  The physical-layer network coding (PNC) approach provides improved
performance in many scenarios over "traditional" relaying techniques or network
coding. This work addresses the generalization of PNC to wireless scenarios
where network nodes have multiple antennas. We use a recent matrix
decomposition, which allows, by linear pre- and post-processing, to
simultaneously transform both channel matrices to triangular forms, where the
diagonal entries, corresponding to both channels, are equal. This
decomposition, in conjunction with precoding, allows to convert any two-input
multiple-access channel (MAC) into parallel MACs, over which single-antenna PNC
may be used. The technique is demonstrated using the two-way relay channel with
multiple antennas. For this case it is shown that, in the high signal-to-noise
regime, the scheme approaches the cut-set bound, thus establishing the
asymptotic network capacity.
