Structured Codes and Cooperative Strategies in Wireless Relay Networks

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 thesis, we rst show that lattice codes may be used to achieve the same performance as known Gaussian random coding techniques for the Gaussian relay channel. Then several examples are given to show how this may be combined with the linearity of lattices codes in multi-source relay networks. Finally we show that lattice codes's advantages in the two-way multi-hop Channel. In particular, we present a nested lattice list decoding technique, by which, lattice codes are shown to achieve the Decode-and-Forward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present a few examples of how this DF scheme may be combined with the linearity of lattice codes to achieve rates which may outperform analogous Gaussian random coding techniques in multi-source relay channels such as the two-way relay channel with direct links and the multiple access relay channel. We furthermore present a lattice Compress-and-Forward (CF) scheme which exploits a lattice Wyner-Ziv binning scheme for the Gaussian relay channel which achieves the same rate as the Cover-El Gamal CF rate using Gaussian random codes. Finally, the linearity of lattice codes is further utilized in two-way multi-hop channels where the "Redistribution Transform" is proposed to fully exploit the transmit power of relays for both directions. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks.