The Gaussian two-way relay channel with wiretapper

Secrecy capacity is analyzed in a Gaussian two-way relay wiretap channel (TRWC), where two legitimate source nodes wish to exchange their messages through a relay in the presence of an eavesdropper. We assume that all intended nodes operate in full-duplex mode and there is no direct path between two sources. In the Gaussian TRWC, we propose an achievable coding scheme composed of superposed lattice codes with both structured and random codebooks. A jamming strategy is further introduced at the two sources as well as at the relay to maximize the achievable secrecy rate regions, where each node allocates part of its power to jam the eavesdropper. Our result indicates that positive achievable secrecy rates are maintained even for the reversely degraded scenario. In addition, assuming two sources with equal power constraint, it is shown that the scheme asymptotically achieves within 1/2 bit from the cut-set bound based on the channel with no secrecy constraints, as the downlink phase is in the high signal-to-noise ratio regime.