The characterization of multi-source multicast with network coding

The capacity region of the single-source multicast network coding has an explicit Max-flow Min-cut representation. But for multi-source multicast networks the problem is still open. In this paper, we mainly discuss the case of independent encoding multi-source multicast network using inter-session network coding. We propose a multi-source independent encoding theorem for this problem which characterizes the admissible coding rate region of independent encoding for relevant multiple sources. The theorem is proposed by the paper according to the strongly typical sequences and random coding. We also point out the connections between our theorem and the general multi-source network coding problem, of which the results are computable and can be used to design the multi-source network coding algorithm.