Improved Channel Coding Performance Through Cost Variability

TL;DR

This paper demonstrates that allowing cost variability in channel coding for DMCs enhances performance, and feedback does not improve second-order rates under strict cost constraints, extending known results to new cost models.

Contribution

It introduces the impact of cost variability on coding performance and shows feedback's limited role under almost-sure cost constraints for DMCs.

Findings

Cost variability improves coding performance.

Feedback does not enhance second-order rates under strict cost constraints.

Results extend to various channel models like AWGN and parallel Gaussian channels.

Abstract

Channel coding for discrete memoryless channels (DMCs) with mean and variance cost constraints has been recently introduced. We show that there is an improvement in coding performance due to cost variability, both with and without feedback. We demonstrate this improvement over the traditional almost-sure (per-codeword) cost constraint that prohibits any cost variation above a fixed threshold. Our result simultaneously shows that feedback does not improve the second-order coding rate of simple-dispersion DMCs under the almost-sure cost constraint. This finding parallels similar results for unconstrained simple-dispersion DMCs, additive white Gaussian noise (AWGN) channels and parallel Gaussian channels.