  In federated learning, a server must periodically broadcast a model to the
agents. We propose to use multi-resolution coding and modulation (also known as
non-uniform modulation) for this purpose. In the simplest instance, broadcast
transmission is used, whereby all agents are targeted with one and the same
transmission (typically without any particular favored beam direction), which
is coded using multi-resolution coding/modulation. This enables high-SNR
agents, with high path gains to the server, to receive a more accurate model
than the low-SNR agents do, without consuming more downlink resources. As one
implementation, we use transmission with a non-uniform 8-PSK constellation,
where a high-SNR receiver (agent) can separate all 8 constellation points
(hence receive 3 bits) whereas a low-SNR receiver can only separate 4 points
(hence receive 2 bits). By encoding the least significant information in the
third bit, the high-SNR receivers can obtain the model with higher accuracy,
while the low-SNR receiver can still obtain the model although with reduced
accuracy, thereby facilitating at least some basic participation of the low-SNR
receiver. We show the effectiveness of our proposed scheme via experimentation
using federated learning with the MNIST data-set.
