Beyond Shannon-Type Inequalities

  • Raymond W. Yeung
Part of the Information Technology: Transmission, Processing and Storage book series (PSTE)

Abstract

In Chapter 12, we introduced the regions Γ* n and Γ n in the entropy space H n for n random variables. From Γ* n , one in principle can determine whether any information inequality always holds. The region Γ n , defined by the set of all basic inequalities (equivalently all elemental inequalities) involving n random variables, is an outer bound on Γ* n . From Γ n , one can determine whether any information inequality is implied by the basic inequalities. If so, it is called a Shannon-type inequality. Since the basic inequalities always hold, so do all Shannon-type inequalities. In the last chapter, we have shown how machineproving of all Shannon-type inequalities can be made possible by taking advantage of the linear structure of Γ n .

Keywords

Entropy 

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Raymond W. Yeung
    • 1
  1. 1.The Chinese University of Hong KongHong Kong

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