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We propose the building of high rate space-time codes for multiple-input multiple-output (MIMO) block fading multipath additive white Gaussian noise channels by layering small compound space-time trellis codes. To recover part of the spatial diversity between the different layers, we also study their concatenation with an outer code. Naturally, our space-time coding architecture puts the burden on the receiver complexity. As a main contribution of this paper, a near-optimal soft-input soft-output reduced-complexity trellis search algorithm is suggested for joint MIMO detection and inner decoding.