Lattice Codes for the Gaussian Relay Channel: Decode-and-Forward and Compress-and-Forward

Lattice codes are known to achieve capacity in the Gaussian point-to-point channel, thereby achieving the same rates as random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, the authors show that lattice codes may be used to achieve the same performance as known Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multi-source relay networks.