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A physical-layer network coded two-way relay system applying Low-Density Parity-Check (LDPC) codes for error correction is considered in this paper, where two sources A and B desire to exchange information with each other by the help of a relay R. The critical process in such a system is the calculation of the network-coded transmit word at the relay on basis of the superimposed channel-coded QPSK words of the two sources. For this joint channel-decoding and network-encoding task a generalized Sum-Product Algorithm (SPA) over F16 is developed. This novel iterative decoding approach outperforms other recently proposed schemes as demonstrated by simulations.
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