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IEEE International Symposium on Information Theory (ISIT)

Asymptotic error performance for reliability-based decoding of binary linear codes

M.P.C. Fossorier, Shu Hwa Lin

Published Nov 22, 2002• 0 citations
Publisher

Abstract

A new and unified method for evaluating the error-correcting radius and thus, the asymptotic error performance of many reliability-based decoding algorithms for binary linear codes is presented.
DOI
10.1109/isit.1997.613223

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This dissertation develops a set of new algorithms for soft decision decoding of binary linear block codes. The performance (i.e. the probability of error) of these algorithms is asymptotically optimum for high signal-to-noise ratio for binary linear block codes transmitted over the additive white gaussian (AWGN) channel using antipodal signalling. Among the algorithms proposed are the generalized Chase algorithms. In contrast to Chase algorithms, which require a {(d-1)/2} hard error-correcting decoder for decoding a binary linear block code of minimum distance d, the generalized Chase algorithms can use a binary decoder that can correct less than {(d-1)/2} hard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. Modified generalized Chase algorithm 2 and 3 are proposed for codes that have an overall parity check. These algorithms use fewer test patterns than the generalized Chase algorithms and they also have asymptotically optimum performance for high signal-to-noise ratio. The erasure information decoding algorithm of Tanaka and Kakigahara is generalized so that any hard decoder that corrects only up to t errors, 0 (LESSTHEQ) t (LESSTHEQ) {(d-1)/2} can be used to obtain asymptotically optimal performance for high signal-to-noise ratio. The modified erasure information decoding algorithm is proposed for codes that have an overall parity check. The modified erasure information decoding algorithm requires fewer test patterns than the erasure information decoding algorithm and its performance is also asymptotically optimum for high signal-to-noise ratio. The algorithms proposed by Dorsch and, Baumert and McEliece are analyzed to determine the conditions under which their performance would be asymptotically optimum for high signal-to-noise ratio. Simulation results for the (47,23) Quadratic Residue code are shown to demonstrate the performance of the algorithms. The results indicate that even for low signal-to-noise ratio the performance of a maximum likelihood decoder can be approached by a relatively simple decoding procedure.