A New Index Coding Scheme Exploiting Interlinked Cycles
Chandra Thapa, Lawrence Ong, Sarah J. Johnson

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.
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