  Recently, federated learning (FL) has sparked widespread attention as a
promising decentralized machine learning approach which provides privacy and
low delay. However, communication bottleneck still constitutes an issue, that
needs to be resolved for an efficient deployment of FL over wireless networks.
In this paper, we aim to minimize the total convergence time of FL, by
quantizing the local model parameters prior to uplink transmission. More
specifically, the convergence analysis of the FL algorithm with stochastic
quantization is firstly presented, which reveals the impact of the quantization
error on the convergence rate. Following that, we jointly optimize the
computing, communication resources and number of quantization bits, in order to
guarantee minimized convergence time across all global rounds, subject to
energy and quantization error requirements, which stem from the convergence
analysis. The impact of the quantization error on the convergence time is
evaluated and the trade-off among model accuracy and timely execution is
revealed. Moreover, the proposed method is shown to result in faster
convergence in comparison with baseline schemes. Finally, useful insights for
the selection of the quantization error tolerance are provided.
