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 1 2 bit for arbitrary channel conditions. 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-touser links, so as to provide flexibility to fully exploit the channel randomness. Finally, judicious power allocation at the relay is necessary to approach the channel capacity under various channel conditions.
I. INTRODUCTIONTwo-way relaying (TWR), in which two users exchange information via a single relay, has attracted much research interest in the past decade. The transmission scheme over a two-way relay channel (TWRC) consists of two links. In the user-to-relay link, the two users transmit signals to the relay; in the relay-to-user link, the relay broadcasts signals to the users. The main idea, termed physical-layer network coding (PNC) [1], is to allow the relay to decode a linear function of incoming messages, and to allow each user to decode the message from the other user by exploiting the self-message. Compared with conventional relaying, PNC-aided two-way