  In federated learning (FL) with top $r$ sparsification, millions of users
collectively train a machine learning (ML) model locally, using their personal
data by only communicating the most significant $r$ fraction of updates to
reduce the communication cost. It has been shown that the values as well as the
indices of these selected (sparse) updates leak information about the users'
personal data. In this work, we investigate different methods to carry out
user-database communications in FL with top $r$ sparsification efficiently,
while guaranteeing information theoretic privacy of users' personal data. These
methods incur considerable storage cost. As a solution, we present two schemes
with different properties that use MDS coded storage along with a model
segmentation mechanism to reduce the storage cost at the expense of a
controllable amount of information leakage, to perform private FL with top $r$
sparsification.
