Joint compute and forward for the two way relay channel with spatially coupled LDPC codes

We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We focus on reliable physical layer network coding as described in [1] 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.