On the Capacity Region for Index Coding

TL;DR

This paper introduces a novel inner bound on the capacity region for general index coding problems using a random coding scheme, providing a simple polymatroidal expression and demonstrating its effectiveness on small problem instances.

Contribution

It presents a new inner bound based on random coding and optimal decoding, differing from traditional graph or algebraic bounds, with a simple single-letter expression.

Findings

Inner bound applicable to all index coding problems with up to five messages

Bound is derived from a random coding scheme with optimal decoding

Demonstrates capacity region for 9846 nonisomorphic small problems

Abstract

A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding, and has a simple polymatroidal single-letter expression. The utility of the inner bound is demonstrated by examples that include the capacity region for all index coding problems with up to five messages (there are 9846 nonisomorphic ones).