Design and analysis of random-like codes for various multiple-input and multiple-output communication systems are addressed in this work. Random-like codes have drawn significant interest because they offer capacity-achieving performance. We first consider the analysis and design of low-density parity-check (LDPC) codes for turbo multiuser detection in multipath 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. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. We then apply the tools of density evolution with mixture Gaussian approximations to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations which include different number of antennas, different channel models and different demodulation schemes. We also study the coding-spreading tradeoff in LDPC coded CDMA systems employing multiuser joint decoding. We solve the coding-spreading optimization based on the extrinsic information SNR evolution curves for the SISO multiuser detectors and the SISO LDPC decoders. Both single-cell and multi-cell scenarios will be considered. For each of these cases, we will characterize the extrinsic information for both finite-size systems and the so-called large systems where asymptotic performance results must be evoked. Finally, we consider the design optimization of irregular repeat accumulate (IRA) codes for MIMO communication systems employing iterative receivers. We present the density evolution-based procedure with Gaussian approximation for optimizing the IRA code ensemble. We adopt an approximation method based on linear programming to design an IRA code with the extrinsic information transfer (EXIT) chart matched to that of the soft MIMO demodulator.
