A New Index Coding Scheme Exploiting Interlinked Cycles

TL;DR

This paper introduces the interlinked cycle cover scheme for index coding, which generalizes existing methods and achieves optimal codes for many directed graphs with linear encoding complexity.

Contribution

The paper proposes a novel interlinked cycle cover scheme that extends previous approaches and proves its optimality for a broad class of digraphs.

Findings

Provides an optimal index coding scheme for many digraphs

Generalizes clique and cycle cover schemes

Achieves linear encoding complexity

Abstract

We study the index coding problem in the unicast message setting, i.e., where each message is requested by one unique receiver. This problem can be modeled by a directed graph. We propose a new scheme called interlinked cycle cover, which exploits interlinked cycles in the directed graph, for designing index codes. This new scheme generalizes the existing clique cover and cycle cover schemes. We prove that for a class of infinitely many digraphs with messages of any length, interlinked cycle cover provides an optimal index code. Furthermore, the index code is linear with linear time encoding complexity.