A Theorem on Convergence of Entropy for Small Distortion
John N. Pierce
Jan 1970 · Air Force Cambridge Research Laboratories, Office of Aerospace Research, United States Air Force
Ebook
17
Pages
About this ebook
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).
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