Approaching the capacity of two-way gaussian relay channel with relay private messages

In this paper, we study a 3-node asymmetric full-duplex AWGN two-way relay channel with relay private messages where two nodes can communicate with each other only through a third node called the relay, while the relay can itself exchange private messages with two other nodes. Cut-set upper bound and single sided genie upper bound are presented for this channel. To obtain an achievable rate, we use a superposition of nested lattice codes and random Gaussian codes for encoding at the senders, and successive interference cancelation for decoding at the receivers. It is shown that capacities are achieved within constant gaps 2/3 and 2.5/3 bits/sec/Hz per user of single sided genie for restricted and non-restricted models, respectively.