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Complexities of information sources.

Yamin Sayyari1, Mohammad Reza Molaei2, Adel Mehrpooya3

  • 1Sirjan University of Technology, Sirjan, Iran.

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Summary
This summary is machine-generated.

This study simplifies entropy calculation for complex systems by identifying information source classes with identical entropy values. It proves topological entropy is additive for products of information sources, reducing computational expense.

Keywords:
37B4037M2554C7094A17Topological entropyinformation sourcemetric entropypermutation metric entropypermutation topological entropyquantum information system

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Area of Science:

  • Information Theory
  • Dynamical Systems
  • Computational Science

Background:

  • Calculating entropy for complex systems is computationally intensive.
  • Direct entropy computation poses significant challenges in science and engineering.

Purpose of the Study:

  • To introduce novel classes of information sources for simplified entropy calculation.
  • To reduce the computational cost associated with entropy estimation.
  • To investigate the properties of topological entropy for product information sources.

Main Methods:

  • Characterization of information sources based on self-mappings on a probability space (Ω) and a finite set (A).
  • Approximation of rank variables for the product of information sources.
  • Mathematical proof of topological entropy additivity for the product of two information sources.

Main Results:

  • Identification of three classes of information sources with equivalent entropy values.
  • Demonstration that the topological entropy of the product of two information sources equals the sum of their individual topological entropies.

Conclusions:

  • The proposed method offers a computationally efficient approach to entropy calculation.
  • The additivity property of topological entropy simplifies analysis of composite information systems.
  • This work has implications for various fields requiring entropy estimation in complex systems.