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.

翻译：我们探讨了率失真理论与最优传输理论之间的关系，尽管二者乍看之下似乎毫无关联。具体而言，我们证明通过极端熵最优传输距离定义的函数等价于率失真函数。我们通过数值实验验证了这一结果，同时也确认了此前将蒙日问题和康托罗维奇问题与最优标量量化相联系的研究结论。因此，我们通过各自对应的最优传输求解器，以另一种方式统一了标量量化与率失真函数的求解。