Polymatroids with Network Coding

Abstract--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 maxflow mini-cut theorem on non-physical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with correlated multiple 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 noisy network for multicasting all the correlated multiple sources to all the multiple sinks. Furthermore, we address also the problem of transmitting "independent" sources over a multiple-access-type of network as well as over a broadcast-type of network, which reveals that the (co...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Te Sun Han
• Keywords: CORR 2010, Education, Multiple Sinks, Reliable Transmission, Sufficient Condition