  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 $MAIS$.
