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Exploiting the Massey Gap.

Andrei Tănăsescu1, Pantelimon George Popescu1

  • 1Department of Computer Science and Engineering, University Politehnica of Bucharest, Splaiul Independentei 313 (6), 060042 Bucharest, Romania.

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Summary
This summary is machine-generated.

Researchers refined the Massey inequality, which connects Shannon and guessing entropies, by introducing the Massey gap. Shrinking this gap improves prior results, offering new mathematical insights without added complexity.

Keywords:
guessingmassey inequalityshannon entropy

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Area of Science:

  • Information Theory
  • Mathematical Inequalities

Background:

  • The Massey inequality establishes a relationship between Shannon entropy and guessing entropy.
  • Existing refinements may introduce additional parameters or lack closed-form solutions.

Purpose of the Study:

  • To introduce a novel concept, the Massey gap, for refining the Massey inequality.
  • To improve upon existing bounds relating Shannon and guessing entropies.
  • To develop parameter-free refinements and numerical procedures.

Main Methods:

  • Introduction of the Massey gap as a measure of difference.
  • Derivation of closed-form strict refinements to the Massey inequality.
  • Development of a numerical procedure for further enhancement.

Main Results:

  • New, strict refinements to the Massey inequality are presented.
  • The Massey gap provides a quantifiable measure for improving entropy bounds.
  • Improvements are achieved without introducing new parameters.

Conclusions:

  • The Massey gap offers a significant advancement in understanding the relationship between Shannon and guessing entropies.
  • The proposed refinements provide tighter bounds and practical computational methods.