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Orthogonal space-time block coding (STBC) has recently raised a lot of research interest due to its inherent mathematical feature that enables simple linear decoding at the receiver and provides full diversity over the multiple-input multiple-output (MIMO) fading channel. In this paper, we derive general closed-form expressions for the Shannon capacity achieved by this transmit-diversity scheme over Rayleigh fading channels under adaptive transmission and channel-estimation errors. Adaptive transmission can be performed on a frame-by-frame basis, provided that a channel state information (CSI), consisting of the signal-to-noise ratio (SNR) level as estimated by the receiver, is fed back to the transmitter, thereby allowing for different compromises between the achievable capacity and the corresponding implementation complexity. The closed-form capacity formulas, derived for different power- and rate-allocation policies, are expressed in terms of the number of transmit and receive antennas, the code rate of the STBC mapping, and a single parameter capturing Gaussian channel-estimation errors. Numerical results showing the effects of these parameters on the capacity of STBC subject to the adaptive-transmission policies under consideration are provided.