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The authors investigate different decoding strategies at the relay over a frequency selective two-way relay channel with Physical-layer Network Coding (PNC). The incorporation of the PNC scheme enables two users exchange information via a relay in two transmission phases. They study two approaches at the relay to decode the XOR of the transmitted code-words namely; an approximately optimal decoding scheme which is implemented using a list decoding algorithm, and a Minimum Mean Square Error (MMSE) based detector followed by a PNC decoder. The list decoding scheme selects L most likely pairs of sequences corresponding to the transmitted code-words and sorts them in the order of decreasing a-posteriori probabilities.
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