On lattice quantization noise

IEEE Transactions on Information Theory

Volumn 42, Issue 4, 1996, Pages 1152-1159

  Zamir, Ram ^a,b   Feder, Meir ^a,c  

^a IEEE

^b University of California   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Divergence from Gaussianity; Lattice; Normalized second moment; Quantization noise; Shaping

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); ERRORS; MATHEMATICAL MODELS; OPTIMIZATION; RANDOM PROCESSES; SIGNAL DISTORTION; SPURIOUS SIGNAL NOISE; VECTORS;

EUCLIDEAN NORM; LATTICE QUANTIZATION NOISE; LINEAR TRANSFORMATION; VORONOI PARTITION;

VECTOR QUANTIZATION;

EID: 0030191118     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.508838     Document Type: Article

References (24)

1. W. R. Bennett, "Spectra of quantized signals," Bell Syst. Tech. J., vol. 27, pp. 446-472. July, 1948.
2. T. Berger, Rate Distortion Theory: A Mathematical Basis far Data Compression. Englewood Cliffs, NJ: Prentice-Hall, 1971.
3. A. R. Calderbank, P. C. Fishburn, and A. Rabinovieh, "Covering properties of convolutional codes and associated lattices," IEEE Trans. Inform. Theory, vol. 41, no. 3, pp. 732-746, May 1995.
4. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. New York: Springer-Verlag, 1988.
5. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
6. P. Diaconis and D. Freedman, "A dozen de-Finetti-style results in search for a theory." Ann. Inst. H. Poincaré, Prob. Stat., vol. 23, suppl. 2, pp. 397-423, 1987.
7. R. Durrett, Probability Teory and Examples. Pacific Grove, CA: Wadsworth and Brooks, 1989.
8. A. Gersho, "Asymptotically optimal block quantization," IEEF, Trans. Inform. Theory, vol. IT-25, pp. 373-380, July 1979.
9. A. Gersho and R. M. Gray. Vector Quantization and Signal Compression. Boston. MA: Kluwer, 1992.
10. R. M. Gray and Jr. T. J. Stockham, "Dithered quantizers," IEEE Trans. Inform. Theory, vol. 39, pp. 805-812, May 1993.
11. A. Kirac and P. P. Vaidyanathan. "Results on lattice quantization with dithering," IEEE Trans. Circuits Syst., submitted.
12. D. H. Lee and D. L. Neuhoff, "Asymptotic distribution of the errors in scalar and vector quantizers," IEEE Trans. Inform. Theory, vol. 42, no.2, pp. 446-460, March 1996.
13. Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer design," IEEE Trans. Commun., vol. COM-28, pp. 84-95. Jan. 1980.
14. T. Linder and K. Zeger, "Asymptotic entropy constrained performance of tesselating and universal randomized lattice quantization," IEEE Trans. Information Theory, vol 40, pp. 575-579, Mar. 1994.
15. S. P. Lloyd, "Least squares quantization in PCM," IEEE Trans. Inform. Theory, vol. IT-28, pp. 129-137, Mar. 1982 (originally presented at the Inst. of Math. Stat. Meet., 1957).
16. M. W. Marcellin and T. R. Fischer, "Trellis coded quantization of memoryless and Gauss-Markov sources," IEEE Trans. Commun., vol. 38, pp. 82-93, Jan. 1990.
17. M. S. Pinsker, Information and Information Stability of Random Variables and Processes. San Francisco. CA: Holden Day, 1964.
18. _, private communications.
19. G. Poityrev, private communications.
20. P. Zador, "Asymptotic quantization error of continuous signals and their quantization dimension," IEEE Trans. Inform. Theory, vol IT-28, pp. 139-149, Mar. 1982 (previously an unpublished Bell Labs, memo, 1966).
21. R. Zamir and M. Feder, "On universal quantization by randomized uniform / lattice quantizer," IEEE Trans. Inform. Theory, vol. 38, pp. 428-436, Mar. 1992.
22. _, "Rate distortion performance in coding band-limited sources by sampling and dithered quantization," IEEE Trans. Inform. Theory, vol. 41. pp. 141-154, Jan. 1995.
23. _, "Information rates of pre/post filtered dithered quantizers," IEEE Trans. Inform. Theory, to be published in vol. 42, no.5, Sept. 1996.
24. _, "A matrix form of the Brunn-Minkowski inequality," in Proc. Int. Symp. on Information Theory (ISIT-95), (Whistler, BC, Canada, Sept. 1995), p. 71.