Data dissemination with side information and feedback

Index coding (IC), which can be regarded as a special class of network coding, deals with the problem of sending a number of packets to a group of receivers, each of which requests one packet and may have some other packets in its cache. This paper generalizes the IC problem in that both the packet requested by a receiver and the packets in its cache can be linear combinations of the packets. To minimize the number of transmissions required, a heuristic algorithm based on the idea of partitioning the users into coding groups is designed. To realize this idea, a polynomial time algorithm to determine whether a set of users form a coding group over the binary field or a field with a size larger than the number of users is constructed. For users that form a coding group, the corresponding encoding vector can be also found. A lower bound is derived in order to evaluate the performance of the heuristic algorithm. Numerical results show that the number of transmissions required by the heuristic algorithm and the lower bound both grow roughly linearly with the number of users, and the heuristic algorithm outperforms some benchmark algorithms.