Optimum threshold soft decision decoding of linear block codes in impulsive noise

The union and upper bounds of the probability of error P_e, for soft decision (unquantised) optimum threshold decoding of binary phase-shift keying (PSK) with the Golay (23,12) code are found. Even though soft decision decoding performs better, as expected than hard decision-bounded distance decoding, the difference in performance between the two decoding schemes decreases as the data sample size N becomes large, while the difference between the upper and union bounds remains almost constant. For example, for P_e approximately=10^-5 improvement greater than 3 dB can be achieved when going from N=100 to 400. This result is in direct contrast with the equivalent result in white Gaussian noise where a 2 dB difference exists between hard and soft-decision decoding for all coded digital communications.