Polarization-Aided Coding for Nonorthogonal Multiple Access

In this article, we propose a polarization-aided polar coding scheme over nonorthogonal multiple access channels operated with physical-layer network coding (PN-NOMA), where $M$ users adopt polar coding for transmission. By exploiting the characteristic of physical-layer network coding and polar encoding, we found that the polar code at the users can be seen as nested codes and subcodeword of a larger polar code. It enables us to construct a single (virtual) polar code at the receiver, which has the length $M$ times longer than that of the original user codes. In this way, we can decode all the user messages within this single polar code. The channel polarization effect as well as the decoding performance can be improved. We further propose a Monte Carlo-based code construction for the virtual polar code with user channel coefficients, and short nested user codes can be individually derived from this code. Simulation results show that the proposed PN-NOMA can achieve significant performance gains of more than 0.5 dB as compared to conventional polar-coded NOMA (PC-NOMA) over power-imbalanced channels, and this gain is more than 2 dB over Rayleigh fading channels.