When Wireless Federated Learning Meets Physical Layer Security: The Fundamental Limits

It has been shown that when federated learning (FL) is implemented in wireless communication systems, the noise of the channel directly serves as a privacy-inducing mechanism, which indicates that un-coded transmission can achieve privacy "for free". However, due to the broadcast nature of wireless communication, the wireless FL is susceptible to eavesdropping, and different from the privacy requirement of the FL ( to preserve the accuracy of data analysis, information leakage is allowed in privacy mechanisms), the physical layer security (PLS) requirement is that the information leakage caused by the eavesdropper should vanish, which indicates that the previous un-coded transmission strategy is not available for the wireless FL in the presence of PLS. In this paper, we propose a novel architecture satisfying both the privacy requirement of the FL and the PLS requirement of the wireless channels, and characterize the corresponding capacity-equivocation region under privacy-utility constraint. The study of this paper is further explained via numerical examples and simulation results.