1058-1068
Publication Date: 1994/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory and Coding Theory
linear block codes,  trellis diagram,  parallel structure and Reed-Muller codes,  

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In an earlier paper, we have shown that each section of the L-section minimal trellis diagram for a linear block code consists of parallel and structurally identical (except branch labels) subgraphs without cross connections. These parallel subgraphs are called parallel components of the section. In this paper, it is shown that if the sets of path label sequences of two parallel components have a common sequence, then the parallel components have the same branch labels, and the number of parallel components with the same branch labels in each section and the detail structure of each parallel component up to its branch labels are analyzed and expressed in terms of the dimensions of specific linear codes related to the given code. As an example, the 2i-section minimal trellis diagram for a Reed-Muller code is analyzed. Complexity measures of soft-decision maximum likelihood decoding for binary linear block codes are also discussed.