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On the Characteristics of MSE-Optimal Symmetric Scalar Quantizers for the Generalized Gamma, Bucklew-Gallagher, and Hui-Neuhoff Sources
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 Title & Authors
On the Characteristics of MSE-Optimal Symmetric Scalar Quantizers for the Generalized Gamma, Bucklew-Gallagher, and Hui-Neuhoff Sources
Rhee, Jagan; Na, Sangsin;
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 Abstract
The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.
 Keywords
scalar quantization;generalized gamma source;Bucklew-Gallagher source;Hui-Neuhoff source;asymptotic formulas;MSE distortion;
 Language
English
 Cited by
 References
1.
S. Yoo and S. Y. Kim, "Conversion loss for the quantizer of GPS civil receiver in heavy wideband gaussian noise environments," J. KICS, vol. 38A, no. 9, pp. 792-797, Sept. 2013. crossref(new window)

2.
D. Lee and W. Sung, "Adaptive quantization scheme for multi-level cell NAND flash memory," J. KICS, vol. 38C, no. 6, pp. 540-549, Jun. 2013. crossref(new window)

3.
B. Hong and W. Choi, "Distributed MIMO systems based on quantize-map-and-forward (QMF) relaying," J. KICS, vol. 39A, no. 7, pp. 404-412, Jul. 2014. crossref(new window)

4.
P. F. Panter and W. Dite, "Quantization distortion in pulse-count modulation with nonuniform spacing of levels," in Proc. IRE, vol. 39, pp. 44-48, 1951.

5.
J. A. Bucklew and N. C. Gallagher, "Some properties of uniform step size quantizers," IEEE Trans. Inf. Theory, vol. 26, pp. 610-613, 1980. crossref(new window)

6.
J. A. Bucklew and G. L. Wise, "Multidimensional asymptotic quantization theory with $\gamma$ th power distortion measures," IEEE Trans. Inf. Theory, vol. 28, pp. 239-247, 1982. crossref(new window)

7.
D. Hui and D. L. Neuhoff, "Asymptotic analysis of optimal fixed-rate uniform scalar quantization," IEEE Trans. Inf. Theory, vol. 47, pp. 957-977, 2001. crossref(new window)

8.
S. Na and D. L. Neuhoff, "On the support of MSE-optimal, fixed-rate, scalar quantizers," IEEE Trans. Inf. Theory, vol. 47, pp. 2972-2982, 2001. crossref(new window)

9.
S. Na and D. L. Neuhoff, "Asymptotic MSE distortion of mismatched uniform scalar quantization," IEEE Trans. Inf. Theory, vol. 58, pp. 3169-3181, 2012. crossref(new window)

10.
J. Rhee and S. Na, "Asymptotic characteristics of MSE-optimal scalar quantizers for generalized gamma sources," J. KICS, vol. 37, no. 5, pp. 279-289, May 2012. crossref(new window)

11.
S. P. Lloyd, "Least squares quantization in PCM," IEEE Trans. Inf. Theory, vol. 28, pp. 129-137, 1982. crossref(new window)

12.
J. Max, "Quantizing for minimum distortion," IRE Trans. Inf. Theory, vol. 46, pp. 7-12, 1960.

13.
E. W. Stacy, "A generalization of the gamma distribution," Ann. Math. Stat., vol. 33, no. 3, pp. 1187-1192, Sept. 1962. crossref(new window)

14.
F. W. J. Olver, Asymptotics and Special Functions, 2nd Ed., A K Peters/CRC Press, 1997.