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This paper studies joint scheduling and network coding in wireless multicast networks with independent sources. Designing a network coding solution for wireless networks involves scheduling interference-free transmissions and optimizing a performance measure for the predetermined scheduling sets, followed by constructing network codes for the specific solution. In such a design process, the results of prior steps need to provide enough information to the subsequent steps. In this paper, we formulate a linear optimization problem whose results can be used to design a coding solution. We build our work on previous works and present statistics that show the importance of incorporating unequal timeshares in designing network codes. In particular, our statistics show a throughput improvement of about 35% in maximum flow problems and energy savings between 13% and 30%, depending on the network size, in minimum energy problems. We also present the requirements of code construction algorithms for wireless networks that capture the broadcast property of these networks and can design proper codes when timeshares are unequal. In particular, the adaptation of a centralized network coding scheme for wireless networks is discussed. Overall, the work reported here provides a three-step solution to derive network codes that optimize a performance criterion of interest while also solving the scheduling problem in multihop wireless networks. [ABSTRACT FROM PUBLISHER]

In this paper, we present matrix game-theoretic models for joint routing, network coding, and scheduling problems. First, routing and network coding are modeled by using a new approach based on a compressed topology matrix that takes into account the inherent multicast gain of the network. Scheduling is optimized by a new approach called network graph soft coloring. Soft graph coloring is designed by switching between different components of a wireless network graph, which we refer to as graph fractals, with appropriate usage rates. The network components, which are represented by graph fractals, are a new paradigm in network graph partitioning that enables modeling of the network optimization problem by using the matrix game framework. In the proposed game, which is a nonlinear cubic game, the strategy sets of the players are links, paths, and network components. The outputs of this game model are mixed strategy vectors of the second and third players at equilibrium. The strategy vector of the second player specifies the optimum multipath routing and network coding solution, whereas the mixed strategy vector of the third player indicates the optimum switching rate among different network components or membership probabilities for an optimal soft-scheduling approach. Optimum throughput is the value of the proposed nonlinear cubic game at equilibrium. The proposed nonlinear cubic game is solved by extending a fictitious playing method. Numerical and simulation results prove the superior performance of the proposed techniques compared with the conventional schemes using hard graph coloring. [ABSTRACT FROM PUBLISHER]