Low-Density Lattice Codes for Full-Duplex Relay Channels

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.