Skip to main content

Convolutional codes and their decoding

  • Chapter
Codes and Turbo Codes

Part of the book series: Collection IRIS ((IRIS))

  • 1443 Accesses

Abstract

It was in 1955 that Peter Elias introduced the notion of convolutional code [5.5]. The example of an encoder described is illustrated in Figure 5.1. It is a systematic encoder, that is, the coded message contains the message to be transmitted, to which redundant information is added. The message is of infinite length, which at first sight limits the field of application of this type of code. It is however easy to adapt it for packet transmissions thanks to tail-biting techniques.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Transactions on Information Theory, IT-20:284–287, March 1974.

    Article  MathSciNet  Google Scholar 

  2. G. Battail. Weighting of the symbols decoded by the viterbi algorithm. Annals of Telecommunications, 42(1–2):31–38, Jan.–Feb. 1987.

    Google Scholar 

  3. C. Berrou, P. Adde, E. Angui, and S. Faudeuil. A low complexity softoutput viterbi decoder architecture. In Proceedin gs of IEEE In t ern at ion al Conference on Communications (ICC′93), pages 737–740, GENEVA, May 1993.

    Google Scholar 

  4. C. Berrou, A. Glavieux, and P. Thitimajshima. Near shannon limit errorcorrecting coding and decoding: turbo-codes. In Proceedings of IEEE In ternational Conference on Communications (ICC′93), pages 1064–1070, GENEVA, May 1993.

    Google Scholar 

  5. P. Elias. Coding for noisy channels. IRE Convention Records, 3(4):37–46, 1955.

    MathSciNet  Google Scholar 

  6. R. M. Fano. A heuristic discussion of probabilistic decoding. IEEE Transactions on Information Theory, IT-9:64–74, Apr. 1963.

    Article  MathSciNet  Google Scholar 

  7. G. D. Forney. Convolutional codes i: Algebraic structure. IEEE Transactions on Information Theory, IT-16:720–738, Nov. 1970.

    Article  MathSciNet  Google Scholar 

  8. G. D. Forney. The viterbi algorithm. Proceedings of the IEEE, 61(3):268–278, March 1973.

    Article  MathSciNet  Google Scholar 

  9. A. Glavieux. Codage de canal, des bases théoriques aux turbocodes. Hermès-Science, 2005.

    Google Scholar 

  10. J. Hagenauer and P. Hoeher. A viterbi algorithm with soft-decision outputs and its applications. In Proceedings of IEEE Global Com m un ications Conference (Globecom′89), pages 1680–1686, Dallas, Texas, USA, Nov. 1989.

    Google Scholar 

  11. R. Johannesson and K. Sh. Zigangirov. Fundamentals of Convolutional Coding. Piscataway, IEEE Press, 1999.

    Chapter  Google Scholar 

  12. H. H. Ma and J. K. Wolf. On tail-biting convolutional codes. IEEE Transactions on Communications, COM-34:104–111, Feb. 1986.

    Article  Google Scholar 

  13. P. Thitimajshima. Les codes convolutifs récursifs systématiques et leur application à la concaténation parallèle. Phd thesis, Université de Bretagne Occidentale, Dec. 1993.

    Google Scholar 

  14. A. J. Viterbi. Coding for noisy channels. IEEE Transactions on Information Theory, IT-13:260–269, Apr. 1967.

    Article  Google Scholar 

  15. J. M. Wozencraft. Sequential decoding for reliable communication. IRE National Convention Records, 5 part 2(2):11–25, 1957.

    Google Scholar 

Download references

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag France, Paris

About this chapter

Cite this chapter

(2010). Convolutional codes and their decoding. In: Berrou, C. (eds) Codes and Turbo Codes. Collection IRIS. Springer, Paris. https://doi.org/10.1007/978-2-8178-0039-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-2-8178-0039-4_5

  • Publisher Name: Springer, Paris

  • Print ISBN: 978-2-8178-0038-7

  • Online ISBN: 978-2-8178-0039-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics