Optimization of LDPC-coded turbo CDMA systems

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 for computing the probability density function (pdf) of the extrinsic messages at the output of the soft-input soft-output (SISO) multiuser detectors as a function of the pdf of input extrinsic messages, user spreading codes, channel impulse responses, and signal-to-noise ratios. Of particular interest is the soft interference cancellation plus minimum mean square error (SIC-MMSE) multiuser detector, for which the pdf of the extrinsic messages can be characterized analytically. For the case of additive white Gaussian noise (AWGN) channels, the extrinsic messages can be well approximated as symmetric Gaussian distributed. For the case of asynchronous multipath fading channels, the extrinsic messages can be approximated by a mixture of symmetric Gaussian distributions. We show that 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.