Decoder error probability of binary linear block codes and its application to binary primitive BCH codes

McEliece and Swanson offered an upper bound on the decoder error probability of Reed-Solomon codes. In this paper, we investigate the decoder error probability of binary linear block codes and verify its properties, and apply it to binary primitive BCH codes. It is shown that the decoder error probability of an (n, k, t) binary linear block code is determined by P-E (=(2(k) - 2) (s=0)Sigma(t)((n)(s))/(2(n) - 2(s=0)Sigma(t)((n)(s)))) uniquely if is a constant. We derive the decoder error probability of (n, k, t) binary primitive BCH codes with n=2(m)-1 and 2t-1 < 2[(m/2)] + 1 and show that the decoder error probabilities of those codes are close to P-E if codelength is large and coderate is high. We also compute and analyze the decoder error probabilities of some binary primitive BCH codes.