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Novel closed-form upper bounds on the error performance of coded modulation systems over fast-fading multi-input multi-output (MIMO) channels are obtained for two different space-time schemes: direct transmission and orthogonal space-time block codes. The concept of the distance spectrum for associated space-time codes is developed and used to derive the bounds which can be calculated readily through polynomial expansion. Comparison of the bounds for the two systems indicates the performance of direct transmission is superior. Comparison with simulation results shows that the bounds are tight and useful for benchmarking the practical iterative decoding process.