Soft-decoding of the (23, 12, 7) Binary Golay Code

binary Golay code is a perfect code, a weight-4 error occurred is always decoded as a weight-3 error pattern by a hard decoding method. In this paper, an efficient soft-decision decoder of the (23, 12, 7) binary Golay code up to the 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 error pattern of weight-4 or weight-3 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 93% and 99% of weight-4 error patterns occurred are corrected if a bit-energy to noise-spectral-density ratios (E b /N 0) are greater than 3 dB and 6 dB, respectively, and at least 96% of weight-3 error patterns occurred are corrected for any dB.