Capacity of broadcast erasure networks using spatial network coding

We study the capacity of a multicast session in point-to-point erasure networks as well as interference-free broadcast erasure networks, under a class of network coding schemes referred to as spatial network coding. In this class of coding, nodes are prohibited from performing coding on successive data units of a link; only combining data units arriving on different incoming links is permitted. We prove that, for both point-to-point and broadcast networks, the capacity of a multicast session is equal to the minimum of the capacities of the constituent unicast sessions. The capacity of a unicast session is equal to the statistical mean of the minimum cut rate of the corresponding random graph, where the notions of graph model and minimum cut rate are extended to apply to broadcast networks.