In this paper,a network scenario of two-way relaying over orthogonal frequency division multiplexing(OFDM) is considered,in which two nodes intend to exchange the information via a relay using physical-layer network coding(PLNC).Assuming that the full channel knowledge is available,an optimization problem,which maximizes the achievable sum rate under a sum-power constraint,is investigated.It is shown that the optimization problem is non-convex,which is difficult to find the global optimum solution in terms of the computational complexity.In consequence,a low-complexity optimal power allocation scheme is proposed for practice implementation.A link capacity diagram is first employed for power allocation on each subcarrier.Subsequently,an equivalent relaxed optimization problem and Karush-Kuhn-Tucker(KKT) conditions are developed for power allocation among each subcarrier.Simulation results demonstrate that the substantial capacity gains are achieved by implementing the proposed schemes efficiently with a low-complexity computational effort. In this paper, a network scenario of two-way relaying over orthogonal frequency division multiplexing (OFDM) is considered, in which two nodes intend to exchange the information via a relay using physical-layer network coding (PLNC) .Assuming that the full channel knowledge is available, an optimization problem, which maximizes the achievable sum rate under a sum-power constraint, is investigated. It is shown that the optimization problem is non-convex, which is difficult to find the global optimum solution in terms of the computational complexity.In consequence, a low-complexity optimal power allocation scheme is proposed for practice implementation. A link capacity diagram is first employed for power allocation on each subcarrier. Subulations, an equivalent relaxed optimization problem and Karush-Kuhn-Tucker (KKT) conditions are developed for power allocation among each subcarrier.Simulation results demonstrate that the substantial capacity gains are achieved by implementing the proposed schemes e fficiently with a low-complexity computational effort.