A class of index coding problems with rate 1/3

TL;DR

This paper expands the class of index coding problems where a symmetric rate of 1/3 is achievable and provides a stricter necessary condition for this rate's feasibility.

Contribution

It introduces a larger class of index coding problems with rate 1/3 and refines the necessary conditions for rate feasibility.

Findings

A broader class of problems achieving rate 1/3

Stricter necessary conditions for rate 1/3 feasibility

Extension of previous characterizations

Abstract

An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\frac{1}{3}$ is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate $\frac{1}{3}$ is achievable. In the process, we also obtain a stricter necessary condition for rate $\frac{1}{3}$ feasibility than what is known in literature.