First-order asymptotics of the BICM mutual information: Uniform vs. nonuniform distributions

Alinear, invertible transformis defined between two vectors or matrices as a tool for analyzing the bit-interleaved coded modulation (BICM) mutual information in the wideband regime. The transform coefficients depend on a set of real values, which can be interpreted as probabilities. The transform relates any BICM system with a nonuniform input distribution to another BICM system with a uniform distribution. Numerical evidence suggests that the two systems have the same first-order behavior, which would make possible to analyze nonuniform BICM systems based on known properties of uniform BICM systems.