  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. Furthermore, when the side information is linear, we
show that the 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
