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Techniques which leverage channel state information (CSI) at a transmitter to adapt wireless signals to changing propagation conditions have been shown to improve the reliability of modern multiple input multiple output (MIMO) communication systems. Due to the difficulty of estimating downlink CSI at the transmitter in many wireless systems, CSI is estimated at the receiver and sent to the transmitter using a feedback channel. To reduce overhead, previous works have proposed to compress CSI matrices using a trained deep autoencoder (AE) at the receiver before feeding it back to the transmitter, and recent work has proposed to quantize the compressed CSI to a finite number of bits to facilitate digital communication. While these techniques are effective, they do not incorporate quantization in the end-toend learning process of the AE from the start of training and do not consider losslessly coding the compressed, quantized CSI to further reduce feedback overhead. In this work, we propose a new AE-based feedback method which uses an entropy bottleneck layer to both quantize and losslessly code the compressed CSI. This bottleneck layer allows us to jointly optimize to achieve a low bit-rate for our compressed CSI representation and a low level of distortion in the reconstructed CSI. Our results indicate that our method is competitive in terms of reconstructed CSI distortion with current state-of-the-art AE-based feedback methods for higher bitrate values, and that it is also able to achieve much lower bitrates than existing state-of-the-art with relatively low distortion.
