  The proliferation of Internet-of-Things (IoT) devices and cloud-computing
applications over siloed data centers is motivating renewed interest in the
collaborative training of a shared model by multiple individual clients via
federated learning (FL). To improve the communication efficiency of FL
implementations in wireless systems, recent works have proposed compression and
dimension reduction mechanisms, along with digital and analog transmission
schemes that account for channel noise, fading, and interference. This prior
art has mainly focused on star topologies consisting of distributed clients and
a central server. In contrast, this paper studies FL over wireless
device-to-device (D2D) networks by providing theoretical insights into the
performance of digital and analog implementations of decentralized stochastic
gradient descent (DSGD). First, we introduce generic digital and analog
wireless implementations of communication-efficient DSGD algorithms, leveraging
random linear coding (RLC) for compression and over-the-air computation
(AirComp) for simultaneous analog transmissions. Next, under the assumptions of
convexity and connectivity, we provide convergence bounds for both
implementations. The results demonstrate the dependence of the optimality gap
on the connectivity and on the signal-to-noise ratio (SNR) levels in the
network. The analysis is corroborated by experiments on an image-classification
task.
