Pseudo Exclusive-OR for LDPC Coded Two-Way Relay Block Fading Channels

We present a novel adaptive physical layer network coding (PLNC) at the relay, called pseudo exclusive-or (PXOR), for LDPC coded two-way relay (TWR) block fading channels. Based on the pairwise check decoding (PCD), the check relationship table generated by the proposed PXOR mapping obtains the same Hamming distances of the PLNC mapped codewords as that of conventional XOR mapping. In the meantime, the PXOR mapping optimizes the Euclidean distances by adjusting the symbol distances dynamically as far as possible in order to compensate the amplitude fading and phase deviation of the TWR block fading channels. For the system end-to-end error probability, simulation results show that the proposed coded PXOR considerably outperforms the coded conventional XOR and achieves the same performance as the complicated coded CNC for considered two TWR block fading channels.