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In this work we study joint code design and MIMO (multiple-input multiple-output) detection based on Markov Chain Monte Carlo (MCMC) approach. The extrinsic information transfer (EXIT) technique is applied to find optimal irregular LDPC codes that are matched to the characteristics of the MCMC detector. For a large system of 8 transmit and 8 receive antennas and 16 QAM modulation, the optimized LDPC code achieves within 1.4 dB of the channel capacity. This result improves best published results by 2.3 dB, where 1.3 dB is due to the MCMC detection and 1 dB is due to code optimization.