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We derive performance bounds for turbo-coded systems with transmit and receive antenna diversity. The bounds are derived by limiting the conditional union bound before averaging over the fading process. It is demonstrated that this approach provides a tight upper bound on the error probability of the turbo-coded multiple antenna systems. We also describe a method for deriving the weight-enumerating function of turbo-coded multiple antenna systems in order to take into account the presence of transmit and receive antenna diversity. Examples of the bounds are presented to illustrate their usefulness.