An analytical method for performance analysis of binary linear block codes

An analytical method for performance evaluation of binary linear block codes using an additive white Gaussian noise (AWGN) channel model with binary phase shift keying (BPSK) modulation is presented. We focus on the probability distribution function (pdf) of the bit log-likelihood ratio (LLR) which is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit LLR. We introduce an analytical method for calculating these moments. It is shown that the estimate of the bit error probability provided by the proposed method will asymptotically converge to the true bit error performance.