We consider the information exchange between two source nodes with the help of a relay node in a two-way relay network (TWRN). Based on physical-layer network coding (PNC), at the relay node, Viterbi or BCJR algorithms based on a full-state trellis can be used for decoding. Since the relay node only needs to decode XORed message rather than two individual messages in PNC, we show that the decoding can be performed using a reduced-state trellis which results in a lower complexity. It is proved that if the source nodes use identical encoders, based on the reduced-state trellis, the diversity order is kept unchanged, which is then confirmed by simulation results.
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