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We consider the full-duplex two-way relay channel with direct link betweentwo users and propose two coding schemes: a partial decode-forward scheme, anda combined decode-forward and compute-forward scheme. Both schemes userate-splitting and superposition coding at each user and generate codewords foreach node independently. When applied to the Gaussian channel, partialdecode-forward can strictly increase the rate region over decode-forward, whichis opposite to the one-way relay channel. The combined scheme usessuperposition coding of both Gaussian and lattice codes to allow the relay todecode the Gaussian parts and compute the lattice parts. This scheme can alsoachieve new rates and outperform both decode-forward and compute-forwardseparately. These schemes are steps towards understanding the optimal coding.

Decode-forward and Compute-forward Coding Schemes for the Two-Way Relay Channel