  We explore a scheme that enables the training of a deep neural network in a
Federated Learning configuration over an additive white Gaussian noise channel.
The goal is to create a low complexity, linear compression strategy, called
PolarAir, that reduces the size of the gradient at the user side to lower the
number of channel uses needed to transmit it. The suggested approach belongs to
the family of compressed sensing techniques, yet it constructs the sensing
matrix and the recovery procedure using multiple access techniques. Simulations
show that it can reduce the number of channel uses by ~30% when compared to
conveying the gradient without compression. The main advantage of the proposed
scheme over other schemes in the literature is its low time complexity. We also
investigate the behavior of gradient updates and the performance of PolarAir
throughout the training process to obtain insight on how best to construct this
compression scheme based on compressed sensing.
