Network Coding for Two-Way Relay Channels using Lattices

In this paper, we propose a network coding using a lattice for the two-way relay channel with two nodes communicating bidirectionally through a relay, which we call modulo-and- forward (MF). Our scheme extends the network coding in the binary channel to the Gaussian channel case, where XOR in the binary case is replaced by mod Lambda for the Gaussian case, where Lambda is a high-dimensional lattice whose shaping gain is close to optimal. If the relay node re-transmits the received signal after the mod Lambda operation, we can reduce the complexity compared to decode-and-forward (DF) and can get a better power efficiency compared to amplify-and-forward (AF). When the transmission powers of two nodes are different, we use superposition coding and partial decoding at the relay node. Finally, we plot and compare the sum rates of three different schemes, i.e., AF, DF, and MF. We show that by applying the proposed scheme, we can get better performance than AF and DF schemes under some conditions.