Distributed optimization for wireless networks with inter-session network coding

Network coding has been applied widely in wireless networks. In this paper, we focus on the cross-layer optimization of wireless networks with multiple unicast sessions and network coding. By exploiting broadcast advantage and one hop opportunistic listening, we develop a fully distributed solution including primal-dual flow control, Markov chain based hyperlink scheduling, session-decomposition coding scheme and session scheduling. We further study the convergence property of the distributed solution without time-scale separation assumption. We show the convergence to optimum with some time-dependent step sizes and update intervals. We also show the convergence to the bounded neighborhood of optimum with constant step sizes and constant update intervals. Our numerical evaluations validate the analytical results. We emphasis that though the analysis for both cases is quite involved, the resulting distributed solutions are actually simple to implement.