Distances and distance bounds for convolutional codes—an overview

  • Rolf Johannesson
  • Kamil Sh. Zigangirov
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 128)


In this paper we give a self-contained overview of known distance measures for convolutional codes and of upper and lower bounds on the free distance. The upper bounds are valid for general trellis codes and for convolutional codes, respectively. The lower bound is valid for time-varying convolutional codes. We also present a new lower bound on the distance profile for fixed convolutional codes.


Random Walk Block Code State Diagram Convolutional Code Trellis Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [CeJ88]
    Cedervall, M. and Johannesson, R. (1988), A FAST algorithm for computing distance spectrum of convolutional codes. Submitted to IEEE Trans. Inform. Theory. May 1988.Google Scholar
  2. [ChC76]
    Chevillat, P. R. and Costello, D. J., Jr. (1976), Distance and computing in sequential decoding. IEEE Trans. Commun., COM-24:440–447.Google Scholar
  3. [Cos69]
    Costello, D. J., Jr. (1969), A construction technique for random-error-correcting convolutional codes. IEEE Trans. Inform. Theory, IT-19:631–636.Google Scholar
  4. [Cos74]
    Costello, D. J., Jr. (1974), Free distance bounds for convolutional codes. IEEE Trans. Inform. Theory, IT-20:356–365.Google Scholar
  5. [For67]
    Forney, G. D., Jr. (1967), Review of random tree codes (NASA Ames. Res. Cen., Contract NAS2-3637, NASA CR 73176, Final Rep.;Appx A). See also Forney, G. D., Jr. (1974), Convolutional codes II. Maximumlikelihood decoding and convolutional codes III: Sequential decoding. Inform Contr., 25:222–297.Google Scholar
  6. [For70]
    Forney, G. D., Jr. (1970), Convolutional codes I: Algebraic structure. IEEE Trans. Inform. Theory, IT-16:720–738.Google Scholar
  7. [Gol67]
    Golomb, S. W. (1967), Shift Register Sequences, Holden-Day, San Fransisco, 1967. Revised ed., Aegean Park Press, Laguna Hills, Cal., 1982.Google Scholar
  8. [Gri60]
    Griesmer, J. H. (1960), A bound for error-correcting codes. IBM J. Res. Develop., 4:532–542.Google Scholar
  9. [Hel68]
    Heller, J. A. (1968), Short constraint length convolutional codes. Jet Propulsion Lab., California Inst. Technol., Pasadena, Space Programs Summary 37–54, 3:171–177.Google Scholar
  10. [Joh75]
    Johannesson, R. (1975), Robustly optimal rate one-half binary convolutional codes. IEEE Trans. Inform. Theory, IT-21:464–468.Google Scholar
  11. [LaM70]
    Layland, J. and McEliece, R. (1970), An upper bound on the free distance of a tree code. Jet Propulsion Lab., California Inst. Technol., Pasadena, Space Programs Summery 37–62, 3:63–64.Google Scholar
  12. [MaC71]
    Massey, J. L. and Costello, D. J., Jr. (1971), Nonsystematic convolutional codes for sequential decoding in space applications. IEEE Trans. Commun. Technol., COM-19:806–813.Google Scholar
  13. [Mas75]
    Massey, J. L. (1975), Error bounds for tree codes, trellis codes, and convolutional codes with encoding and decoding procedures, in G. Longo (ed.), Coding and Complexity—CISM Courses and Lectures No. 216, Springer Verlag, Wien.Google Scholar
  14. [MaS68]
    Massey, J. L. and Sain, M. K. (1968), Inverses of linear sequential circuits. IEEE Trans. Comput., C-17:330–337.Google Scholar
  15. [Vit71]
    Viterbi, A. J. (1971), Convolutional codes and their performance in communication systems. IEEE Trans. Commun. Technol., COM-19:751–772.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Rolf Johannesson
    • 1
  • Kamil Sh. Zigangirov
    • 2
  1. 1.Department of Information TheoryUniversity of LundLundSweden
  2. 2.Institute for Problems of Information TransmissionUSSR Academy of SciencesMoscow GSP-4USSR

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