Approximate capacity region of the two-pair bidirectional Gaussian relay network

We study the capacity of the Gaussian two-pair fullduplex directional (or two-way) relay network with a single-relay supporting the communication of the pairs. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We propose a novel transmission technique which is based on a specific superposition of lattice codes and random Gaussian codes at the source nodes. The relay attempts to decode the Gaussian codewords and the superposition of the lattice codewords of each pair. Then it forwards this information to all users. We analyze the achievable rate of this scheme and show that for all channel gains it achieves to within 2 bits/sec/Hz per user of the cut-set upper bound on the capacity region of the two-pair bidirectional relay network.