Moderate deviation analysis of channel coding: Discrete memoryless case

Abstract

Moderate deviation behavior of coding for discrete-memoryless channels is investigated. That is, we consider block codes whose rate converges to the channel capacity from below with increasing block length with a certain rate and examine the best ‘sub-exponential’ decay in the maximal probability of error. We prove that a moderate deviation principle (M.D.P.) holds for all convergence rates between the large deviation and the central limit theorem regimes, under some mild assumptions on the channel. The rate function of the M.D.P. is explicitly characterized.