Multicasting Multiple Correlated Sources to Multiple Sinks Over a Noisy Channel Network

The problem of network coding for multicasting a single source to multiple sinks has first been studied by Ahlswede, Cai, Li, and Yeung in 2000, in which they have established the celebrated max-flow min-cut theorem on nonphysical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with multiple correlated sources and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network. This paper presents an attempt to unify both cases, which leads to establish a necessary and sufficient condition for reliable transmission over a network for multicasting multiple correlated sources to multiple sinks. Here, the problem of separation of source coding and network coding is also discussed.