An algorithm for calculating the exact bit error probability of a binary linear code over the binary symmetric channel

An efficient algorithm for calculating the ith bit error probability of a binary linear code over the binary symmetric channel (BSC) is presented. It is proved that the exact ith bit error probability of maximum-likelihood (ML) decoding, bounded distance decoding, and symbol-wise maximum a posteriori probability (MAP) decoding can be obtained with time complexity O(n2^n-k), where n and k denote the length and the dimension of the target code. The proposed methods are applicable to any binary linear code with redundancy up to nearly 25-30 bits with a typical personal computer.