A Rate-Distortion Analysis for Composite Sources Under Subsource-Dependent Fidelity Criteria

TL;DR

This paper derives a rate-distortion function for composite sources with subsource-dependent fidelity criteria, analyzes the performance of classify-then-compress coding, and identifies conditions under which its performance loss is negligible.

Contribution

It introduces subsource-dependent fidelity criteria for composite sources, provides a single-letter rate-distortion expression, and analyzes the performance gap of classify-then-compress coding.

Findings

Single-letter rate-distortion function derived

Classify-then-compress coding often has performance loss

Performance loss is negligible under certain conditions

Abstract

A composite source, consisting of multiple subsources and a memoryless switch, outputs one symbol at a time from the subsource selected by the switch. If some data should be encoded more accurately than other data from an information source, the composite source model is suitable because in this model different distortion constraints can be put on the subsources. In this context, we propose subsource-dependent fidelity criteria for composite sources and use them to formulate a rate-distortion problem. We solve the problem and obtain a single-letter expression for the rate-distortion function. Further rate-distortion analysis characterizes the performance of classify-then-compress (CTC) coding, which is frequently used in practice when subsource-dependent fidelity criteria are considered. Our analysis shows that CTC coding generally has performance loss relative to optimal coding, even if the classification is perfect. We also identify the cause of the performance loss, that is, class labels have to be reproduced in CTC coding. Last but not least, we show that the performance loss is negligible for asymptotically small distortion if CTC coding is appropriately designed and some mild conditions are satisfied.