Skip to main content
SpringerLink
Log in

Iterative Decoding Algorithms

  • Chapter
Wireless Communications

Abstract

In this tutorial paper we present iterative algorithms which can be used for decoding of concatenated codes. The decoding operation is based on either a maximum a posteriori (MAP) algorithm or a Viterbi algorithm generating a weighted soft estimate of the input sequence. The iterative algorithm performs the information exchange between the two component decoders. The performance gain of the MAP algorithm over the Viterbi algorithm at low SNR leads to a slight performance advantage.

The MAP algorithm is computationally much more complex than the Viterbi algorithm. The operations in the MAP algorithm are multiplications and exponentiations while in the Viterbi algorithm they are simple add, compare and select operations.

As an example these algorithms are applied to decoding of turbo codes and their performance is compared on a Gaussian channel

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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.

References

  1. G. D. Forney, JR. “The Viterbi Algorithm”, Proceeding of IEEE, Vol. 61, No. 3, March 1973.

    Google Scholar 

  2. Yamamoto H. and Itoh K., “Viterbi Decoding for Convolutional Codes with Repeat Request”, IEEE on Inform. Theory, vol. IT-26, pp. 540–547, Sept. 1980.

    Google Scholar 

  3. J. Hagenauer, P. Hoeher, “A Viterbi Algorithm with Soft-Decision Outputs and its Applications,” Conf. Rec. GLOBECOM’89, Dallas, Texas, Vol. 3, pp. 47.1.1–47. 1. 7, Nov. 1989.

    Google Scholar 

  4. Y. Li, B. Vucetic and Y. Sato, “Optimum Soft Output Detection for Channels with Intersymbol Interference”, IEEE Trans. Inform. Theory, Vol-41, No-3, May 1995, p. 704–713.

    Google Scholar 

  5. Yunxin Li and Branka Vucetic, “A Low-complexity Soft-output TDMA Receiver”, TELFOR ‘95, Belgrade, 3–8 Dec. 1995, Yugoslavia.

    Google Scholar 

  6. Yunxin Li and Branka Vucetic, “A Genmeralized MLSE Algorithm”, INNSP ‘95, China, December 10–13, 1995.

    Google Scholar 

  7. T. Hashimoto “A list-Type Reduced-Constraint Generalization of the Viterbi Algorithm,” IEEE Trans. Inform. Theory, Vol. IT-33, No. 6, pp. 866–876, Nov. 1987.

    Google Scholar 

  8. B. Vucetic, “Bandwidth Efficient Concatenated Coding Schemes on Fading Channels” IEEE Trans. Commun., Jan. 1993.

    Google Scholar 

  9. T. Schaub and J.W. Modestino “An Erasure Declaring Viterbi Decoder and its Application to Concatenated Coding Systems,” ICC’86, IEEE Cat. No. CH23143/86, pp. 1612–1616, 1986

    Google Scholar 

  10. Branka Vucetic, Elvio Leonardo and Lin Zhang,”Soft Output Multistage Decoding of Multilevel Block Codes”, IEEE ITW’95 Proceedings, Ry-dzyna, Poland, June 15–19 1995.

    Google Scholar 

  11. N. Seshadri and C-E.W. Sundberg, “Generalized Viterbi Algorithms for Error Detection with Convolutional Codes,” Conf. Rec. GLOBECOM’89, Dallas, Texas, Vol$13, pp. 43.3.1–43. 3. 5, Nov. 1989.

    Google Scholar 

  12. C. Berrou, A. Glavieux and P. Thitimajshima, Near Shannon Limit Error-Correcting Coding and Decoding Turbo Codes (1), Proc. ICC’93, Geneva, Switzerland, pp. 1064–1070, May 1993.

    Google Scholar 

  13. S. Hirasawa et al, Modified Product Codes, IEEE Trans. Inform. Theory, Vol. IT-30, March 1984, pp. 299–306.

    Google Scholar 

  14. G.D. Forney, Concatenated Codes, MIT, Cambridge, MA, USA, 1966.

    Google Scholar 

  15. P. Elias, Error-free Coding, IEEE Trans. Inform. Theory, Vol. IT-4, pp. 29–37, Sept. 1954.

    Google Scholar 

  16. H. Imai and S. Hirakawa, A New Multilevel Coding Method Using Error-Correcting Codes”, IEEE Trans. Inform. Theory, Vol. IT-23, May 1975.

