Approximately achieving Gaussian relay network capacity with lattice codes

Recently, it has been shown that a quantize-map-and-forward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we show that the same approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays.