Multiuser broadcast erasure channel with feedback and side information, and related index coding results

In this paper we consider the N-user broadcast erasure channel with public feedback and side information. Before the beginning of transmission, each receiver knows a function of the messages of some of the other receivers. This situation arises naturally in wireless and in particular cognitive networks where a node may overhear transmitted messages destined to other nodes before transmission over a given broadcast channel begins. We provide an upper bound to the capacity region of this system. When the side information is linear, this bound is tight for the case of two-user broadcast channels. The special case where each user knows the whole or nothing of the message of each other node, constitutes a generalization of the index coding problem. For this instance, and when there are no channel errors, we show that the bound reduces to the known Maximum Weighted Acyclic Induced Subgraph bound. We also show how to convert the capacity upper bound to transmission completion rate (broadcast rate) lower bound and provide examples of codes for certain information graphs for which the bound is either achieved of closely approximated.