  In this paper, we study the randomized distributed coordinate descent
algorithm with quantized updates. In the literature, the iteration complexity
of the randomized distributed coordinate descent algorithm has been
characterized under the assumption that machines can exchange updates with an
infinite precision. We consider a practical scenario in which the messages
exchange occurs over channels with finite capacity, and hence the updates have
to be quantized. We derive sufficient conditions on the quantization error such
that the algorithm with quantized update still converge. We further verify our
theoretical results by running an experiment, where we apply the algorithm with
quantized updates to solve a linear regression problem.
