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A decode-and-forward two-way relay system benefits from orthogonal frequency division multiplexing (OFDM) and relay transmission. In this paper, we consider a decode-and-forward two-way relay system over OFDM with two strategies: A joint subcarrier matching algorithm and a power allocation algorithm operating with a total power constraint for all subcarriers. The two strategies are studied based on average capacity using numerical analysis by uniformly allocating power constraints for each subcarrier matching group. An optimal subcarrier matching algorithm is proposed to match subcarriers in order of channel power gain for both transmission sides. Power allocation is defined based on equally distributing the capacity of each hop in each matching group. Afterward, a modified water-filling algorithm is also considered to allocate the power among all matching groups in order to increase the overall capacity of the network. Finally, Monte Carlo simulations are completed to confirm the numerical results and show the advantages of the joint subcarrier matching, power allocation and water filling algorithms, respectively.