  Federated data analytics is a framework for distributed data analysis where a
server compiles noisy responses from a group of distributed low-bandwidth user
devices to estimate aggregate statistics. Two major challenges in this
framework are privacy, since user data is often sensitive, and compression,
since the user devices have low network bandwidth. Prior work has addressed
these challenges separately by combining standard compression algorithms with
known privacy mechanisms. In this work, we take a holistic look at the problem
and design a family of privacy-aware compression mechanisms that work for any
given communication budget. We first propose a mechanism for transmitting a
single real number that has optimal variance under certain conditions. We then
show how to extend it to metric differential privacy for location privacy
use-cases, as well as vectors, for application to federated learning. Our
experiments illustrate that our mechanism can lead to better utility vs.
compression trade-offs for the same privacy loss in a number of settings.
