Capacity of Network Coding for Wireless Multicasting

In this paper, the authors consider the network coding in networks with broadcast channels (called hypernetworks) as the first step for applying network coding to wireless networks. The authors first prove a max-flow min-cut theorem for such networks. While the authors propose an algorithm to achieve this bound, the authors introduce new definitions and provide sufficient tools to extend many of the theorems stated for flows in wireline networks to the case of hypernetworks. As an example, the authors extend the max-flow min-cut condition for feasibility of the point-to-point connection in wireline networks to the case of hypernetworks. Then, the authors extend the algebraic approach of Koetter and Medard, 2003 to the hypernetwork setup whereas we show how the results of recent works based on the model of [Koetter and Medard, 2003] (e. g. random linear coding), can be straightforwardly generalized to the case of the networks with broadcast channels.