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Computing Rate-Distortion Functions of Continuous Memoryless Sources via Discrete Algorithms: An Integrated Scheme
Lingyi Chen1, Haoran Tang1, Hao Wu1
1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
Entropy (Basel, Switzerland)
|March 28, 2026
Summary
This study develops numerical algorithms for the rate-distortion (RD) function of continuous sources. It establishes convergence guarantees and derives computational costs for discrete algorithms, improving RD theory for continuous data.
Area of Science:
- Information Theory
- Applied Mathematics
- Computer Science
Background:
- The rate-distortion (RD) function is crucial for data compression and information theory.
- Efficient numerical computation of the RD function is well-established for discrete sources.
- A rigorous and efficient solution for continuous sources remains a significant challenge.
Purpose of the Study:
- To bridge the gap between RD problems of continuous memoryless sources and existing discrete numerical algorithms.
- To provide theoretical convergence guarantees for approximating continuous RD functions using discrete methods.
- To analyze and improve the computational efficiency of RD function computation for continuous sources.
Main Methods:
- Theoretical analysis of convergence guarantees for discrete approximations of continuous RD problems.
- Review and analysis of the Blahut-Arimoto (BA) and constrained BA algorithms.
- Derivation of arithmetic operation estimates for achieving ε-accuracy in continuous RD computation.
- Development of acceleration techniques tailored for specific distortion measures (squared-error, absolute-error).
Main Results:
- Established theoretical convergence guarantees for approximating continuous RD functions via discrete methods.
- Derived estimates for the computational complexity of discrete RD algorithms applied to continuous sources.
- Developed novel acceleration techniques for specific distortion measures, enhancing computational efficiency.
- Provided a framework for numerically computing the RD function for continuous memoryless sources.
Conclusions:
- The proposed integrated approach successfully bridges RD problems of continuous sources with discrete numerical algorithms.
- The derived convergence guarantees and computational cost estimates offer a rigorous foundation for practical RD function computation.
- Acceleration techniques significantly improve the efficiency of solving RD problems for continuous sources with common distortion measures.
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