Network Coding for Unicast: Exploiting Multicast Subgraphs to Achieve Capacity in 2-User Networks

In this paper, we address optimal network coding schemes for two-user unicast networks. Using previous results on the relationship between graph structure and informationtheoretic capacity, we characterize the capacity region for a class of two-user unicast networks by finding a combination network coding/routing scheme to achieve an outer bound on capacity. This scheme has the remarkable property of decomposing the difficult unicast network coding problem into three sub-problems: a multicast network coding sub-problem, and two multi-commodity flow sub-problems. Using insights from the rate assignment scheme, we construct a distributed rate control algorithm based on optimization and dual theory that achieves capacity of the network. Formulating the unicast network coding problem in terms of optimization theory also allows us to implement a transport-type mechanism that provides systemwide performance objectives.