A THEOREM ON CONVERGENCE OF ENTROPY FOR SMALL DISTORTION.

Abstract

Let X be a random variable with an absolutely continuous distribution function, and (Uk) be a sequence of random variables, independent of X, whose r-th mean converges to zero. Then it is shown that the existence of the R-th mean of X, for some positive R, is sufficient to guarantee the convergence of the entropy of X+(U sub k) to that of X. This theorem is useful in determining asymptotic approximations to the rate-distortion function and is thus pertinent to the problem of establishing the bit rate necessary to communicate at a specified small distortion. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1970
Accession Number
AD0709357

Entities

People

  • John N. Pierce

Organizations

  • Air Force Cambridge Research Laboratories

Tags

DTIC Thesaurus Topics

  • Convergence
  • Distortion
  • Distribution Functions
  • Guarantees
  • Mathematics
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.