  Because of its privacy-preserving capability, federated learning (FL) has
attracted significant attention from both academia and industry. However, when
being implemented over wireless networks, it is not clear how much
communication error can be tolerated by FL. This paper investigates the
robustness of FL to the uplink and downlink communication error. Our
theoretical analysis reveals that the robustness depends on two critical
parameters, namely the number of clients and the numerical range of model
parameters. It is also shown that the uplink communication in FL can tolerate a
higher bit error rate (BER) than downlink communication, and this difference is
quantified by a proposed formula. The findings and theoretical analyses are
further validated by extensive experiments.
