Linear Physical-layer Network Coding for Fading Two-way Relay Channels: Design Criterion and Performances

Physical-layer network coding (PNC) can potentially boost the throughput or reliability of a multi-user wireless communication network, such as a two-way relay channel. In a realistic fading channel environment, however, the amplitude variation and carrier phase asynchrony effects may limit the performance of a PNC scheme. Therefore, one key challenge is how to efficiently tackle these effects in designing a high-performance PNC scheme. In this talk, I will introduce a technique, referred to as linear PNC, to address the amplitude variation and carrier phase asynchrony problems in a realistic Rayleigh fading two-way relay channel. The main feature is that the relay will select a “good” pair of integer coefficients, according to the fading channel realization, and compute the associated linearly network-coded message. In particular, the integer coefficients are carefully selected so that the error probability at the relay is minimized. A “minimum set distance maximization” design criterion for the linear PNC scheme is developed. For the high SNR regime, a parametrical solution that meets this criterion is derived. The average error-probability performance of the linear PNC scheme over a Rayleigh fading two-way relay channel is analyzed, and a high-SNR closed-form result is derived. The result shows that the designed linear PNC scheme asymptotically achieves the interference-free error probability lower bound. In addition, the linear PNC scheme significantly outperforms existing schemes, e.g., with complete decoding and conventional PNC.