Channel Decoding for Nonbinary Physical-Layer Network Coding in Two-Way Relay Systems

In this paper, we propose a generalized channel decoding scheme for nonbinary physical-layer network coding (CD-NC) in two-way relay channels (TWRCs), where two source nodes A and B exchange their nonbinary symbols via a relay. The two sources use the same nonbinary low-density parity-check (LDPC) channel code over the integer ring Z_M and M-pulse-amplitude modulation, respectively. The existing channel decoding schemes for nonbinary network coding suffer severe rate loss compared with the cut-set bound of TWRC, especially in the low-to-medium signal-to-noise ratio regime. The proposed CD-NC can decrease the rate loss. Our contributions are as follows: 1) We develop a generalized nonbinary sum product algorithm (G-SPA) for CD-NC according to the principle of virtual encoding of the superimposed symbols. Simulation results show that our CD-NC can achieve significant performance gains over the conventional nonbinary network coding for both additive white Gaussian noise and fading channels; and 2) We exploit two-dimensional fast-Fourier-transform-based belief propagation (2-D-FFT-BP) and extended min-sum (EMS) decoding algorithms to reduce the decoding complexity of G-SPA. Simulation results show that the 2-D-FFT-BP has the same performance as G-SPA, while EMS can greatly reduce the decoding complexity of G-SPA at the cost of slight performance degradation.

I. Introduction

Physical-layer network coding (PNC), originally proposed in [1], [2], can significantly boost the throughput of multi-user wireless communication networks. Generally, PNC transmissions in a relay network consist of two phases: multiple access phase and broadcast phase. In the multiple access phase, multiple source nodes transmit signals to a relay simultaneously. The relay aims to decode the overlapped signals into network coded (NC) messages. One basic setup for PNC is a wireless two-way relay channel (TWRC), in which two users exchange information from each other via an intermediate relay. The simplest form for the target NC messages is the bit-wise exclusive-or (XOR) of the two source messages [1]–[5].