  We discuss a relationship between rate-distortion and optimal transport (OT)
theory, even though they seem to be unrelated at first glance. In particular,
we show that a function defined via an extremal entropic OT distance is
equivalent to the rate-distortion function. We numerically verify this result
as well as previous results that connect the Monge and Kantorovich problems to
optimal scalar quantization. Thus, we unify solving scalar quantization and
rate-distortion functions in an alternative fashion by using their respective
optimal transport solvers.
