The Design of Network Low Density Parity Check Codes for Wireless Multiple-Access Relay Networks

Based on the relaying scheme which permits the relay node to jointly encode the data information from two source nodes, a new network low density parity check (NLDPC) code is designed for the Rayleigh fading channel. Since the log-likelihood ratio (LLR) of the signal received from the fading channel is not a Gaussian random variable, the Gaussian Approximation algorithm cannot be employed directly in the density evolution. In this paper, a new hybrid bilayer Gaussian Approximation algorithm is derived to predict the performance of NLDPC codes over Rayleigh fading channels, based on which an optimization algorithm is developed to search for the degree distribution of the NLDPC code. Simulations show that, in a network with two sources, one relay and one destination, the system with the designed NLDPC code holds a performance gap of less than 0.6dB from the threshold.