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Data transmission using self-organizing feature map (SOFM) based vector quantizer (VQ) and channel optimized vector quantizer (COVQ) with various space-time trellis codes (STTC) over wireless channels are studied. It is interesting to note that in a SOFM-STTC system, even with a weak STTC, the overall performance in terms of reconstruction error does not degrade a lot, compared with a stronger STTC. Hence, a system of low complexity but satisfactory performance could be built. Our simulation results also show that the performance of SOFM-STTC is marginally worse than that of COVQ.