Evaluation of the Union Bound Using Characteristic Functions for Coded Transmission over Memoryless Channels

摘要

A procedure to evaluate exact union bound on the error decoding probability for a wide class of memoryless channel models is proposed. Namely, an exact expression for the pairwise error probability is used for the union bound instead of the conventional upper bound. To this end a new integral expression obtained using characteristic functions of the symbol log-likelihood ratios (LLR) is derived. The resulting integral expression for the union bound turns out to be very convenient for numerical calculation with excellent accuracy.