  We consider efficient communications over the multiple-input multiple-output
(MIMO) multiway distributed relay channel (MDRC) with full data exchange, where
each user, equipped with multiple antennas, broadcasts its message to all the
other users via the help of a number of distributive relays. We propose a
physical-layer network coding (PNC) based scheme involving linear precoding for
channel alignment nested lattice coding for PNC, and lattice-based precoding
for interference mitigation, We show that, with the proposed scheme,
distributed relaying achieves the same sum-rate as cooperative relaying in the
high SNR regime. We also show that the proposed scheme achieve the asymptotic
sum capacity of the MIMO MDRC within a constant gap at high SNR. Numerical
results demonstrate that the proposed scheme considerably outperforms the
existing schemes including decode-and-forward and amplify-and-forward.
