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IEEE Transactions on Communications

On maximum likelihood soft decoding of some binary self-dual codes

Moshe Ran, Jakov Snyders

Published Mar 1, 1993• 13 citations
Publisher

Abstract

Efficient algorithms are derived for maximum likelihood (ML) soft-decision decoding of some binary self-dual codes. A family of easily decodable self-dual codes is derived by modifying a known F/sub 24/, which has a weight distribution resembling that of the (24, 12, 8) Golay code G/sub 24/. The ML decoding of F/sub 24/ is accomplished by only 227 real additions, compared to 651 required for G/sub 24/, yet the error rates of the two decoders are similar for moderate noise conditions.>

DOI
10.1109/26.221070

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Efficient algorithms are derived for maximum likelihood (ML) soft-decision decoding of some binary self-dual codes. A family of easily decodable self-dual codes is derived by modifying a known F/sub 24/, which has a weight distribution resembling that of the (24, 12, 8) Golay code G/sub 24/. The ML decoding of F/sub 24/ is accomplished by only 227 real additions, compared to 651 required for G/sub 24/, yet the error rates of the two decoders are similar for moderate noise conditions.>
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Maximum likelihood (ML) decoding is the optimal error-correction method but is NP-hard in general, implying that there would be no polynomial-time ML decoding algorithm that capable of decoding arbitrary linear codes. Consequently, researchers have developed a variety of ML decoding algorithms with different characteristics so that they can be used in a complementary manner. Although many modern codes such as Turbo, LDPC, and Polar codes, can be efficiently decoded without ML algorithms, there remains continual demand for developing new ML decoding algorithms and evaluating ML decoding performance in various contexts. In this study, we propose an ML decoding algorithm applicable to general non-binary linear codes, formulated as a generalization of the adaptive and recursive ML decoding algorithm previously developed for binary codes. The proposed algorithm is implemented and applied to Generalized Reed-Muller codes, and its computational complexity of soft-decision ML decoding is discussed and compared with the complexity of the Viterbi decoder, in terms of the number of addition-equivalent operations, to demonstrate the efficiency of the approach. The substantial reduction in decoding complexity enables us performing practical decoding simulation of some classes of Generalized Reed-Muller codes. This paper also shows numerical evaluation results of the error-correcting capabilities of the codes, providing insights into their performance under optimal decoding conditions.