  In this paper, we propose a new framework named Communication Optimal
Transport (CommOT) for computing the rate distortion (RD) function. This work
is motivated by observing the fact that the transition law and the relative
entropy in communication theory can be viewed as the transport plan and the
regularized objective function in the optimal transport (OT) model. However,
unlike in classical OT problems, the RD function only possesses one-side
marginal distribution. Hence, to maintain the OT structure, we introduce
slackness variables to fulfill the other-side marginal distribution and then
propose a general framework (CommOT) for the RD function. The CommOT model is
solved via the alternating optimization technique and the well-known Sinkhorn
algorithm. In particular, the expected distortion threshold can be converted
into finding the unique root of a one-dimensional monotonic function with only
a few steps. Numerical experiments show that our proposed framework (CommOT)
for solving the RD function with given distortion threshold is efficient and
accurate.
