A Method and Performance of the Optimum Scalar Quantizer for a Simple Class of Probability Density

Hiroyasu SAKAMOTO; Teiji OHTA; Hiroshi KONDO

A Method and Performance of the Optimum Scalar Quantizer for a Simple Class of Probability Density

Hiroyasu SAKAMOTO, Teiji OHTA, Hiroshi KONDO

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A design method of rate-distortion optimum scalar quantizer is developed, and performance of the optimum quantizer is compared with those of linear quantizers using mean square error and output entropy, for a simple class of probability density function (pdf.). The simple class means that pdf. is unimodal and symmetric about its mode value, and is differentiable in both sides of symmetry. The method proposed here is based on solving Kuhn-Tucker condition and is essentially the same as those reported before (by Berger or by Farvardin and Modestino), but is shown to be a more advantageous method. Moreover, it has the rules in what region the initial value must be given and how one stop of iteration is solved, and checkpoints for the existence and number of solutions, those have not been shown before except empirically. Without these rules, it seems to be very perplexed problem to check upon the solutions, and algorithm of calculation would be very complicated and time consuming, for even a pdf. of the simple class. Performance of the optimum quantizer is obtained for standard normal distribution and Laplacian distribution with unit variance. It is compared with two kinds of linear quantizers. One is ordinary linear quantizer and the other is equi-interthreshold quantizer with optimized reconstruction levels. Detailed comparisons seem to show that equi-interthreshold quantizer has the most recommendable performance, at least for the pdf's examined here.

Publication: IEICE TRANSACTIONS on transactions Vol.E68-E No.5 pp.309-316

Publication Date: 1985/05/25

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Type of Manuscript: PAPER

Category: Communication Theory

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Hiroyasu SAKAMOTO
Teiji OHTA
Hiroshi KONDO

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Hiroyasu SAKAMOTO, Teiji OHTA, Hiroshi KONDO, "A Method and Performance of the Optimum Scalar Quantizer for a Simple Class of Probability Density" in IEICE TRANSACTIONS on transactions, vol. E68-E, no. 5, pp. 309-316, May 1985, doi: .
Abstract: A design method of rate-distortion optimum scalar quantizer is developed, and performance of the optimum quantizer is compared with those of linear quantizers using mean square error and output entropy, for a simple class of probability density function (pdf.). The simple class means that pdf. is unimodal and symmetric about its mode value, and is differentiable in both sides of symmetry. The method proposed here is based on solving Kuhn-Tucker condition and is essentially the same as those reported before (by Berger or by Farvardin and Modestino), but is shown to be a more advantageous method. Moreover, it has the rules in what region the initial value must be given and how one stop of iteration is solved, and checkpoints for the existence and number of solutions, those have not been shown before except empirically. Without these rules, it seems to be very perplexed problem to check upon the solutions, and algorithm of calculation would be very complicated and time consuming, for even a pdf. of the simple class. Performance of the optimum quantizer is obtained for standard normal distribution and Laplacian distribution with unit variance. It is compared with two kinds of linear quantizers. One is ordinary linear quantizer and the other is equi-interthreshold quantizer with optimized reconstruction levels. Detailed comparisons seem to show that equi-interthreshold quantizer has the most recommendable performance, at least for the pdf's examined here.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e68-e_5_309/_p

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@ARTICLE{e68-e_5_309,
author={Hiroyasu SAKAMOTO, Teiji OHTA, Hiroshi KONDO, },
journal={IEICE TRANSACTIONS on transactions},
title={A Method and Performance of the Optimum Scalar Quantizer for a Simple Class of Probability Density},
year={1985},
volume={E68-E},
number={5},
pages={309-316},
abstract={A design method of rate-distortion optimum scalar quantizer is developed, and performance of the optimum quantizer is compared with those of linear quantizers using mean square error and output entropy, for a simple class of probability density function (pdf.). The simple class means that pdf. is unimodal and symmetric about its mode value, and is differentiable in both sides of symmetry. The method proposed here is based on solving Kuhn-Tucker condition and is essentially the same as those reported before (by Berger or by Farvardin and Modestino), but is shown to be a more advantageous method. Moreover, it has the rules in what region the initial value must be given and how one stop of iteration is solved, and checkpoints for the existence and number of solutions, those have not been shown before except empirically. Without these rules, it seems to be very perplexed problem to check upon the solutions, and algorithm of calculation would be very complicated and time consuming, for even a pdf. of the simple class. Performance of the optimum quantizer is obtained for standard normal distribution and Laplacian distribution with unit variance. It is compared with two kinds of linear quantizers. One is ordinary linear quantizer and the other is equi-interthreshold quantizer with optimized reconstruction levels. Detailed comparisons seem to show that equi-interthreshold quantizer has the most recommendable performance, at least for the pdf's examined here.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - A Method and Performance of the Optimum Scalar Quantizer for a Simple Class of Probability Density
T2 - IEICE TRANSACTIONS on transactions
SP - 309
EP - 316
AU - Hiroyasu SAKAMOTO
AU - Teiji OHTA
AU - Hiroshi KONDO
PY - 1985
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E68-E
IS - 5
JA - IEICE TRANSACTIONS on transactions
Y1 - May 1985
AB - A design method of rate-distortion optimum scalar quantizer is developed, and performance of the optimum quantizer is compared with those of linear quantizers using mean square error and output entropy, for a simple class of probability density function (pdf.). The simple class means that pdf. is unimodal and symmetric about its mode value, and is differentiable in both sides of symmetry. The method proposed here is based on solving Kuhn-Tucker condition and is essentially the same as those reported before (by Berger or by Farvardin and Modestino), but is shown to be a more advantageous method. Moreover, it has the rules in what region the initial value must be given and how one stop of iteration is solved, and checkpoints for the existence and number of solutions, those have not been shown before except empirically. Without these rules, it seems to be very perplexed problem to check upon the solutions, and algorithm of calculation would be very complicated and time consuming, for even a pdf. of the simple class. Performance of the optimum quantizer is obtained for standard normal distribution and Laplacian distribution with unit variance. It is compared with two kinds of linear quantizers. One is ordinary linear quantizer and the other is equi-interthreshold quantizer with optimized reconstruction levels. Detailed comparisons seem to show that equi-interthreshold quantizer has the most recommendable performance, at least for the pdf's examined here.
ER -