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arXiv · 1711.06487

Optimal Index Codes via a Duality between Index Coding and Network Coding

Ashok Choudhary·Vamsi Krishna Gummadi·Prasad Krishnan
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Abstract

In Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph $G$ (with number of vertices $n$ equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by $MAIS$ is a lower bound on the \textit{broadcast rate}. For IC problems with $MAIS=n-1$ and $MAIS=n-2$, prior work has shown that binary (over ${\mathbb F}_2$) linear index codes achieve the $MAIS$ lower bound for the broadcast rate and thus are optimal. In this work, we use the the duality relationship between NC and IC to show that for a class of IC problems with $MAIS=n-3$, binary linear index codes achieve the $MAIS$ lower bound on the broadcast rate. In contrast, it is known that there exists IC problems with $MAIS=n-3$ and optimal broadcast rate strictly greater than $MAIS$.

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Ashok Choudhary, Vamsi Krishna Gummadi, Prasad Krishnan. 2017-11-17. Optimal Index Codes via a Duality between Index Coding and Network Coding. https://arxiv.org/abs/1711.06487

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