Next-generation wireless networks, such as edge intelligence and wireless distributed learning, face two critical challenges: communication efficiency and privacy protection. In this work, our focus is on addressing these issues in a distributed learning framework. We consider a new approach that simultaneously achieves communication efficiency and privacy protection by exploiting the privacy advantage offered by quantization. Specifically, we use a quantization scheme called \textbf{Gau}ssian \textbf{L}ayered \textbf{R}andomized \textbf{Q}uantization (Gau-LRQ) that compresses the raw model gradients using a layer multishift coupler. By adjusting the parameters of Gau-LRQ, we shape the quantization error to follow the expected Gaussian distribution, thus ensuring client-level differential privacy (CLDP). We demonstrate the effectiveness of our proposed Gau-LRQ in the distributed stochastic gradient descent (SGD) framework and theoretically quantify the trade-offs between communication, privacy, and convergence performance. We further improve the convergence performance by enabling dynamic private budget and quantization bit allocation. We achieve this by using an optimization formula that minimizes convergence error subject to the privacy budget constraint. We evaluate our approach on multiple datasets, including MNIST, CIFAR-10, and CIFAR-100, and show that our proposed method outperforms the baselines in terms of learning performance under various privacy constraints. Moreover, we observe that dynamic privacy allocation yields additional accuracy improvements for the models compared to the fixed scheme.

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