# Computing Rate–Distortion Functions of Continuous Memoryless Sources via Discrete Algorithms: An Integrated Scheme with Convergence Guarantee and Algorithmic Acceleration

## TL;DR

This paper presents a method to compute rate-distortion functions for continuous sources using discrete algorithms with guaranteed convergence and improved efficiency.

## Contribution

An integrated scheme with convergence guarantees and algorithmic acceleration for continuous source rate-distortion computation.

## Key findings

- Theoretical convergence is established by solving a sequence of discrete problems.
- Estimates of arithmetic operations for ε-accuracy are derived for discrete algorithms.
- Acceleration techniques for specific distortion measures are developed.

## Abstract

Numerical computation of the rate–distortion (RD) function is a key problem in RD theory. Thus far, efficient algorithms have been well studied for discrete sources, but for continuous sources, there is still lack of a rigorously developed solution. In this article, an integrated approach is conducted that bridges RD problems of continuous memoryless sources and discrete numerical algorithms. First, we analyze and establish the theoretical convergence guarantee when progressively approaching the continuous RD problem via a sequence of discrete problems. Next, discrete algorithms including the Blahut–Arimoto (BA) and constrained BA algorithms are reviewed, and estimates of their required amount of arithmetic operations to attain ε-accuracy in solving the continuous RD problem are derived. Finally, acceleration techniques that exploit structures of special distortion measures (i.e., squared-error and absolute-error) are developed.