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In this paper, we consider the two-way relay channel with the two-phase protocol. In the first phase, two terminals simultaneously transmit their packets to the relay, creating a multiple-access channel (MAC), while in the second phase the relay sends a network-coded combination of the two packets to both terminals. We focus on the multiple-access phase and propose a practical decoding scheme based on practical binary block codes in order to obtain the combined packet at the relay. This scheme is found to perform well for a wide range of code rates and is superior to lattice coding at low rates.