Scheduling for Network-Coded Multicast

We consider multicasting using random linear network coding over a multihop wireless network in the bandwidth limited regime. We address the associated medium access problem and propose a scheduling technique that activates hyperarcs rather than links, as in classical scheduling approaches. We encapsulate the constraints on valid network configurations in a conflict graph model and formulate a joint optimization problem taking into account both the network coding subgraph and the schedule. Next, using Lagrangian relaxation, we decompose the overall problem into two subproblems, a multiple-shortest-paths problem and a maximum weighted stable set (MWSS) problem. We show that if we use a greedy heuristic for the MWSS part of the problem, the overall algorithm is completely distributed. We provide extensive simulation results for both the centralized optimal and the decentralized algorithms. The optimal algorithm improves performance by up to a factor of two over widely used techniques such as orthogonal or two-hop-constrained scheduling. The decentralized algorithm is shown to buy its distributed operation with some throughput losses. Experimental results on randomly generated networks suggest that these losses are not large. Finally, we study the power consumption of our scheme and quantify the tradeoff between power and bandwidth efficiency.