Design of low density parity check codes for turbo multiuser detection

We consider the analysis and design of low density parity check (LDPC) codes for turbo multiuser detection in multipath code-division multiple-access (CDMA) channels. We develop techniques to compute the probability density function (pdf) of the extrinsic information at the output of the multiuser detector. We show that the output pdf can be modeled as symmetric Gaussian for synchronous CDMA in additive white Gaussian noise (AWGN) channel and as a mixture of symmetric Gaussian densities for asynchronous CDMA system over fading channel. The expectation-maximization (EM) algorithm can be used to compute the parameters of this mixture. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds and the designed irregular LDPC codes outperform regular ones significantly.