Broadcasting with coded side information

In the original index coding problem, each user has a set of uncoded packets as side information, and wants to decode some other packets from the source node. The source node aims at satisfying the demands of all users as quickly as possible. With linear network coding, this is accomplished by broadcasting linear combinations of the source packets over some finite field. Since the broadcast is performed over a wireless channel, a user may overhear some coded packets that are not intended to him/her. This motivates a generalization of the index coding problem to the case where linearly coded packets are used as side information. We show that this generalized linear index coding problem is equivalent to solving a system of multi-variable polynomial equations. A heuristic solution is constructed and is applied to the broadcast relay channel.