Correction of Mismatched L-values in BICM Receivers

In this work we analyze the problem of correction of the reliability metrics (L-values) in bit-interleaved coded modulation (BICM) receivers. First, we propose a method for finding the linear correction factors that minimize the probability of error of a maximum likelihood decoder that uses the corrected L-values. To this end, we use the efficient approximation of the pairwise error probability in the domain of the cumulant generating functions (CGF) of the L-values and conclude that the optimal correction factors are equal to the twice of value of the saddlepoint of the CGF. Next, a simple extension of the proposed method to the non-linear correction is presented. We provide numerical examples demonstrating improvements attainable with the proposed method comparing it to the competitive solutions.