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In a multiple-input multiple-output (MIMO) system, the availability of channel state information (CSI) at the transmitter is essential for performance improvement. Recent convolutional neural network (NN)-based techniques show competitive ability in realizing CSI compression and feedback. By introducing a new NN architecture, we enhance the accuracy of quantized CSI feedback in MIMO communications. The proposed NN architecture invokes a module named long short-term memory that admits the NN to benefit from exploiting temporal and frequency correlations of wireless channels. Compromising performance with complexity, we further modify the NN architecture with a significantly reduced number of parameters to be trained. Finally, experiments show that the proposed NN architectures achieve better performance in terms of both CSI compression and recovery accuracy.