Physical layer network coding is able to improve frequency utilization efficiency in bi-directional wireless communications via a relay. This paper proposes a novel error correction scheme for physical layer XOR network coding. The proposed scheme not only improves transmission performance but also to reduce complexity at the relay. The proposed scheme applies a unitary precoding to offset phase rotation in the channel by exploiting the reciprocity between channels in the uplink and the downlink in systems with time division duplex (TDD). Moreover, a novel complexity reduced maximum likelihood detection technique is applied in the proposed scheme. It is evaluated by computer simulation that the proposed scheme attains a gain of 8dB at BER=10-5 compared with AF network coding in a system with the use of OFDM.