  We consider the design and analysis of coding schemes for the binary input
two way relay channel with erasure noise. We are particularly interested in
reliable physical layer network coding in which the relay performs perfect
error correction prior to forwarding messages. The best known achievable rates
for this problem can be achieved through either decode and forward or compute
and forward relaying. We consider a decoding paradigm called joint compute and
forward which we numerically show can achieve the best of these rates with a
single encoder and decoder. This is accomplished by deriving the exact
performance of a message passing decoder based on joint compute and forward for
spatially coupled LDPC ensembles.
