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This paper presents a quasi-random approach to space-time (ST) codes. The basic principle is to transmit randomly interleaved versions of forward error correction (FEC)-coded sequences simultaneously from all antennas in a multilayer structure. This is conceptually simple, yet still very effective. It is also flexible regarding the transmission rate, antenna numbers, and channel conditions (e.g., with intersymbol interference). It provides a unified solution to various applications where the traditional ST codes may encounter difficulties. We outline turbo-type iterative joint detection and equalization algorithms with complexity (per FEC-coded bit) growing linearly with the transmit antenna number and independently of the layer number. We develop a signal-to-noise-ratio (SNR) evolution technique and a bounding technique to assess the performance of the proposed code in fixed and quasi-static fading channels, respectively. These performance assessment techniques are very simple and reasonably accurate. Using these techniques as a searching tool, efficient power allocation strategies are examined, which can greatly enhance the system performance. Simulation results show that the proposed code can achieve near-capacity performance with both low and high rates at low decoding complexity.