Fast decoding of the (23, 12, 7) Golay code with four-error-correcting capability

Abstract

In this paper, a fast and efficient decoding algorithm for correcting the (23, 12, 7) Golay code up to four errors is presented. The aim of this paper is to develop a fast syndrome-group search method for finding the candidate codewords by utilizing the property that the syndromes of the weight-4 error patterns are identical to that of the weight-3 error pattern. When the set of the candidate codewords is constructed, the most likely one is determined by assessing the corresponding correlation metrics. The well-known Chase-II decoder, which needs to perform the hard-decision decoder multiple times, acts as a comparison basis. Simulation results over the additive white Gaussian noise channel show that the decoding complexity of the proposed method is averagely reduced by at least 86% in terms of the decoding time. Furthermore, the successful decoding percentage of the new decoder in the case of four errors is always superior to Chase-II decoder. At the signal-to-noise ratio of 0 dB, the proposed algorithm still can correct up to 97.40% weight-4 error patterns. The overall bit error rate performance of the proposed decoder is close to that of Chase-II decoder. It implies that the new decoder is beneficial to the practical implementation. Copyright © 2011 John Wiley & Sons, Ltd.