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Semantic communications have shown great potential to boost the end-to-end transmission performance. To further improve the system efficiency, in this paper, we propose a class of novel semantic coded transmission (SCT) schemes over multiple-input multiple-output (MIMO) fading channels. In particular, we propose a high-efficiency SCT system supporting concurrent transmission of multiple streams, which can maximize the multiplexing gain of end-to-end semantic communication system. By jointly considering the entropy distribution on the source semantic features and the wireless MIMO channel states, we design a spatial multiplexing mechanism to realize adaptive coding rate allocation and stream mapping. As a result, source content and channel environment will be seamlessly coupled, which maximizes the coding gain of SCT system. Moreover, our SCT system is versatile: a single model can support various transmission rates. The whole model is optimized under the constraint of transmission rate-distortion (RD) tradeoff. Experimental results verify that our scheme substantially increases the throughput of semantic communication system. It also outperforms traditional MIMO communication systems under realistic fading channels.