Lifetime Maximization in Wireless Ad Hoc Networks with Network Coding and Matrix Game

In this paper, we present a matrix game cross-layer optimization formulation to maximize the network lifetime in wireless ad hoc networks with network coding. To this end, we introduce a cross-layer formulation of general NUM ( Maximization) that accommodates routing, scheduling, and stream control from different layers in the coded networks. Specifically, develop a matrix game with the strategy sets of the players corresponding to hyperlinks and transmission modes, and design payoffs specific to the lifetime. Given that, our cross programming formulation can benefit from both game NUM-based approaches at the same time by cooperating the programming model for the matrix game with that for the other layers in a consistent framework. Finally, our numerical example demonstrates its performance results on a well butterfly network to verify the cross-layer optimization scheme. Keywords—Cross-layer design, Lifetime maximization, game, Network coding.