On the capacity of non-coherent network coding

We consider the problem of multicasting information from a source to a set of receivers over a network where interme- diate network nodes perform randomized linear network coding operations on the source packets. We propose a channel model for the noncoherent network coding introduced by Koetter and Kschischang in [6], that captures the essence of such a network op- eration, and calculate the capacity as a function of network param- eters. We prove that use of subspace coding is optimal, and show that, in some cases, the capacity-achieving distribution uses sub- spaces of several dimensions, where the employed dimensions de- pend on the packet length. This model and the results also allow us to give guidelines on when subspace coding is beneficial for the pro- posed model and by how much, in comparison to a coding vector approach, from a capacity viewpoint. We extend our results to the case of multiple source multicast that creates a virtual multiple ac- cess channel.