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Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources
1Department of Information and Communication Engineering, Chosun University, 309 Pilmoondae-ro Dong-gu, Gwangju 61452, Korea.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
We introduce a new method to estimate Rényi entropy, a generalized measure of randomness that includes Shannon entropy. This technique helps detect deviations in random data sources and is particularly useful for Rényi entropy of order 2.
Area of Science:
- Information Theory
- Statistical Signal Processing
- Randomness Measurement
Background:
- Entropy is a key measure of randomness in data.
- Existing methods focus on estimating various entropy types from random samples.
- Rényi entropy generalizes Shannon entropy, offering a broader measure of randomness.
Purpose of the Study:
- To propose a novel estimation method for Rényi entropy of order α.
- To develop a technique capable of detecting significant deviations in ergodic stationary random sources.
- To provide an estimation method applicable to generalized entropy measures.
Main Methods:
- Development of a new estimation scheme for Rényi entropy.
- Derivation of a general representation for the estimator's parameters.
- Analysis of specific cases: α → 1, α = 1/2, and α = 2.
- Presentation of an iterative estimation method for Rényi entropy of order 2.
Main Results:
- The proposed estimation method is shown to be equivalent to the Rényi entropy of order α in expectation.
- The method effectively detects deviations in random data sources.
- An efficient iterative algorithm is provided for the commonly used Rényi entropy of order 2.
Conclusions:
- The proposed method offers a robust way to estimate Rényi entropy.
- This technique enhances the analysis of randomness in stationary data.
- The iterative approach for order 2 entropy is suitable for resource-constrained applications.
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