    Google Scholar 

  17. J. Hagenauer and P. Robertson, Iterative (Turbo) Decoding of Systematic Convolutional Codes with the MAP and SOVA Algorithms”, Proc. ITG Conf. Frankfurt, Germany, Oct. 1994.

    Google Scholar 

  18. S. Le Goff et al, Turbo Codes and High Spectral Efficiency Modulation, Proc. Globecom’94, San Francisco, California, USA, pp. 645–649, Dec. 1994.

    Google Scholar 

  19. P. Robertson, Illuminating the Structure of Code and Decoder of Parallel Concatenated Recursive Systematic (Turbo) Codes, Proc. Globecom’94, San Francisco, California, USA, pp. 1298–1303, Dec. 1994.

    Google Scholar 

  20. A.J. Viterbi and J.K. Omura, Principles of Digital Communications and Coding, New York McGraw Hill, 1979.

    Google Scholar 

  21. Claude Berrou and Alain Glavieux, Turbo-codes: General Principles and Applications, Audio and Video Digital Radio Broadcasing System and Techniques 1994, pp.215–226,

    Google Scholar 

  22. P. Jung, Novel Low Complexity Decoder for Turbo-Codes, Electronics Letters, 1995, Jan., Vol. 31, No. 2, pp. 86–87,

    Google Scholar 

  23. A.S. Barbulescu and S.S. Pietrobon, Terminating the Trellis of Turbo-Codes in the Same State, Electronics Letters, 1995, Jan., Vol. 31, No. 1, pp. 22–23

    Article  Google Scholar 

  24. P. Jung and M. Nabhan Performance Evaluation of Turbo Codes for Short Frame Transmission Systems, Electronics Letters, 1994, Jan., Vol. 30, No. 2, pp. 111–113

    Article  Google Scholar 

  25. Joachim Hagenauer and Lutz Papke, Iterative Decoding of Binary Block and Convolutional Codes, IEEE Trans. Inform. Theory, 1996, March, Vol. 42, No. 2, pp. 429–445.

    MATH  Google Scholar 

  26. S. Benedetto and G. Montorsi, Average Performance of Parallel Concatenated Block Codes, Electronics Letters, 1995, Feb., Vol. 31, No. 3, pp. 156–158.

    Article  Google Scholar 

  27. S. Benedetto and G. Montorsi, Performance Evaluation fo Turbo Codes, Electronics Letters, 1995, Feb., Vol. 31, No. 3, pp. 163–165.

    Google Scholar 

  28. S. Benedetto and G. Montorsi, Design of Parallel Concatenated Convolutional Codes, IEEE Trans. Commun. 1996, May, Vol. 44, No. 5, pp. 591–600.

    Article  MATH  Google Scholar 

  29. S. Benedetto, G. Montorsi, D. Divsalar and F. Pollara, Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding, TDA Progress Report 42–126, Aug. 1996.

    Google Scholar 

  30. S. Benedetto and G. Montorsi, Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes, IEEE Trans. Inform. Theory, Vol. 42, No. 2, March 1996, pp. 409–428.

    Article  MATH  Google Scholar 

  31. Claude Berrou, Patrick Adde, Ettiboua Angui and Stephane Faudeil, A Low Complexity Soft-Output Viterbi Decoder Architecture, ICC93, 1993, pp. 737–740.

    Google Scholar 

  32. J. Lodge, R.Young, P. Hoeher, J. Hagenauer, Separable MAP “Filters” for the Decoding of Product and Concatenated Codes, ICC93, 1993, pp. 1740–1745.

    Google Scholar 

  33. Robert J. McEliece, Eugene R. Rodemich, Jung-Fu Cheng, The Turbo Decision Algorithm, The 33rd Alerton Conference on Communications, Computing and Control, October 1995, pp. 1–11.

    Google Scholar 

  34. K.Fazel, L.Papke, Combined Multilevel Turbo-code With 8PSK Modulation, GLOBECOM95. 1995, pp. 649–653.

    Google Scholar 

  35. Stephane Le Goff, Alain Glavieux and Claude Berrou, Turbo-Codes and High Spectral Efficiency Modulation, GLOBECOM94, 1994, pp. 645–649.

