  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-to-user 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.
