A Monotonicity Principle for Information Theory

  • Authors:
  • Konstantinos Chatzikokolakis;Keye Martin

  • Affiliations:
  • Oxford Computing Lab and LIX École Polytechnique;Naval Research Laboratory

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

We establish a monotonicity principle for convex functions that enables high-level reasoning about capacity in information theory. Despite its simplicity, this single idea is remarkably applicable. It leads to a significant extension of algebraic information theory, a solution of the capacity reduction problem, intuitive graphical methods for comparing channels, new inequalities that provide useful estimates on the information transmitting capability of a channel operating in an unknown environment, further explication of the fascinating relationship between capacity and Euclidean distance, and the solution of an open problem in quantum steganography.