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Serial concatenation of simple error control codes and differential space-time modulation is considered. Decoding is performed iteratively by passing symbol-wise a posteriori probability values between the decoders of the inner space-time code and the outer code. An extrinsic information transfer analysis is used to predict thresholds for outer convolutional codes of various memory orders and a simple outer parity-check code. This parity-check code is well matched to the inner differential space-time code and achieves a bit-error rate (BER) of 10-6 less than 2 dB from the Shannon capacity of the fast fading multiple antenna channel. The differential space-time code can also be used to generate a priori information in the absence of channel knowledge. This information can be exploited by a channel estimator inserted into the decoding iteration. It is demonstrated that the inner space-time code provides soft training symbols from periodically inserted training symbols. The reliability of these soft training symbols does not depend on the speed of the channel variations, but on the structure of the inner code and the signal-to-noise ratio (SNR). Simulation studies confirm these findings and show that the proposed system with no initial channel knowledge achieves a performance very close to that of the system with perfect channel knowledge.