Lattice Coding over the Relay Channel

It has been conjectured that lattice codes are good for (almost) everything. As an additional bit of evidence for this claim, we offer a few results showing the utility of lattice codes for the AWGN relay channel. We show that the decode-and-forward rates of the relay channel can be achieved using lattice encoding and decoding. We present an encoding/decoding technique that uses a doubly-nested lattice code. Encoding is accomplished using a combination of superposition encoding and block Markov encoding, while decoding is accomplished using a strategy reminiscent of Cover and El Gamal´s list decoding. Our technique can be extended to a wide variety of relay topologies, including the half-duplex relay channel and the cooperative multiple-access channel.