Advanced physical layer techniques for wireless mesh networks with network coding

We consider wireless mesh networks where information is multicasted to multiple terminals in a multi-hop fashion. Due to their strong interdependence, we seek a joint optimization of network and physical layer that are coupled by the per link flow constraint. A common approach is to dualize this constraint and decompose the dual problem into a layered structure; routing at the network layer and rate assignment at the physical layer. For the network layer subproblem, linear network coding is an optimal routing strategy and the solution can be computed by solving a linear or convex program. The physical layer subproblem turns out to be more challenging, due to the nature of the wireless medium and the resulting diminishing effect of multiple access interference. Existing approaches try to avoid interference by full orthogonalization of the channels or building on the concept of conflict graphs. Contrary to these approaches, we are taking into account interference management, for example by exploiting the advanced abilities of multiple antenna systems. Our approach is the factorization of the achievable edge rate region into known rate regions of subgraphs, called Elementary Capacity Graphs (ECGs), which allows for taking into account the half duplex constraint implicitly. The parametrization of the achievable rate region of an ECG depends on the transmission technique used and is in general nonconvex. We demonstrate how the nonconvexity of the physical layer parametrization can be handled within a primal-dual framework without loss of optimality. As our solution is optimal for a given factorization we show by numerically simulations the advances compared to non-optimal schemes.