  Communication on heterogeneous edge networks is a fundamental bottleneck in
Federated Learning (FL), restricting both model capacity and user
participation. To address this issue, we introduce two novel strategies to
reduce communication costs: (1) the use of lossy compression on the global
model sent server-to-client; and (2) Federated Dropout, which allows users to
efficiently train locally on smaller subsets of the global model and also
provides a reduction in both client-to-server communication and local
computation. We empirically show that these strategies, combined with existing
compression approaches for client-to-server communication, collectively provide
up to a $14\times$ reduction in server-to-client communication, a $1.7\times$
reduction in local computation, and a $28\times$ reduction in upload
communication, all without degrading the quality of the final model. We thus
comprehensively reduce FL's impact on client device resources, allowing higher
capacity models to be trained, and a more diverse set of users to be reached.
