Asymptotics of quantizers revisited

Laszlo Gyorfi, Tamas Linder, Edward C. van der Meulen

Research output: Contribution to conferencePaper

Abstract

Summary form only given, as follows. The authors reanalyze the results by Gish and Pierce (1968) on asymptotically efficient quantizing. In particular, asymptotic bounds are derived on the difference between the entropy of the uniform quantizer and that of the optimal quantizer when the mean-square error becomes small. No assumptions are made at all on the density of the random variable being quantized, and use is made of some classical results by Renyi (1959) and Csisar (1973). Also, following the work by Ziv (1985), nonasymptotic and distribution-free bounds on the difference between the entropy of the uniform quantizer and that of the optimal quantizer are derived, if both have the same distortion. Finally, nonuniform quantizers are considered. For the latter case the asymptotic relationship between the entropy of the quantizer and the entropy of the random variable being quantized is investigated with no assumption at all on the density.

Original languageEnglish
Number of pages1
Publication statusPublished - Dec 1 1990
Event1990 IEEE International Symposium on Information Theory - San Diego, CA, USA
Duration: Jan 14 1990Jan 19 1990

Other

Other1990 IEEE International Symposium on Information Theory
CitySan Diego, CA, USA
Period1/14/901/19/90

ASJC Scopus subject areas

  • Engineering(all)

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    Gyorfi, L., Linder, T., & van der Meulen, E. C. (1990). Asymptotics of quantizers revisited. Paper presented at 1990 IEEE International Symposium on Information Theory, San Diego, CA, USA, .