Linear physical-layer network coding over hybrid finite ring for rayleigh fading two-way relay channels

Dong Fang*, Alister Burr, Jinhong Yuan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number6860266
Pages (from-to)3249-3261
Number of pages13
JournalIEEE Transactions on Communications
Issue number9
Early online date18 Jul 2014
Publication statusPublished - 1 Sept 2014


  • constellation constrained capacity
  • finite ring
  • Physical-layer network coding
  • two-way relay channels

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