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We propose a class of codes which combine the principles of turbo coding and space-time trellis codes. It is first shown that several classes of space-time codes have an equivalent recursive realization. This fact is then exploited to design serial concatenated coding schemes with an outer code, interleaver, and an inner recursive space-time encoder. Two solutions are proposed in this paper - the use of convolutional outer codes aimed mainly to improve the power efficiency and the use of very high-rate outer codes to obtain significant improvement in power efficiency with a marginal decrease in spectral efficiency. We show that single parity check based turbo product codes are a good candidate for very high-rate outer codes. Finally, we propose an automatic repeat request scheme based on recursive realizations of space-time codes and show that the proposed scheme provides significant reduction in frame error rate.