On Soft-decoding of the (24,12,8) Extended Golay Code up to Six Errors

In this paper, a new soft-decision decoder of the (24, 12, 8) binary extended Golay code up to six errors is proposed. First, by using the error pattern obtained from hard decoder, the method of determining possible error patterns is developed. The emblematic probability value of each error pattern is then defined as the product of the individual bit-error probabilities corresponding to the locations of the possible error patterns. The most likely one among these error patterns is obtained by choosing the maximum of the emblematic probability values of possible error patterns. Finally, simulation results in additive white Gaussian noise (AWGN) show that this decoder reduce the decoding complexity although it performs a slight loss of coding gain than the modified Chase's II algorithm proposed by Hackett.