Constrained Source Coding with Side Information

TL;DR

This paper investigates the minimal rate for source coding with side information at the decoder, considering constraints on the encoder's ability to reconstruct the source within specified distortions, providing explicit formulas for discrete and Gaussian sources.

Contribution

It derives a new expression for the minimal description rate under distortion constraints when the encoder cannot access side information, extending to multiple distortion constraints and complex distortion functions.

Findings

Explicit rate-distortion formula for discrete sources with side information

Minimal rate computation for Gaussian sources with squared-error distortion

Generalization to multiple distortion constraints and complex distortion functions

Abstract

The source-coding problem with side information at the decoder is studied subject to a constraint that the encoder---to whom the side information is unavailable---be able to compute the decoder's reconstruction sequence to within some distortion. For discrete memoryless sources and finite single-letter distortion measures, an expression is given for the minimal description rate as a function of the joint law of the source and side information and of the allowed distortions at the encoder and at the decoder. The minimal description rate is also computed for a memoryless Gaussian source with squared-error distortion measures. A solution is also provided to a more general problem where there are more than two distortion constraints and each distortion function may be a function of three arguments: the source symbol, the encoder's reconstruction symbol, and the decoder's reconstruction symbol.