Approaches to Network Coding for Multiple Unicasts

In this paper, we survey the application of linear network coding to a multiple unicasts scenario in directed graphs. We discuss related work concerning the complexity of the construction of capacity-achieving linear network codes. We briefly review the algebraic formulation of the problem and in the remainder of the paper, we investigate two approaches to construct network codes. One is based on state-space realizations and the other is a suboptimal, yet simpler approach based on linear optimization