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Logical Entropy of Information Sources
Peng Xu1, Yamin Sayyari2, Saad Ihsan Butt3
1School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, China.
Entropy (Basel, Switzerland)
|September 23, 2022
Summary
This study introduces logical entropy concepts, including bounds for random variables and properties of joint distributions. Logical entropy is shown to be subadditive, offering new insights into information theory.
Area of Science:
- Information Theory
- Mathematical Analysis
- Probability Theory
Background:
- Existing entropy measures provide foundational understanding of information uncertainty.
- The need for novel entropy formulations, such as logical entropy, arises from complex systems analysis.
Purpose of the Study:
- To introduce and define logical entropy of order m, logical mutual information, and logical entropy for information sources.
- To establish bounds for logical entropy of random variables.
- To investigate the properties of logical entropy in joint distributions and information systems.
Main Methods:
- Utilizing convex functions to derive upper and lower bounds for logical entropy.
- Analyzing the subadditivity property of logical entropy for joint distributions.
- Defining and examining logical Shannon entropy and logical metric permutation entropy.
Main Results:
- Established upper and lower bounds for the logical entropy of a random variable.
- Demonstrated that the logical entropy of joint distributions is less than the sum of individual logical entropies (subadditivity).
- Defined and explored properties of logical Shannon entropy and logical metric permutation entropy within information systems.
Conclusions:
- The introduced logical entropy concepts offer a new framework for quantifying information.
- The subadditivity property of logical entropy has significant implications for understanding information decomposition.
- Further examination of logical metric entropy and permutation logical entropy for maps is warranted.
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