A Rate-Distortion Approach to Index Coding

TL;DR

This paper models index coding as a rate-distortion problem with multiple receivers, providing bounds on the optimal coding rate using rate-distortion techniques, and demonstrating their tightness in certain cases.

Contribution

It introduces new bounds on index coding rates by leveraging rate-distortion methods, including a novel lower bound that matches upper bounds in specific scenarios.

Findings

Bounds coincide for all instances with up to three decoders

New lower bound improves understanding of index coding limits

Upper bounds derived from rate-distortion techniques are effective

Abstract

We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds and one lower bound on the optimal index coding rate. The upper bounds involve specific choices of the auxiliary random variables in the best existing scheme for the rate-distortion problem. The lower bound is based on a new lower bound for the general rate-distortion problem. The bounds are shown to coincide for a number of (groupcast) index coding instances, including all instances for which the number of decoders does not exceed three.