Efficient decoding of the (23, 12, 7) Golay code up to five errors

A novel and efficient algorithm for decoding the (23, 12, 7) Golay code with the five-error correcting capability is developed. Core to the key idea is innovatively utilizing the relationship of syndromes among error patterns, which is derived from the property of perfect code. Consequently, two methods of fast searching candidate codewords are proposed, both of which only perform the algebraic hard decision decoder once, rather than iterative decoding of Chase-like algorithm. With the set of the possible codewords, the most likely one is chosen as an output codeword based on the correlation metric. In comparison to Chase-2 algorithm, simulation results over the AWGN channel reveal the decoding times of the proposed algorithm equipped with codeword matching and syndrome-group search are reduced by 25% and 75%, respectively. In terms of the percentage of correct decoding, it turns out that the proposed algorithm outperforms Chase-2 algorithm, especially in the error-prone transmission environment. These favorable results demonstrate that the new algorithm is beneficial to implement in practice.