Wireless Multicasting Using Network Coding

In this paper, we consider the network coding in networks with broadcast channels (called hypernetworks) as the first step for applying network coding to wireless networks. We first prove a max-flow min-cut theorem for such networks. While we propose an algorithm to achieve this bound, we will 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, we will extend the max-flow min-cut condition for feasibility of the point-to-point connection in wireline networks to the case of hypernetworks. Then, we will extend the algebraic approach of Koetter and Medard in 2003, to the hypernetwork setup whereas we show how the results of recent works based on the model of R. Koetter et al., (2003), (e.g. random linear coding), can be straightforwardly generalized to the case of the networks with broadcast channels. Therefore, a complete set of results on using linear network coding in such networks will be provided