Capacity of the Gaussian Two-way Relay Channel to within 1/2 Bit

In this paper, a Gaussian two-way relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in full-duplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. We show that the scheme achieves within 1/2 bit from the cut-set bound for all channel parameters and becomes asymptotically optimal as the signal to noise ratios increase.