Skip to main content
SpringerLink
Log in

Lattices based on linear codes

  • 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:

  • 150 Accesses

Abstract

The Conway and Sloane construction A method is applied to evaluation of a class of lattices. The points of the lattices belong to a scaled set of n-dimensional vectors with integer components and the lattices constructed with the aide of linear over GF(p) codes, p is prime. It is known that the Minkowski-Hlawka bound on the normalized logarithm of packing density is attained asymptotically by such construction of lattices. We show that the capacity of an AWGN channel without restriction can be also attained by these class of lattices.

This research was supported by the Ministry of Science and Technology.

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. G. Poltyrev, ”On Coding without Restrictions for the AWGN Channel”, to be appear in IEEE Trans. Information Theory.

    Google Scholar 

  2. J.A. Rush and N.J. Sloane, “An Improvement to the Minkowski Hlawka Bound for Packing Superballs,” Mathematika, vol. 34, pp. 8–18, 1987.

    Google Scholar 

  3. J.A. Rush, “A lower bound on packing density,” Inventiones mathematicae, vol. 98, pp. 499–509, 1989.

    Google Scholar 

  4. R. Gallager “Low-density parity-check codes”, M.I.T.Press, Cambridge, Massachusets, 1963.

    Google Scholar 

  5. H. Herzberg and G. Poltyrev, ”Techniques for Bounding the Probability of Decoding Error in Block Coded Modulation Structures”, to be appear in IEEE Trans. Information Theory.

    Google Scholar 

  6. C.E. Shannon, “Probability of error for optimal codes in a Gaussian channel,” Bell Syst. Tech. J., vol. 38, pp. 611–656, May 1959.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering - Systems, Tel Aviv University, 69978, Ramat Aviv, Israel

    Gregory Poltyrev

Authors
  1. Gregory Poltyrev
    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

Poltyrev, G. (1994). Lattices based on linear codes. 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_22

Download citation

  • DOI: https://doi.org/10.1007/3-540-57843-9_22

  • 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