Lattice-based coding scheme for MIMO bi-directional relaying with three nodes

This paper proposes a general method for bi-directional relaying with three nodes over four time intervals, composed of alternate MAC phases and broadcast phases. Different nodes transmit in MAC phases, and the data stored in broadcast phases allows decoding of all information. The physical layer network coding strategy for this relaying protocol is a lattice-based coding scheme combined with power control, so that the relay receives an integer linear combination of the nodes codewords. This strategy is analyzed for MIMO with 2 receive and transmit antennas. Analytical expressions of the exchange rate and transmit powers under high SNR approximation are provided, and numerically validated with respect to the general SNR mode. The proposed method is then compared with Amplify-and-Forward. It is shown that lattice-based coding provides a gain of 4.5 dB in average SNR on the achievable exchange rate, and is totally fair, contrary to Amplify-and-Forward.