LP Bounds for Rate-Distortion with Variable Side Information

TL;DR

This paper develops new linear programming-based upper and lower bounds for the rate-distortion problem with multiple decoders having variable side information, advancing the theoretical understanding of this complex problem.

Contribution

It introduces a novel linear program for upper bounds and a new lower bound inspired by index coding, covering general instances and subsuming previous bounds.

Findings

The bounds are tight for certain Gaussian analogues of index coding.

The lower bound generalizes most existing bounds in the literature.

The explicit characterization of the rate-distortion function for a specific problem.

Abstract

We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this problem, which takes the form of a linear program, by utilizing random binning and simultaneous decoding techniques and compare it with the existing bounds. We also provide a lower bound for the general problem, which was inspired by a linear-programming lower bound for index coding, and show that it subsumes most of the lower bounds in literature. Using these upper and lower bounds, we explicitly characterize the rate-distortion function of a problem that can be seen as a Gaussian analogue of the "odd-cycle" index coding problem.