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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

Markov Chain Entropy Function Markov Condition Elemental Inequality Data Storage System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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