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We propose a new space-time coding scheme for the quasi-static multiple-antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter. In our scheme, codewords produced by a trellis encoder are formatted into space-time codeword arrays such that decoding can be implemented efficiently by minimum mean-square error (MMSE) decision-feedback interference mitigation coupled with Viterbi decoding, through the use of per-survivor processing. We discuss the code design for the new scheme, and show that finding codes with optimal diversity is much easier than for conventional trellis space-time codes (STCs). We provide an upper bound on the word-error rate (WER) of our scheme which is both accurate and easy to evaluate. Then, we find upper and lower bounds on the information outage probability with discrete independent and identically distributed (i.i.d). inputs (as opposed to Gaussian inputs, as in most previous works) and we show that the MMSE front-end yields a large advantage over the whitened matched filter (i.e., zero-forcing) front-end. Finally, we provide a comprehensive performance/complexity comparison of our scheme with coded vertical Bell Labs layered space-time (V-BLAST) architecture and with the recently proposed threaded space-time codes. We also discuss the concatenation of our scheme with block space-time precoders, such as the linear dispersion codes.