PIECEWISE UNIFORM PRODUCT POLAR QUANTIZATION

Authors

  • Zoran H. Peric
  • Daniela M. Milovic

DOI:

https://doi.org/10.47839/ijc.2.3.245

Keywords:

Asymptotical analysis, piecewise uniform product polar quantization, optimal distortion

Abstract

In this paper, simple and complete asymptotical analysis is given for a piecewise uniform product polar quantizer (PUPPQ) with respect to mean-square error (MSE) i.e. distortion (D). PUPPQ is based on uniform product polar quantizers. PUPPQ consists of L different uniform product polar quantizers. Uniform product polar quantizer conditions for optimality and all main equations for number of phase divisions and optimal number of levels for each partition are presented. These systems, although not optimal, may have asymptotic performance close to the optimum. Furthermore, the analysis and implementation can be simpler than those of optimal systems. PUPPQ has implementation complexity between optimal nonuniform polar quantization (NPQ) and uniform product polar quantization (UPPQ). The gain of PUPPQ over optimum uniform product polar quantization is also obtained (2 dB for the rate of 8 bits/sample).

References

W. A. Pearlman, “Polar quantization of complex Gaussian random variable,“ IEEE Trans. Commun., vol. COM-27, pp. 892-899, June 1979.

P. F. Swaszek, “Uniform spherical coordinate quantization of spherically symmetric sources” , IEEE Trans. Commun., vol. COM-33, pp. 518-521, June 1985.

P. W. Moo, D. L. Neuhoff, "Uniform Polar Quantization Revisited," In Proc. IEEE Int. Symp. Information Theory ISIT’98, pp. 100, Cambridge, USA, August 1998.

P. F. Swaszek, T. W. Ku, “Asymptotic Performance of Unrestricted Polar Quantizer”, IEEE Transactions on Information Theory, vol. 32, pp. 330-333, 1986.

D. Hui, D. L. Neuhoff, "Asymmptotic Analysis of Optimal Fixed-Rate Uniform Scalar Quantization," IEEE Transaction on Information Theory, vol.47, pp. 957-977, March 2001.

S. Na, D. L. Neuhoff, "On the Support of MSE-Optimal, Fixed-Rate Scalar Quantizers" IEEE Transaction on Information Theory, vol.47, pp. 2972-2982, November 2001.

F. Kuhlmann and J. A. Bucklew, “Piecewise Uniform Vector Quantizers”, IEEE Transactions on Information Theory, vol. 34, pp. 1259-1263, 1988.

P. F. Swaszek, “Unrestricted Multistage Vector Quantizers”, IEEE Transactions on Information Theory, vol. 38, pp. 1169-1174, 1992.

R. M. Gray and D. L. Neuhoff, "Quantization", IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2325-2384, October 1998.

S. Na D. L. Neuhoff, "Bennett’s Integral for Vector Quantizers," IEEE Transaction on Information Theory, vol.41, pp. 886-900, July 1995.

A. Gersho and R. M. Gray, "Vector Quantization and signal Compression", Kluwer Academ.Pub(1992).

A. Gersho, “Asymptotically Optimal Block Quantization” IEEE Transaction on Information Theory, vol.25 pp. 373-380, July 1979.

N. S. Jayant and P. Noll, "DIGITAL CODING OF WAVEFORMS Principles and Applications to Speech and Video", Prentice-Hall, New Jersey (1984).

Z. H. Peric, J. D. Jovkovic, “Application of the Optimal Uniform Polar Quantization on Complex Reflectivity Function” Advances in Electrical and Computer Engineering, vol.2 (9) Nr 1(17), pp. 80-85,2002.

D. Minoli, "Voice Over MPLS Planning and Designing Networks", McGraw-Hill.Pub(2002).

D. G. Jeong, J. Gibson" Uniform and Piecewise Uniform Lattice Vector Quantization for Memoryless Gaussian and Laplacian Sources", IEEE Trans., 1993, IT-39(3), pp. 786-804.

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Published

2014-08-01

How to Cite

Peric, Z. H., & Milovic, D. M. (2014). PIECEWISE UNIFORM PRODUCT POLAR QUANTIZATION. International Journal of Computing, 2(3), 144-152. https://doi.org/10.47839/ijc.2.3.245

Issue

2003, Volume 2, Issue 3

Section

Articles

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