MULTIDIMENSIONAL LOGARITHMIC SPHERICAL ΜU-LAW QUANTIZATION

Authors

  • ANDREJA SAMČOVIĆ University of Belgrade – Transport and Traffic Engineering, Vojvode Stepe 305, Belgrade Author

Keywords:

Logarithmic spherical quantization

Abstract

Several researchers considered logarithmic spherical signal quantization. The design of a logarithmic spherical quantizer in k dimensions is considered in this paper. Logarithmic quantization is here used for vectors consisting of samples in sphere coordinates. The combination of logarithmic and spherical quantization (LSQ) is an efficient multi-dimensional quantization method at a high dynamic range, by preserving the original signal as close as possible.  The signal-to-noise ratio (SNR) and its dependence on the sphere dimension at lower bit rates are derived and discussed in this paper.

References

(1) D. Neuhoff, Quantization, IEEE Transactions on Information Theory, 44, 6, pp. 2325-2383 (1998).

(2) Gersho, R. M. Gray, Vector Quantization and Signal Compression, Boston: Kluwer (1992).

(3) S. Preihs, T. Lamprecht, J. Ostermann, Error robust low delay audio coding using spherical logarithmic quantization, in 24th European Signal Processing Conference (EUSIPCO), pp. 1970-1974, Budapest, Hungary, (29 August-2 September 2016).

(4) H. Kruger, R. Schreiber, B. Geiser, P. Vary, On logarithmic spherical vector quantization, in International Symposium on Information theory and its applications ISITA 2008, Auckland, New Zelland, (7-10 December 2008).

(5) P. Swaszek, J. B. Thomas, Multidimensional spherical coordinates quantization, IEEE Transactions on Information Theory, 29, 4, pp. 570-576 (July 1983).

(6) J. Hamkins, K. Zegger, Gaussian source coding with spherical codes, IEEE Transactions on Information Theory, 48, 11, pp. 2980-2989 (November 2002).

(7) J. Conway, N. Sloane, Sphere Packings, Lattices and Groups, Springer (1993).

(8) Z. Perić, J. Lukić, J. Nikolić, D. Denić, Design of nonuniform dead-zone quantizer with low number of quantization levels for the Laplacian source, Rev. Roum. Sci. Techn - Elektrotechn. et Energ., 58, 1, pp. 93-100 (2013).

(9) H. H. Henning, J. W. Pan, D2 channel bank: System aspects, The Bell System Technical Journal, 51, 8, pp. 1641-1657 (1972).

(10) N. S. Jayant, P. Noll, Digital Coding of Waveforms, Englewood Cliffs, NJ: Prentice-Hall (1984).

(11) Z. Perić, D. Aleksić, M. Stefanović, J. Nikolić, New approach to support region determination of the μ-law quantizer, Elektronika Ir Elektrotechnika, 19, 8, pp. 111-114 (2013).

(12) Z. Perić, D. Aleksić, Quasilogarithmic quantizer for Laplacian source: supporting region ubiquitous optimization task, Rev. Roum. Sci. Techn - Elektrotechn. et Energ., 64, 4, pp. 403-408 (2019).

(13) J. B. Huber, B. Matschkal, Spherical logarithmic quantization and its application for DPCM, in 5th International ITG Conference on source and channel coding, pp. 349-356, Erlangen, Germany (January 2004).

(14) B. Matschkal, F. Bergner, J. B. Huber, Joint signal processing for spherical logarithmic quantization and DPCM, in 6th International ITG Conference on source and channel coding, Munich, Germany (April 2006).

(15) Z. Utkovski, A. Utkovski, T. Eriksson, High-dimensional spherical quantization of Gaussian sources, in Canadian Workshop on Information Theory, pp. 211-214, Montreal, Quebec (June 2005).

(16) J. Hamkins, Design and analysis of spherical codes, Ph.D. dissertation, University Illinois at Urbana-Champaign, USA (September 1996).

(17) H. S. M. Coxeter, Regular Polytopes, 3rd edition, New York: Dover (1973).

Downloads

Published

01.07.2022

Issue

Section

Électronique et transmission de l’information | Electronics & Information Technology

How to Cite

MULTIDIMENSIONAL LOGARITHMIC SPHERICAL ΜU-LAW QUANTIZATION. (2022). REVUE ROUMAINE DES SCIENCES TECHNIQUES — SÉRIE ÉLECTROTECHNIQUE ET ÉNERGÉTIQUE, 67(2), 157-160. https://journal.iem.pub.ro/rrst-ee/article/view/163