Wireless network coding design based on LDPC codes for a multiple‐access relaying system

In this paper, we investigate wireless network coding WNC in a multiple-access relay channel MARC with two sources, one relay and one destination. We focus on a MARC with binary-input additive white Gaussian noise AWGN channels, where two sources' signals interfere at both the relay and the destination. Firstly, we derive the achievable rates for the WNC in the MARC over binary-input AWGN channels. Secondly, considering the strong interference between the two sources, we propose a novel joint WNC and multi-edge type low-density party-check LDPC code structure, which we refer to as the WNC-LDPC code. Then, on the basis of our code structure and the iterative receiver at the destination, we optimise the degree distributions of our WNC-LDPC code to approach the achievable sum rate of the MARC by utilising the extrinsic mutual information transfer EXIT analysis. In the simulations, we utilise physical-layer network coding PNC as a benchmark for comparison purposes and design an LDPC code for the PNC i.e. PNC-LDPC, which is used to compare with our WNC-LDPC code. Numerical results show that our WNC-LDPC code offers a much better bit error ratio performance relative to the PNC-LDPC code. Copyright © 2013 John Wiley & Sons, Ltd.