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In a multiple input multiple output (MIMO) context, we present, in this paper, a space-time bit interleaved coded modulation (STBICM) system combined with a space-time spreader called linear precoding. We propose a practical low-complexity receiver structure performing iteratively space-time detection and channel decoding. The novelty lies in the linearity of the space-time detector which consists of an MMSE MIMO PSIC equalizer and a linear deprecoder. Spectral efficiency and diversity can easily be tuned while keeping a feasible receiver. In the case of independent flat Rayleigh fading, simulation results show that such a system exploits both spatial diversity and capacity provided by the multi-antenna system.