Rate-Convergence Tradeoff of Federated Learning Over Wireless Channels

In this article, we consider a federated learning (FL) problem over wireless channel that takes into account the coding rate and packet transmission errors. Communication channels are modeled as packet erasure channels (PECs), where the probability of erasure is determined by block length, code rate, and signal-to-noise ratio (SNR). In spite of fluctuations in instantaneous loss of FL, we prove that the expectation of loss converges even in the presence of packet erasure. To mitigate the impact of packet erasure on FL performance, we suggest a paradigm in which the central node (CN) makes use of memory. In particular, we propose two schemes in which, in the event of packet erasure, the CN retains either the most recent local updates or the most recent global parameters. We investigate the impact of coding rate, SNR, and the CN memory on the convergence of FL. For both short- and long-packet communications, we examine a realistic scenario of a massive IoT under the assumption of error-prone transmissions. Our simulation results demonstrate that even a single memory unit has a considerable effect on the FL's efficiency in erroneous communication.