This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within$\frac{1}{ 2}$bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions.

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that our scheme can achieve the capacity of the two-pair TWRC to within 1/2 bit per user. In the proof, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. Further, we present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide more flexibility to fully exploit the channel randomness. We also show that judicious power allocation among the superimposed codeword components at the relay is needed to approach the channel capacity.