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In Index Coding, the goal is to use a broadcast channel as efficiently aspossible to communicate information from a source to multiple receivers whichcan possess some of the information symbols at the source as side-information.In this work, we present a duality relationship between index coding (IC) andmultiple-unicast network coding (NC). It is known that the IC problem can berepresented using a side-information graph $G$ (with number of vertices $n$equal to the number of source symbols). The size of the maximum acyclic inducedsubgraph, 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 thatbinary (over ${\mathbb F}_2$) linear index codes achieve the $MAIS$ lower boundfor the broadcast rate and thus are optimal. In this work, we use the theduality relationship between NC and IC to show that for a class of IC problemswith $MAIS=n-3$, binary linear index codes achieve the $MAIS$ lower bound onthe broadcast rate. In contrast, it is known that there exists IC problems with$MAIS=n-3$ and optimal broadcast rate strictly greater than $MAIS$.

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