Vector Gaussian Rate-Distortion with Variable Side Information

TL;DR

This paper investigates the rate-distortion problem with two Gaussian decoders having different side information, providing bounds and solutions when the usual degradedness condition is not met.

Contribution

It introduces a hierarchy of four lower bounds for the Gaussian vector case and determines the optimal rate for various instance classes.

Findings

Four lower bounds on the optimal rate are proposed.

Optimal rates are characterized for several classes of Gaussian vector instances.

The work extends understanding beyond the degradedness condition.

Abstract

We consider rate-distortion with two decoders, each with distinct side information. This problem is well understood when the side information at the decoders satisfies a certain degradedness condition. We consider cases in which this degradedness condition is violated but the source and the side information consist of jointly Gaussian vectors. We provide a hierarchy of four lower bounds on the optimal rate. These bounds are then used to determine the optimal rate for several classes of instances.