Typical Random Coding Exponent for Finite-State Channels

Abstract

We derive a lower bound on the typical random-coding (TRC) exponent of pairwise-independent codeword ensembles used over a finite-state channel (FSC) at rates below capacity. Under some conditions, we also show that the probability of selecting a code from the ensemble with an error exponent larger than our lower bound tends to one as the codeword length tends to infinity. Our result, presented here for the FSC, also applies to compound channels.