Accession Number : AD0709357

Title :   A THEOREM ON CONVERGENCE OF ENTROPY FOR SMALL DISTORTION.

Descriptive Note : Physical sciences research papers,

Corporate Author : AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS

Personal Author(s) : Pierce,John N.

Report Date : MAY 1970

Pagination or Media Count : 24

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)

Descriptors :   (*INFORMATION THEORY, ENTROPY), NUMERICAL INTEGRATION, PROBABILITY, DISTORTION, CONVERGENCE, THEOREMS

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE