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

Abstract

ABSTRACTIn 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.