We study the capacity of a multicast session in an interference-free broadcast erasure network, under a 115%; TEXT-INDENT: 11.35pt; MARGIN: 0cm 0cm 0pt" In this thesis, first we prove that 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. Then we show that the capacity of a multicast session is equal to the minimum of the capacities of the constituent unicast sessions. Our approach is to first develop these results for a point-to-point erasure network. Then, we devise a kind of equivalence relationship between pairs of point-to-point and broadcast erasure networks (each coming with a specified network coding scheme). Using this equivalence relationship, we are able to extend the capacity results obtained for point-to-point networks to the more general case of interference-free broadcast erasure networks. In order to study the efficiency of spatial network coding, we evaluate the capacity of point-to-point and broadcast multi-layer erasure networks. We suppose that the network size goes to infinity such that the number of nodes in each layer increases faster than the number of layers. We prove that when the network size enlarges, the ratio of capacity under spatial network coding to the capacity under general network coding converges to one.
