Decode-forward and compute-forward coding schemes for the two-way relay channel

We consider the full-duplex two-way relay channel with direct link between two users and propose two coding schemes: a partial decode-forward scheme, and a combined decode-forward and compute-forward scheme. Both schemes use rate-splitting and superposition coding at each user and generate codewords for each node independently. When applied to the Gaussian channel, partial decode-forward can strictly increase the rate region over decode-forward, which is opposite to the one-way relay channel. The combined scheme uses superposition coding of both Gaussian and lattice codes to allow the relay to decode the Gaussian parts and compute the lattice parts. This scheme can also achieve new rates and outperform both decode-forward and compute-forward separately. These schemes are steps towards understanding the optimal coding.