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Electronics Letters

Difference between two soft-decisiondecoding algorithms

Jan Nilsson

Published Sep 29, 1994• 1 citation
Publisher

Abstract

A relationship between two well-known soft-decision decoding algorithms is derived; the generalised minimum distance (GMD) algorithm and the Chase algorithm. The relation shows, in the case of soft-decision decoding of binary block codes, that the weakest third version of the Chase algorithm is more powerful than the GMD algorithm.
DOI
10.1049/el:19941169

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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.
A well known soft decoding algorithm that can make use of algebraic decoding techniques is the GMD algorithm introduced by Forney. This algorithm is based on several error-erasure decoding trails where unreliable positions are successively erased. Chase proposed a closely related family of algorithms for binary codes where unreliable positions are switched', i.e. different estimates for the positions are used in intermediate steps during the decoding process. In our algorithm, suitable for non binary codes, we try to combine erasures and switchings in a favourable way. A version of the algorithm comparable in complexity with the GMD algorithm is investigated. Simulations show that our algorithm in many cases has a somewhat better error correcting capability then the GMD algorithm.
Soft decision decoding of binary linear block codes transmitted over the additive white Gaussian channel (AWGN) using antipodal signaling is considered. A set of decoding algorithms called generalized Chase algorithms is proposed. In contrast to Chase algorithms, which require a\lfloor (d- 1)/2 \rfloorbinary error-correcting decoder for decoding a binary linear block code of minimum distanced, the generalized Chase algorithms can use a binary decoder that can correct less than\lfloor ( d - 1)/2 \rfloorhard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. The performance of all proposed algorithms is asymptotically optimum for high signal-to-noise ratio (SNR). Simulation results for the(47, 23)quadratic residue code indicate that even for low SNR the performance level of a maximum likelihood decoder can be approached by a relatively simple decoding procedure.
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.