    Google Scholar 

  36. Lin Zhang, Weimin Zhang, Jeff T. Ball and Martin C. Gill, MILCOM96, An Extremely Robust Tutbo Coded HF Modem, 1996.

    Google Scholar 

  37. W.J. Blackert and S.G. Wilson, Turbo Trellis Coded Modulation, Proc. CISS’96, 1996, Princeton, NJ, USA.

    Google Scholar 

  38. W.J. Blackert, E.K. Hall and S.G. Wilson, An Upper Bound on Turbo Code Free Distance, ICC96, 1996, pp. 957–961.

    Google Scholar 

  39. Patrick Robertson and Thomas Worz, A Novel Bandwidth Efficient Coding Scheme Employing Turbo Codes, ICC96, 1996, pp. 962–967.

    Google Scholar 

  40. Ramesh Pyndiah, Annie Picart and Alain Glavieux, Performance of Block Coded 16-QAM and 64-QAM Modulations, GLOBECOM95, 1995, pp. 1039–1043

    Google Scholar 

  41. Joachim Hagenauer and Peter Hoeher, A Viterbi Algorithm with Soft-Decision Outputs and its Applications, GLOBECOM89, 1989, pp. 1680–1686.

    Google Scholar 

  42. U. C. G. Fiebig and P. Robertson, Soft Decision Decoding in Fast Frequency Hopping Systems with Convolutional Codes and Turbo Codes, ICC96, 1996, pp. 1064–1070.

    Google Scholar 

  43. Stefan Kaiser and Lutz Papke, Optimal Detection when Combining OFDM-CDMA with Convolutional and Turbo Channel Coding, ICC96, 1996, pp. 343–348.

    Google Scholar 

  44. Gerard Battail, Claude Berrou and Alain Glavieux, Pseudo-Random Recusive Convolutional Coding for Near-Capacity Performance, GLOBECOM93, 1993.

    Google Scholar 

  45. D. Divsalar, S. Dolinar, R. J. Mceliece and F. Pollara, Transfer Function Bounds on the Performance of Turbo Codes, JPL TDA Progress Report 42–122, Aug. 1995.

    Google Scholar 

  46. D. Divsalar and F. Pollara, Turbo Codes for Deep-Space Communications, JPL TDA Progress Report 42–120, Feb. 1995

    Google Scholar 

  47. D. Divsalar and F. Pollara, Mutiple Turbo Codes for Deep-Space Communications, JPL TDA Progress Report 42–121, May. 1995

    Google Scholar 

  48. K. Abend and B.D. Fritchman, “Statistical Detection for Communication Channels with Intersymbol Interference,” Proc. IEEE, Vol. 58, No. 5, pp. 779–785, May 1970.

    Article  Google Scholar 

  49. J. Raviv, “Decision Making in Markov Chains Applied to the Problem of Pattern Recognition,” IEEE Trans. Inform. Theory, Vol. IT-13, pp. 536–551, Oct. 1967

    Google Scholar 

  50. L.R. Bahl, J. Cocke, F. Jelinek and J. Raviv, “Optimal Decoding of Linear Codés for Minimizing Symbol Error Rate,” IEEE Trans. Inform. Theory, Vol. IT-20, pp. 284–287, Mar. 1974.

    Google Scholar 

  51. R.W. Chang and J.C. Hancock “On Receiver Structures for Channels Having Memory,” IEEE Trans. Inform. Theory, Vol. IT-12, pp. 463 - 468, Oct. 1966.

    Google Scholar 

  52. P.R. Chevillat and E. Eleftheriou, “Decoding of Trellis-Encoded Signals in the Presence of Intersymbol Interference and Noise,” IEEE Trans. Commun., Vol. 37, No. 7, pp. 669–676, Jul. 1989.

    Article  Google Scholar 

Download references

Authors
  1. Branka Vucetic
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Vucetic, B. (1997). Iterative Decoding Algorithms. In: Wireless Communications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2604-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-2604-6_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5017-8

  • Online ISBN: 978-1-4757-2604-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation