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Iteratively decoded bit-interleaved space-time coded modulation (BI-STCM) greatly lowers bit error rate (BER) over fast Rayleigh fading multiple-input multiple-output (MIMO) channels. We develop a general, tight and efficient theoretical error-free feedback bound (EF bound) to analyze the asymptotic BER. The convergence to the EF bound and the accuracy of the prediction are verified by simulation. With the best rate 1/2 4-state convolutional code and the 16-QAM modified set partitioning labeling, the BER of 10-6 can be achieved at Eb/N0=1.6 dB with 2 transmit and 2 receive antennas.