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IEEE Transactions on Communications

Chase-type and GMD coset decodings

M.P.C. Fossorier, Shu Lin

Published Mar 1, 2000• 31 citations
Publisher

Abstract

In this letter, Chase decoding algorithms are generalized into a family of bounded distance decoding algorithms, so that the conventional Chase algorithm-2 and Chase algorithm-3 become the two extremes of this family. Consequently, more flexibility in the tradeoffs between error performance and decoding complexity is provided by this generalization, especially for codes with large minimum distance. Finally this approach is extended to decoding with erasures.

DOI
10.1109/26.837034

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In this letter, Chase decoding algorithms are generalized into a family of bounded distance decoding algorithms, so that the conventional Chase algorithm-2 and Chase algorithm-3 become the two extremes of this family. Consequently, more flexibility in the tradeoffs between error performance and decoding complexity is provided by this generalization, especially for codes with large minimum distance. Finally this approach is extended to decoding with erasures.
A soft-decision decoder for an error-correcting block code of Hamming distance d is said to achieve bounded-distance (BD) decoding if its error-correction radius is equal to that of a complete Euclidean distance decoder. The Chase decoding algorithms are reliability-based algorithms achieving BD decoding. The least complex version of the original Chase algorithms ("Chase-3") uses about d/2 trials of a conventional binary decoder. In this paper, we propose two Chase-like decoding algorithms which also achieve BD decoding: a static method requiring about d/6 trials, and a dynamic method requiring only about d/12 trials. Hence, the complexity is reduced by factors of three and six, respectively, compared to the Chase-3 algorithm.
The generalized minimum distance (GMD) and Chase (1972) decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for binary linear block codes over an additive white Gaussian noise (AWGN) channel. We compute the limitation of the ratio between the probability of decoding error for the GMD or any one of the Chase decoding algorithms and that of the maximum-likelihood (ML) decoding when the signal-to-noise ratio (SNR) approaches infinity. If the minimum Hamming distance of the code is greater than 2, the limitation is shown to be equal to 1 and thus the GMD and Chase decoding algorithms are asymptotically optimum.