Decoding strategies for physical-layer network coding over frequency selective channels

We 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. We study two approaches at the relay to decode the XOR of the transmitted codewords namely; a) an approximately optimal decoding scheme which is implemented using a list decoding algorithm, and b) 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 codewords and sorts them in the order of decreasing a-posteriori probabilities. From this list, estimates of the highly likely network coded sequences are obtained. Numerical examples show that a joint detector/physical-layer network coded sequence decoder (JD/PNCD) has a performance similar to the list decoding scheme and can be implemented with a lower complexity. The detection scheme based on the MMSE criterion is a suboptimal approach that generates soft information corresponding to the linear sum of the received symbols and is particularly useful in scenarios where the number of channel taps is large.