Bidirectional Syndrome Decoding for Binary Rate (n-1)/n Convolutional Codes

Masato TAJIMA  Keiji TAKIDA  Zenshiro KAWASAKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A   No.3   pp.510-513
Publication Date: 1998/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory and Coding Theory
bidirectional decoding,  syndrome decoding,  syndrome former,  convolutional code,  reciprocal dual code,  

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The structure of bidirectional syndrome decoding for binary rate (n-1)/n convolutional codes is investigated. It is shown that for backward decoding based on the trellis of a syndrome former HT, the syndrome sequence must be generated in time-reversed order using an extra syndrome former H*T, where H* is a generator matrix of the reciprocal dual code of the original code. It is also shown that if the syndrome bits are generated once and only once using HT and H*T, then the corresponding two error sequences have the intersection of n error symbols, where is the memory length of HT.