Distribution of L-values in Gray-mapped M^2-QAM: Closed-form Approximations and Applications

In this paper we develop closed form approximations for the probability density function (PDF) of the reliability metrics (L-values) in bit-interleaved coded modulation (BICM). The expressions are valid for M^2-ary quadrature amplitude modulations (M^2-QAM) with Gray mapping when the metrics are calculated using the so-called max-log approximation. Based on the developed expressions, we also propose two simple Gaussian mixture approximations that are analytically tractable. We apply our developments to efficiently calculate the BICM channel capacity, and to develop bounds on the coded bit-error rate when a convolutional code is used. The coded performance of an hybrid automatic repeat request (HARQ) based on constellation rearrangement is also evaluated