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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
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Summary
This summary is machine-generated.

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.

Keywords:
convex functionentropyinformation sourcelogical entropyrandom variable

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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.