An Iterative Algorithm for Computing the Optimal Exponent of Correct Decoding Probability for Rates below the Rate Distortion Function

TL;DR

This paper introduces an iterative algorithm to compute the optimal exponent of correct decoding probability for rates below the rate distortion function, extending previous work on similar exponents for channels above capacity.

Contribution

The paper presents a new iterative algorithm specifically designed for calculating Csiszár and Körner's exponent in lossy source coding, also applicable to cutoff rate and rate distortion function.

Findings

Algorithm accurately computes the exponent for rates below the rate distortion function.

The method can also be used to determine cutoff rate and rate distortion function.

Provides a practical computational approach for information theory exponents.

Abstract

The form of Dueck and K\"orner's exponent function for correct decoding probability for discrete memoryless channels at rates above the capacity is similar to the form of Csisz\'ar and K\"orner's exponent function for correct decoding probability in lossy source coding for discrete memoryless sources at rates below the rate distortion function. We recently gave a new algorithm for computing Dueck and K\"orner's exponent. In this paper, we give an algorithm for computing Csisz\'ar and K\"orner's exponent. The proposed algorithm can be also used to compute cutoff rate and the rate distortion function.