  Federated Learning (FL) is an emerging paradigm that holds great promise for
privacy-preserving machine learning using distributed data. To enhance privacy,
FL can be combined with Differential Privacy (DP), which involves adding
Gaussian noise to the model weights. However, FL faces a significant challenge
in terms of large communication overhead when transmitting these model weights.
To address this issue, quantization is commonly employed. Nevertheless, the
presence of quantized Gaussian noise introduces complexities in understanding
privacy protection. This research paper investigates the impact of quantization
on privacy in FL systems. We examine the privacy guarantees of quantized
Gaussian mechanisms using R\'enyi Differential Privacy (RDP). By deriving the
privacy budget of quantized Gaussian mechanisms, we demonstrate that lower
quantization bit levels provide improved privacy protection. To validate our
theoretical findings, we employ Membership Inference Attacks (MIA), which gauge
the accuracy of privacy leakage. The numerical results align with our
theoretical analysis, confirming that quantization can indeed enhance privacy
protection. This study not only enhances our understanding of the correlation
between privacy and communication in FL but also underscores the advantages of
quantization in preserving privacy.
