  In this work we analyze the problem of linear correction of the reliability
metrics (L-values) in 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.
