High SNR Error Analysis for Bidirectional Relaying with Physical Layer Network Coding

We consider a large class of bidirectional relaying scenarios with physical layer network coding, and analytically characterize the relay's error performance in decoding the network-coded combination at high signal-to-noise ratio (SNR). Our analysis applies to scenarios with 1) binary or higher order real/complex modulation, 2) real or complex channel coefficients, and 3) linear or non-linear network maps for network coding at the relay. We consider block fading and allow the relay to choose from a set of network maps based on the channel coefficients of the source to relay links in every block. We derive expressions for pairwise error probability and approximate expected overall error probability. We also derive lower bounds for these error probabilities. We validate these expressions using simulations and show that our approximations are tight in the high SNR regime.