Network coding for the Multiple Access Relay channel using lattices

We consider the problem of two transmitters would like to communicate with a destination with the help of a half-duplex relay. In this work, we are presenting the advantages of using nested lattices for the AWGN channels. The sources map their messages using lattice code and then broadcast them to the relay and the destination. The relay receives two independent symbols at the same channel. The relay either combines the two symbols using lattice modulo and then decode or decode the two symbols separately also using modulo lattice, then forwards the new symbol to the destination. The destination tries to recover the two messages using different decoding strategies. One of the strategies is to recover two linear equations in function of the two received symbols with integer coefficients then, solve these equations to recover the two messages. The integer coefficients need to be optimally selected to reduce the noise at the receivers. The other strategy is to use successive decoding at the relay and the destination. This strategy outperforms the first when two integer coefficients are zero. The strategies are discussed and compared with the traditional DF (Decode and Forward). The simulation results show the advantages of using lattice codes and the improvement in rates for certain regimes.