Skip to main content
SpringerLink
Log in

Enumeration of convolutional codes and minimal encoders

  • Conference paper
  • First Online:
Crytography and Coding (Cryptography and Coding 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1355))

Included in the following conference series:

  • 119 Accesses

Abstract

A full analysis of equivalent encoders is presented which is subsequently used to enumerate the minimal encoders generating a convolutional code. We extend the known results on rate 1/n minimal encoders to the rate k/n case and derive enumerators for minimal encoders, canonical systematic encoders and Convolutional codes. Numerical results show that the majority of codes have minimal encoders whose overall constraint length is more of less evenly distributed among the k rows and these codes are more likely to have good distance properties.

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.D. Forney, Jr., “Convolutional codes I: Algebraic structure,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 720–738, Nov. 1970. Correction in IEEE Trans. Inform. Theory, vol. IT-17, No. 3, p. 360, May 1971.

    Article  Google Scholar 

  2. W.J. Rosenberg, Structural Properties of Convolutional Codes, Ph.D. dissertation, University of California, Los Angeles, 1971.

    Google Scholar 

  3. G.D. Forney, Jr., Unpublished material.

    Google Scholar 

  4. T.J. Shusta, “Enumeration of minimal convolutional encoders,” IEEE Trans. Inform. Theory, vol. IT-23, No. 1, pp. 127–132, Jan. 1977.

    Article  Google Scholar 

  5. E. Paaske, “Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4,” IEEE Trans. Inform. Theory, vol. IT-20, No. 5, pp. 683–9, Sept. 1974.

    Article  Google Scholar 

  6. D.G. Daut, J.W. Modestino and L.D. Wismer, “New short constraint length convolutional code constructions for selected rational rates,” IEEE Trans. Inform. Theory, vol. IT-28, No. 5, pp.794–800, Sept. 1982.

    Article  Google Scholar 

  7. M. Cedervall and R. Johannesson, “A fast algorithm for computing distance spectrum of convolutional codes,” IEEE Trans. Inform. Theory, vol. IT-35, No. 6, pp. 1146–1159, Nov. 1989.

    Article  Google Scholar 

  8. G. Seguin, “A random coding bound for fixed convolutional codes of rate 1/n,” IEEE Trans. Inform. Theory, vol. IT-40, No. 4, pp. 1668–1670, Sept. 1994.

    Article  MathSciNet  Google Scholar 

  9. G.D. Forney, Jr., “Minimal bases of rational vector spaces, with applications to multivariable linear systems,” SIAM J. Control, vol. 13, pp.493–520, May 1975.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electronic Engineering, University of Limerick, Limerick, Ireland

    Conor P. O'Donoghue & Cyril J. Burkley

Authors
  1. Conor P. O'Donoghue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cyril J. Burkley
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michael Darnell

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

O'Donoghue, C.P., Burkley, C.J. (1997). Enumeration of convolutional codes and minimal encoders. In: Darnell, M. (eds) Crytography and Coding. Cryptography and Coding 1997. Lecture Notes in Computer Science, vol 1355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024471

Download citation

  • DOI: https://doi.org/10.1007/BFb0024471

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63927-5

  • Online ISBN: 978-3-540-69668-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation