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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 scheme to assign sessions to different groups for performing PNC at the relay. We combine power allocation and group allocation to further improve performance. The formulated joint optimization problem is NP-hard. Therefore, a suboptimal heuristic algorithm is proposed and implemented at the relay to solve this problem. From the simulation results, the proposed joint group assignment and power-allocation scheme achieves up to 64% overall data rate gain for the multi-unicast system compared with a single-group system with no relay power assignment. This observation shows that PNC can be efficiently harnessed in a multi-unicast cooperative network by exploiting proposed approaches.