Indirect Rate Distortion Functions with Side Information: Structural Properties and Multivariate Gaussian Sources

TL;DR

This paper investigates the properties of indirect rate distortion functions with side information, revealing conditions for their equivalence and providing explicit solutions for Gaussian sources using a novel realization theory approach.

Contribution

It introduces structural properties of RDFs with side information, shows when they coincide, and derives water-filling solutions for Gaussian sources with a new realization theory method.

Findings

Side information at both encoder and decoder does not reduce compression for Gaussian sources.

Structural properties of RDFs are established for general spaces.

Water-filling solutions are derived for multivariate Gaussian sources.

Abstract

In this paper, we analyze the indirect source coding problem with side information at both the encoder and decoder, as well as only at the decoder. We first derive structural properties of the two rate distortion functions (RDFs) for general abstract spaces and identify conditions under which the RDFs coincide. For multivariate jointly Gaussian random variables with square-error fidelity, we establish structural properties of the optimal test channels, show that side information at both the encoder and decoder does not reduce compression, and provide water-filling solutions using parallel Gaussian channel realizations. This paper uses a novel realization theory approach to establish achievability of the converse coding theorem lower bounds of the two RDFs.