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This paper takes into account the design optimization of the random-like ensemble of irregular repeat accumulate (IRA) codes for multiple-input multiple-output (MIMO) communication systems employing iterative receivers. First, the density evolution-based procedure for optimizing the IRA code ensemble is presented. An approximation method based on linear programming is adopted to design an IRA code with the extrinsic information transfer (EXIT) chart matched to that of the soft MIMO demodulator. The authors then reveal the relationship between the IRA codes and the low-density parity-check (LDPC) codes. With a code ensemble mapping relationship between an IRA code and an LDPC code, a quasi-optimal IRA code can be obtained by transforming an optimal LDPC code designed for MIMO systems. Two types of soft MIMO detectors are treated, namely, the maximum a posteriori (MAP) detector and the soft interference canceller with linear MMSE filtering (SIC-MMSE). The results show that with the MAP receiver the designed IRA codes can perform within 1 dB from the ergodic capacities of the MIMO systems under consideration. The authors also treat the short-length IRA code design for block fading MIMO channels. They adopt design techniques for short-length LDPC codes to improve the performance of the short-length IRA code and to reduce the error floor.