On the achievable rate-regions for the Gaussian two-way diamond channel

In this paper,we study rate region of a gaussian two-way diamond channel which operates in half- duplex mode. in the channel that we consider in this paper,two transceiver (tr) nodes exchange their messages with the cooperation of two relay nodes. we consider a special case of the gaussian two-way diamond channels which is called compute-and-forward multiple access channel (cf-mac). in the cf-mac,the tr nodes transmit their messages to the relay nodes which are followed by a simultaneous communication from the relay nodes to the trs. adopting rate splitting method in the terminal encoders and then using compute-and-forward (cf) relaying and decoding the sum of messages at the relay nodes,an achievable rate region for this channel is obtained. to this end,we use a superposition coding based on lattice codes. using numerical results,we show that our proposed scheme outperforms the other similar methods and achieves a tighter gap to the outer bound.