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=nβ1 and MAIS=nβ2, prior work has shown that
binary (over F2β) 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=nβ3, 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=nβ3 and optimal broadcast rate strictly greater than MAIS