| In this thesis, we investigate network coding from two novel viewpoints: (a) when communication resource allocation and network coding can be jointly designed, and (b) when nodes have the capability to broadcast messages.; When resource allocation and network coding can be jointly designed, it is not clear a priori whether the two tasks can be performed separately without loss of optimality. Lun et al. showed such a separation in the context of minimum cost multicast. In this thesis we show that the subproblem of resource allocation for minimum cost multicast can be optimally solved by a distributed algorithm. However, in the context of multiple unicast, a separation between coding and allocation has not been shown. In this thesis we specify two programs (a linear program and an integer program) that can be used to perform joint resource allocation and network coding. To the best of our knowledge, these programs are the first network coding schemes for multiple unicast in arbitrary networks.; With the aim of understanding network coding in wireless scenarios, we investigate multicasting in Aref networks. These networks do not capture interference, but they do incorporate deterministic broadcasting. We characterize the multicast capacity of Aref networks, the achievability of which is shown using an ensemble of random codes. In order to construct structured capacity achieving codes, we consider a natural layered coding scheme and show that this coding scheme is suboptimal. |
