The Rate-Distortion Function for Product of Two Sources with Side-Information at Decoders

TL;DR

This paper derives the rate-distortion function for a source coding problem involving the product of two correlated sources with side-information at decoders, revealing how degradation order affects the function.

Contribution

It provides the first explicit characterization of the rate-distortion function for product sources with degraded components and analyzes the impact of degradation order.

Findings

Rate-distortion function equals sum of component functions when degradation orders match.

Rate-distortion function is smaller when degradation orders are mismatched.

Explicit evaluations for binary Hamming and Gaussian sources.

Abstract

This paper investigates a lossy source coding problem in which two decoders can access their side-information respectively. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case such that each component is degraded. We show the rate-distortion function for that case, and give the following observations. When the components are degraded in matched order, the rate distortion function of the product sources is equal to the sum of the component-wise rate distortion functions. On the otherhand, the former is strictly smaller than the latter when the component sources are degraded in mismatched order. The converse proof for the mismatched case is motivated by the enhancement technique used for broadcast channels. For binary Hamming and Gaussian examples, we evaluate the rate-distortion functions.