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On Branch Labels of Parallel Components of the LSection Minimal Trellis Diagrams for Binary Linear Block Codes
Tadao KASAMI Toru FUJIWARA Yoshihisa DESAKI Shu LIN
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E77A
No.6
pp.10581068 Publication Date: 1994/06/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Information Theory and Coding Theory Keyword: linear block codes, trellis diagram, parallel structure and ReedMuller codes,
Full Text: PDF(867KB)>>
Summary:
In an earlier paper, we have shown that each section of the Lsection 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 2^{i}section minimal trellis diagram for a ReedMuller code is analyzed. Complexity measures of softdecision maximum likelihood decoding for binary linear block codes are also discussed.

