On Linear Physical-Layer Network Coding with Non-Identical Modulation

Physical-layer network coding (PNC) is able to boost the error probability performance or throughput of a set of multi-source and multi-hop wireless networks. In this paper, we put forth a new asymmetric linear PNC (A-LPNC) scheme for the setup where the users are subject to non-identical power and modulation schemes. For deterministic channel, we show that given any unequal average symbol energy, the effective minimum distance of A-LPNC constellation can be made to be identical to the single-user minimum distance lower bound, translated into optimal error probability performance at a medium to high SNR. For fading channels, we show that the optimized network coding coefficients can be found and employed such that the effective minimum distance of A-LPNC is equal to the single-user minimum distance lower bound for integer channel gains. For real-valued channel gains, we present the optimal NC coefficients selection that minimizes the error probability of A-LPNC. These results are verified via simulations.