| Summary: | In this paper, we investigate the problem associated with minimizing the total energy consumption used by all devices when recovering their missing packets. It is accomplished by applying network coding based on the selection of the transmission rates in a device-to-device network. First, this paper formulates the problem as an integer nonlinear programming optimization by means of constructing a graph model with a limiting parameter to control the number of edges and thereby confirms it as an NPC. Second, this paper investigates the relationship between the energy-saving benefit and the value of the limiting parameter and thereby indicates that the benefit is maximized when the limiting parameter equals 2. Furthermore, two coding algorithms based on the selection of the maximum-weighted clique are proposed. In detail, they are selecting the best clique in terms of the weight of the vertex (SBWV) algorithm and selecting the best clique in terms of the weight of the edge (SBWE) algorithm. The former consider selecting the maximum-weighted clique on the local NC graph which is based on the weight of vertex, while the latter consider selecting the maximum-weighted cliques of the global NC graph based on the weight of the edge. Finally, the simulation results show that both the SBWV and SBWE can significantly reduce the energy of transmission and average delay when compared with COPE, content-and loss-aware IDNC, as well as TS-MIS.
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