Achievable Rates and Error Exponents for a Class of Mismatched Compound Channels

TL;DR

This paper analyzes the limits of mismatched decoding in channels close to a given metric, providing approximations for achievable rates and error exponents for both discrete and continuous systems, accounting for channel uncertainty.

Contribution

It introduces a method to approximate achievable rates and error exponents for mismatched channels within a relative entropy ball, extending analysis to various channel types and decoding metrics.

Findings

Derived approximations for worst-case achievable rates.

Quantified the impact of channel estimation errors.

Applied results to specific metrics like symmetric and modulo-additive noise.

Abstract

This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and continuous-alphabet channels, we derive approximations of the worst-case achievable information rates and error exponents as a function of the radius of a small relative entropy ball centered at the decoding metric, allowing the characterization of the loss incurred due to imperfect channel estimation. We provide a number of examples including symmetric metrics and modulo- additive noise metrics for discrete systems, and nearest neighbor decoding for continuous-alphabet channels, where we derive the approximation when the channel admits arbitrary statistics and when it is assumed noise-additive with unknown finite second-order moment.