Entropy-Constrained VQ-VAE for Deep-Learning-Based CSI Feedback

Deep-learning (DL)-based channel state information (CSI) feedback has attracted a great deal of attention due to its effectiveness in compressing CSI in massive multiple-input multiple-output systems. This technique harnesses an autoencoder architecture, where an encoder network transforms CSI into a low-dimensional latent vector, and a decoder network reconstructs the CSI from the latent vector. In this paper, we propose a vector quantization (VQ) framework for DL-based CSI feedback to provide an efficient finite-bit representation of the latent vector. In our framework, a trainable VQ module is employed after the encoder network, and entropy coding is applied to the output of the VQ module. To jointly train the encoder and decoder networks with the VQ codebook, we design a quantization criterion and loss function of vector-quantized variational autoencoder based on the rate-distortion theory. We also devise two practical strategies to make the proposed framework applicable under a strict bit budget constraint. Using simulations, we demonstrate that DL-based CSI feedback with the proposed framework outperforms existing quantization-aware DL-based CSI feedback methods.