Linear Physical-Layer Network Coding Over Hybrid Finite Ring for Rayleigh Fading Two-Way Relay Channels

In this paper, we propose a novel linear physical-layer network coding scheme over hybrid finite ring (HFR-LPNC) for Rayleigh fading two-way relay channels. The relay maps the superimposed signal of the two users to a linear network coded combination (LNCC) in hybrid finite ring, rather than using the simple bit-wise eXclusive-OR mapping. The optimal linear coefficients are selected to generate the LNCC, aiming to: 1) maximize the sum-rate in the MAC phase; and 2) ensure unambiguous decoding. To avoid the performance degradation caused by high-order irregular mappings, properly designed source coding is used for compressing the LNCC alphabet over the hybrid finite ring into the unifying 4-ary alphabet. We derive the constellation constrained sum-rates for HFR-LPNC in comparison with 5QAM denoise-and-forward (5QAM-DNF), which we use as a reference scheme. Furthermore, we explicitly characterize the rate difference between HFR-LPNC and 5QAM-DNF. Our analysis and simulation show that: 1) HFR-LPNC has a superior ability to mitigate the singular fading compared with 5QAM-DNF; and 2) HFR-LPNC is superior to 5QAM-DNF over a wide range of SNRs.