Asymptotically Optimal Error-Rate Performance of Linear Physical-Layer Network Coding in Rayleigh Fading Two-Way Relay Channels
The authors study a new Linear Physical-layer Network Coding (LPNC) scheme for fading two-way relay channels. In the uplink phase, two users transmit simultaneously. The relay selects some integer coefficients and computes a linear combination (in a size-q finite set) of the two users' messages, which is broadcast in the downlink phase. They develop a design criterion for choosing the integer coefficients that minimizes the error probability. Based on that, they derive an asymptotically tight bound, in a closed-form, for the error probability of the LPNC scheme over Rayleigh fading channels.