Index Coding Capacity: How far can one go with only Shannon Inequalities?

Understand

An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, no more than 2 interfering messages at any destination) of index coding problems where non-Shannon information inequalities are necessary for capacity characterization.

• In particular, this includes the first known example of a multiple unicast (one destination per message) index coding problem where non-Shannon information inequalities are shown to be necessary.
• The simplest multiple unicast example has 7 edges in the alignment graph and 11 messages.
• The simplest multiple groupcast (multiple destinations per message) example has 6 edges in the alignment graph, 6 messages, and 10 receivers.