Computation of the Optimal Error Exponent Function for Fixed-Length Lossy Source Coding in Discrete Memoryless Sources

Marton's optimal error exponent for the lossy source coding problem is defined as a non-convex optimization problem. This fact had prevented us to develop an efficient algorithm to compute it. This problem is caused by the fact that the rate-distortion function <inline-formula> <tex-ma...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 71; no. 5; pp. 3360 - 3372
Main Author: Jitsumatsu, Yutaka
Format: Journal Article
Language:English
Published: IEEE 01.05.2025
Subjects:
Arimoto-Blahut algorithm
Computational efficiency
Convex functions
Distortion
Distortion measurement
Error exponent
Linear programming
lossy source coding
Optimization
Probability distribution
Programming
Rate-distortion
rate-distortion theory
Source coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Marton's optimal error exponent for the lossy source coding problem is defined as a non-convex optimization problem. This fact had prevented us to develop an efficient algorithm to compute it. This problem is caused by the fact that the rate-distortion function <inline-formula> <tex-math notation="LaTeX">R(\Delta |P) </tex-math></inline-formula> is potentially non-concave in the probability distribution P for a fixed distortion level <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. The main contribution of this paper is the development of a parametric expression that is in perfect agreement with the inverse function of the Marton exponent. This representation has two layers. The inner layer is convex optimization and can be computed efficiently. The outer layer, on the other hand, is a non-convex optimization with respect to two parameters. We give a method for computing the Marton exponent based on this representation.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2025.3547033