Optimal linear correction of mismatched L-values in BICM receivers

In this work we analyze the problem of linear correction of the reliability metrics (L-values) in bit-interleaved coded modulation (BICM) receivers. We want to find the 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 the saddlepoint of the CGF. We provide a simple numerical example of transmission in the presence of interference where we demonstrate a notable improvement attainable with the proposed method. The proposed method is compared with the one based on the maximization of generalized mutual information.