On soft-decoding of the (24, 12, 8) Golay code

In this paper, an efficient soft-decision decoder of the (24, 12, 8) binary Golay code for the four errors, composed of two stages: a conventional hard decoder up to three errors and the soft decoding for four errors, is proposed. All probable patterns of occurred weight-4 error, which are always decoded to the same weight-3 error pattern, are determined from the look-up table of weight-7 codewords. And the most possible one will be obtained by estimating the emblematic probability values of all probable patterns. The simulation result of this decoder in additive white Gaussian noise (AWGN) shows that at least 92% and 99% of weight-4 error patterns occurred are corrected if a bit-energy to noise-spectral-density ratios (E_b/N₀) are greater than 2 dB and 5 dB, respectively.