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In this paper, we consider physical-layer network coding (PNC) in a multi-unicast wireless cooperative network with a single relay. We aim to deal with the NC noise, i.e., an additional noise term due to applying NC, with the objective of improving the network data rate. Our approaches are based on relay power-allocation and group-allocation techniques. To this end, we provide a mathematical framework for the achievable information rate of the system with the notion of power assignment at the relay. Based on this framework, we present a novel power-allocation scheme to maximize the total information rate among all the source-destination communication sessions in the network. Further, we provide a closed-form solution for the two-unicast case. Simulation results show that the proposed relay power allocation can significantly help alleviate the adverse effects of NC noise. Next, we propose a group-allocation …