Optimal degree distribution for two-user regular LDPC codes over GMAC by fixed-point analysis

An analytical expression of the check nodes (CNs) degree in a two-user regular Low-Density Parity-Check (LDPC) code is derived over a Gaussian multiple access channel, and a Fixed Point Analysis (FPA) method is developed to determine the optimal degree distribution that maximizes the achievable sum rate of the system. Specifically, firstly, an analytical expression of the CNs degree is derived as a function of mutual information outputs. Secondly, based on this, a reliable region is obtained by taking a complement of a unified unreliable region. Finally, the optimal degree distribution is determined over this reliable region to achieve the optimal sum rate. Numerical results indicate that the proposed method offers superior accuracy and much lower computational complexity compared to the extrinsic information transfer (EXIT) chart.