### 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 language | English |
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Number of pages | 1 |

Publication status | Published - Dec 1 1990 |

Event | 1990 IEEE International Symposium on Information Theory - San Diego, CA, USA Duration: Jan 14 1990 → Jan 19 1990 |

### Other

Other | 1990 IEEE International Symposium on Information Theory |
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City | San Diego, CA, USA |

Period | 1/14/90 → 1/19/90 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Asymptotics of quantizers revisited*. Paper presented at 1990 IEEE International Symposium on Information Theory, San Diego, CA, USA, .