  In this paper, the problem of federated learning (FL) through digital
communication between clients and a parameter server (PS) over a multiple
access channel (MAC), also subject to differential privacy (DP) constraints, is
studied. More precisely, we consider the setting in which clients in a
centralized network are prompted to train a machine learning model using their
local datasets. The information exchange between the clients and the PS takes
places over a MAC channel and must also preserve the DP of the local datasets.
Accordingly, the objective of the clients is to minimize the training loss
subject to (i) rate constraints for reliable communication over the MAC and
(ii) DP constraint over the local datasets. For this optimization scenario, we
proposed a novel consensus scheme in which digital distributed stochastic
gradient descent (D-DSGD) is performed by each client. To preserve DP, a
digital artificial noise is also added by the users to the locally quantized
gradients. The performance of the scheme is evaluated in terms of the
convergence rate and DP level for a given MAC capacity. The performance is
optimized over the choice of the quantization levels and the artificial noise
parameters. Numerical evaluations are presented to validate the performance of
the proposed scheme.
