Moderate-Deviations of Lossy Source Coding for Discrete and Gaussian Sources

TL;DR

This paper investigates the moderate-deviations regime in lossy source coding for discrete and Gaussian sources, establishing fundamental limits and highlighting the role of dispersion similar to central limit results.

Contribution

It extends the moderate-deviations analysis to lossy source coding, deriving fundamental limits and demonstrating the importance of dispersion in this setting.

Findings

Dispersion plays a key role in the moderate-deviations regime for lossy source coding.

Derived fundamental compression limits for sources with rates near the rate-distortion function.

Extended the moderate-deviations framework to both finite alphabet and Gaussian sources.

Abstract

We study the moderate-deviations (MD) setting for lossy source coding of stationary memoryless sources. More specifically, we derive fundamental compression limits of source codes whose rates are $R(D) \pm \epsilon_n$, where $R(D)$ is the rate-distortion function and $\epsilon_n$ is a sequence that dominates $\sqrt{1/n}$. This MD setting is complementary to the large-deviations and central limit settings and was studied by Altug and Wagner for the channel coding setting. We show, for finite alphabet and Gaussian sources, that as in the central limit-type results, the so-called dispersion for lossy source coding plays a fundamental role in the MD setting for the lossy source coding problem.