Linear Physical-layer Network Coding in Galois Field for Rayleigh fading 2-Way Relay Channels

TL;DR

This paper introduces a novel linear physical-layer network coding scheme in Galois Field for Rayleigh fading 2-way relay channels, demonstrating its advantages over existing methods in low SNR conditions.

Contribution

The paper proposes a new LPNC method in GF(2^2) that outperforms 5QAM-DNF in low SNR regimes without sacrificing spectral efficiency.

Findings

LPNC in GF(2^2) outperforms 5QAM-DNF at low SNR

Both schemes achieve similar performance at high SNR

Explicit capacity difference between LPNC and 5QAM-DNF derived

Abstract

In this paper, we propose a novel linear physicallayer network coding (LPNC) for Rayleigh fading 2-way relay channels (2-WRC). Rather than the simple modulo-2 (bit-XOR) operation, the relay directly maps the superimposed signal of the two users into the linear network coded combination in GF(2^2) by multiplying the user data by properly selected generator matrix. We derive the constellation constrained capacities for LPNC and 5QAM denoise-and forward (5QAM-DNF) [2] and further explicitly characterize the capacity difference between LPNC and 5QAM-DNF. Based on our analysis and simulation, we highlight that without employing the irregular 5QAM mapping and sacrificing the spectral efficiency, our LPNC in GF(2^2) is superior to 5QAM-DNF scheme in low SNR regime while they achieve equal performance in the the moderate-to-high SNR regime.