  In this paper, we study a half-duplex two-way relay channel (TWRC) with
correlated sources exchanging bidirectional information. In the case, when both
sources have the knowledge of correlation statistics, a source compression with
physical-layer network coding (SCPNC) scheme is proposed to perform the
distributed compression at each source node. When only the relay has the
knowledge of correlation statistics, we propose a relay compression with
physical-layer network coding (RCPNC) scheme to compress the bidirectional
messages at the relay. The closed-form block error rate (BLER) expressions of
both schemes are derived and verified through simulations. It is shown that the
proposed schemes achieve considerable improvements in both error performance
and throughput compared with the conventional non-compression scheme in
correlated two-way relay networks (CTWRNs).
