Scheduling and network coding in wireless multicast networks: A case for unequal time shares

In this paper, we investigate the problem of network coding and media scheduling in wireless multihop networks. Unique characteristics of the wireless media, such as omnidirectional transmissions and destructive interference, as well as having one transceiver per wireless node, imply new code design constraints for wireless networks. Here, we formulate a linear program to solve the joint scheduling and network coding problem. Using our formulation, we demonstrate that for a large percentage of randomly generated wireless networks, the optimal scheduling time shares are unequal. All the existing network code design algorithms are based on equal scheduling time shares or the considered joint optimization problems do not have sufficient information for scheduling flows during unequal time shares. Therefore, we provide these statistics to emphasize the importance of enabling the code design algorithms to include unequal time shares. Our simulations further show that the network throughput can be significantly improved if the network code is properly designed to incorporate unequal time shares.