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We present a natural and low-complexity technique for achieving the capacityof the Gaussian relay network in the high SNR regime. Specifically, we proposethe use of end-to-end structured lattice codes with the amplify-and-forwardstrategy, where the source uses a nested lattice code to encode the messagesand the destination decodes the messages by lattice decoding. All intermediaterelays simply amplify and forward the received signals over the network to thedestination. We show that the end-to-end lattice-coded amplify-and-forwardscheme approaches the capacity of the layered Gaussian relay network in thehigh SNR regime. Next, we extend our scheme to non-layered Gaussian relaynetworks under the amplify-and-forward scheme, which can be viewed as aGaussian intersymbol interference (ISI) channel. Compared with other schemes,our approach is significantly simpler and requires only the end-to-end designof the lattice precoding and decoding. It does not require any knowledge of thenetwork topology or the individual channel gains.

Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes