Skip to main content
SpringerLink
Log in

Quantizing and decoding for usual lattices in the L p -metric

  • Sphere Packings and Lattices
  • Conference paper
  • First Online:
Algebraic Coding (Algebraic Coding 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 781))

Included in the following conference series:

  • 140 Accesses

Abstract

We generalize the Conway-Sloane algorithm for the decoding of usual lattices to the L p norm. In particular, the Voronoi diagrams and covering radii of some of these lattices, namely ℤn, Dn, D *n A n, are computed. Some of the results hold only for the L 1-metric.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Bourbaki. Groupes et algèbres de Lie, Chapitres 4, 5 et 6. Hermann, 1968.

    Google Scholar 

  2. J.H. Conway and N.J.A. Sloane. Spheres packings, lattices and groups. Springer-Verlag, 1st edition, 1988.

    Google Scholar 

  3. J.H. Conway and N.J.A. Sloane. The cell structures of certain lattices. In P. Hilton, F. Hirzebruch, and R. Remmert, editors, Miscellanea mathematica, pages 71–107. Springer-Verlag, 1991.

    Google Scholar 

  4. J.H. Conway and N.J.A. Sloane. Fast quantizing and decoding algorithms for lattices quantizers and codes. IEEE Trans. Inform. Theory, 28(2):227–232, March 92.

    Google Scholar 

  5. H.S.M. Coxeter. Regular Polytopes. Dover, 3rd edition, 1973.

    Google Scholar 

  6. N. Farvardin and J.W. Modestino. Optimum quantizer performance for a class of nongaussian memoryless sources. IEEE Trans. Inform. Theory, 30:485–497, May 84.

    Google Scholar 

  7. Robert M. Gray. Source coding theory. Kluwer academic publishers, 1990.

    Google Scholar 

  8. M. Vedat Eyuboğlu and G. David Forney. Lattice and trellis quantization with latticeand trellis-bounded codebooks-high-rate theory for memoryless sources. IEEE Trans. Inform. Theory, 39(1):46–59, January 93.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. I3S, 250 avenue Albert Einstein, 06560, Valbonne, France

    P. Loyer & P. Solé

Authors
  1. P. Loyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Solé
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. Cohen S. Litsyn A. Lobstein G. Zémor

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Loyer, P., Solé, P. (1994). Quantizing and decoding for usual lattices in the L p -metric. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-57843-9_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57843-7

  • Online ISBN: 978-3-540-48357-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation