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This paper investigates the role of dimensionality reduction in efficient communication and differential privacy (DP) of the local datasets at the remote users for over-the-air computation (AirComp)-based federated learning (FL) model. More precisely, we consider the FL setting in which clients are prompted to train a machine learning model by simultaneous channel-aware and limited communications with a parameter server (PS) over a Gaussian multiple-access channel (GMAC), so that transmissions sum coherently at the PS globally aware of the channel coefficients. For this setting, an algorithm is proposed based on applying federated stochastic gradient descent (FedSGD) for training the minimum of a given loss function based on the local gradients, Johnson-Lindenstrauss (JL) random projection for reducing the dimension of the local updates, and artificial noise to further aid user's privacy. For this scheme, our results show that the local DP performance is mainly improved due to injecting noise of greater variance on each dimension while keeping the sensitivity of the projected vectors unchanged. This is while the convergence rate is slowed down compared to the case without dimensionality reduction. As the performance outweighs for the slower convergence, the trade-off between privacy and convergence is higher but is shown to lessen in high-dimensional regime yielding almost the same trade-off with much less communication cost.

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.

In this paper, we study relay networks with orthogonal components in presence of noncausal channel state information (CSI) available at the source. We propose an upper bound on the capacity of the discrete memoryless model (DM)for the case in which just the source component intended for the destination is encoded against the CSI known non-causally at the source. Also, we derive capacity for two special classes of the Gaussian structure of the model. The first class is the one for which we have obtained the upper bound and the second class is the one in which all of the source components intended for the relays and destination are encoded against the noncausal CSI, however, no interference at the relays and destination exists in this case., Comment: This paper has been withdrawn by the author due to an error in derivation of a relation