Fast Quantizing and Decoding Algorithms for Lattice Quantizers and Codes

IEEE Transactions on Information Theory

Volumn 28, Issue 2, 1982, Pages 227-232

  Conway, J H ^a   Sloane, N J A ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CODES, SYMBOLIC - ENCODING;

QUANTIZATION;

DATA CONVERSION, ANALOG TO DIGITAL;

EID: 0020102220     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1982.1056484     Document Type: Article

References (18)

1. T. Berger, “Optimum quantizers and permutation codes,” IEEE Trans. Inform. Theory, vol. IT-18, no. 6, 759–765, Nov. 1972.
2. N. Bourbaki, Groupes et Algebres de Lie, Chapitres 4, 5 et 6. Paris: Hermann, 1968.
3. J. A. Bucklew, “Companding and random quantization in several dimensions,” IEEE Trans. Inform. Theory, vol. IT-27, no. 2, 207–211, March 1981.
4. J. W. S. Cassels, An Introduction to the Geometry of Numbers. New York: Springer-Verlag, 1971.
5. I. H. Conway and N. J. A. Sloane, “On the enumeration of lattices of determinant one,” J. Number Theory, to be published.
6. J. H. Conway and N. J. A. Sloane, “Voronoi regions of lattices, second moments of polytopes, and quantization,” IEEE Trans. Inform. Theory, this issue on pp. 211–226.
7. H. S. M. Coxeter, Regular Polytopes, 3rd ed. New York: Dover, 1973.
8. N. C. Gallagher, Jr., and J. A. Bucklew, “Some recent developments in quantization theory,” in Proc. 12th Annu. Sympos. System Theory, Virginia Beach, VA, May 19–20, 1980.
9. A. Gersho, “Asymptotically optimal block quantization,” IEEE Trans. Inform. Theory, vol. IT-25, no. 4, 373–380, July 1979.
10. D. E. Knuth, The Art of Computer Programming, vol. 3, Sorting and Searching. Reading, MA: Addison-Wesley, 1973.
11. J. Leech and N. J. A. Sloane, “Sphere packing and error-correcting codes,” Canad. J. Math., 23, 718–745, 1971.
12. H. V. Niemeier, “Definite quadratische Formen der Dimension 24 und Diskriminante 1,” J. Number Theory, 5, 142–178, 1973.
13. E. M. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1977.
14. K. D. Rines and N. C. Gallagher, Jr., “The design of multidimensional quantizers using prequantization,” in Proc. 18th Allerton Conf. Commun., Control, and Computing, Univ. of Illinois, Monticello, IL, Oct. 8–10, 1980, pp. 446–453.
15. N. J. A. Sloane, “Binary codes, lattices and sphere packings,” in Combinatorial Surveys (Proc. 6th British Combinatorial Conference), P. J. Cameron, Ed. London and New York: Academic, 1977, pp. 117–164.
16. N. J. A. Sloane, “Tables of sphere packings and spherical codes,” IEEE Trans. Inform. Theory, vol. IT-27, no. 3, 327–338, May 1981.
17. Y. Yamada, S. Tazaki, and R. M. Gray, “Asymptotic performance of block quantizers with difference distortion measures,” IEEE Trans. Inform. Theory, vol. IT-26, no. 1, 5–14, Jan. 1980.
18. P. Zador, “Topics in the asymptotic quantization of continuous random variables,” IEEE Trans. Inform. Theory, this issue on pp. 139–149.