Moderate Deviations in Channel Coding

TL;DR

This paper investigates the decay rate of error probabilities in channel coding as block length increases, establishing a moderate deviation principle across a range of convergence speeds near channel capacity.

Contribution

It introduces a moderate deviation principle for block codes approaching channel capacity, bridging large deviation and central limit theorem regimes.

Findings

Moderate deviation principle holds for all convergence rates between large deviation and CLT regimes.

Error probability decay rates are characterized for codes near channel capacity.

Results unify different asymptotic regimes in channel coding error analysis.

Abstract

We consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. We prove that a moderate deviation principle holds for all convergence rates between the large deviation and the central limit theorem regimes.