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Space-time coding has been proposed recently for MIMO wireless communication systems. Most of these space-time coding schemes use the assumption that either no channel state information, or the channel mean/covariance information, is available at the transmitter. We propose a new space-time coding scheme for a close-loop transmission system, where quantized channel phase information is available at the transmitter. A new performance criterion is derived for the quasi-static fading channel. This design criterion is then used to construct a new class of space-time trellis codes. The proposed code construction is based on the concatenation of a standard M-TCM outer code with an inner code. The inner code is selected from a series of inner codes using the channel phase feedback. The series of inner codes is constructed based on the systematic set partitioning of two classes of space-time signal designs. Simulation results show significant improvement over other space-time trellis codes. In addition, the proposed coding scheme enjoys low peak-to-average power ratio, simple decoding, and easy implementation without complicated eigenanalysis.