Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals.

Area of Science:

• Information Theory
• Computational Statistics
• Data Analysis

Background:

• Shannon entropy is a fundamental measure of information uncertainty.
• Accurate and efficient entropy estimation is crucial for large datasets.
• Existing methods may face limitations in speed and scalability.

Purpose of the Study:

• To introduce a novel method for estimating Shannon entropy.
• To enable fast computations and ranking of data samples by entropy.
• To provide a more accurate and efficient alternative to current state-of-the-art algorithms.

Main Methods:

• Development of a new entropy estimation algorithm.
• Theoretical exploration of positional entropy and integer entropy.
• Computational experiments to demonstrate relationships and validate the method.

Main Results:

• The proposed method achieves faster and more accurate Shannon entropy estimation.
• Experimental verification on diverse data samples confirms its usefulness and scalability.
• Demonstrated superior performance compared to existing state-of-the-art algorithms.

Conclusions:

• The novel method offers a significant advancement in fast and accurate Shannon entropy estimation.
• The approach is robust and applicable to large-scale data analysis.
• This work provides a valuable tool for researchers and practitioners in data science.