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Concatenated Codes

  • Chris Heegard
  • Stephen B. Wicker
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 476)

Abstract

In this chapter we introduce concatenated error control systems. Concatenated systems use two or more component codes in an effort to provide a high level of error control performance at the expense of only a moderate level of complexity. The encoder consists of two or more component encoders that combine to generate a long code with good properties. The decoder uses the component code substructure of the concatenated encoder to realize a multi-stage implementation that is much less complex than a single-stage approach. In this chapter we consider both the original, serial form of concatenation as well as the more recent, parallel form. The former allows for various forms of iterative decoding that will be discussed briefly here. The latter, of course, was developed in conjunction with turbo iterative decoding, which will be the subject of a later chapter. Parallel concatenation is introduced here, and the details of performance and decoding are developed in the two chapters that follow. The chapter concludes with a generic description of concatenated codes that relates the two basic forms, while allowing for useful generalizations.

Keywords

Error Forecast Turbo Code Convolutional Code Iterative Decode Maximum Distance Separable 
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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Bibliography

  1. [BCJR74]
    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, 1974.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [BP66]
    L.E. Baum and T. Pétrie. Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Stat 37:1554–1563, 1966.zbMATHCrossRefGoogle Scholar
  3. [BS68]
    L.E. Baum and G.R. Sell. Growth transformations for functions on manifolds. Tac. J. Math. 27(2):211–227, 1968.MathSciNetzbMATHGoogle Scholar
  4. [BPGW70]
    L.E. Baum, T. Pétrie, G. Soûles and N. Weiss. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Stat. 41:164–171, 1970.zbMATHCrossRefGoogle Scholar
  5. [BDMP96]
    S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara. Serial concatenation of iterleaved codes: Performance analysis, design and iterative decoding. DRAFT, July 1996.Google Scholar
  6. [Ber82]
    E. R. Berlekamp. Bit-Serial Reed-Solomon Encoders. IEEE Transactions on Information Theory, IT-28(6):869–874, 1982.zbMATHCrossRefGoogle Scholar
  7. [BGT93C]
    Berrou, A. Glavieux, and P. Thitimajshima. Near Shannon limit error-correcting coding and decoding: Turbo Codes. Proceedings of the 1993 International Conference on Communications, pages 1064–1070, 1993.Google Scholar
  8. [BG96]
    C. Berrou and A. Glavieux. Near optimum error correcting coding and decoding: Turbo-Codes. IEEE Transactions on Communications, COM-44(10):1261–1271, 1996.CrossRefGoogle Scholar
  9. [BG98]
    C. Berrou and A. Glavieux. Reflections on the Prize Paper: Near optimum error correcting coding and decoding: Turbo-Codes. IEEE Information Theory Society Newsletter, 48(2):1, 24–31, 1998.Google Scholar
  10. [BM96a]
    S. Benedetto and G. Montorsi. Design of parallel concatenated convolutional codes. IEEE Transactions on Communications, COM-44:591–600, 1996.zbMATHCrossRefGoogle Scholar
  11. [BM96b]
    S. Benedetto and G. Montorsi. Unveiling turbo codes: Some results on parallel concatenated coding schemes. IEEE Transactions on Information Theory, IT-42:409–428,1996.zbMATHCrossRefGoogle Scholar
  12. [GCCC81]
    G. C. Clark, Jr. and J. B. Cain. Error-Correction Coding for Digital Communications. New York: Plenum Press, 1981.Google Scholar
  13. [CCSDS87]
    Recommendations for Space Data Systems Standard: Telemetry Channel Coding. Consultative Committee for Space Data Systems. Blue Book Issue 2, CCSDS 101.0-B2, January 1987.Google Scholar
  14. [Col89]
    O. Collins. Coding Beyond the Computational Cutoff Rate. Ph.D. Dissertation, California Institute of Technology, Pasadena, May 1989,Google Scholar
  15. [Col92]
    O. Collins. The Subtleties and Intricacies of Building a Constraint Length 15 Convolutional Decoder IEEE Transactions on Communications, COM-40(12):1810–1819, 1992.CrossRefGoogle Scholar
  16. [Col93a]
    O. Collins. Pruning the Trellis. Proceedings of the International Symposium on Information Theory, San Antonio, Texas, p. 50, January 1993.Google Scholar
  17. [Col93b]
    O. Collins and M. Hizlan. Determinate State Convolutional Codes IEEE Transactions on Communications, COM-41(12):1785–1794, 1993.zbMATHCrossRefGoogle Scholar
  18. [DP95]
    D. Divsalar and F. Pollara. Multiple turbo codes for deep-space communications. TDA Progress Report 42–121, JPL, May 1995.Google Scholar
  19. [Dol93]
    S. Dolinar and M. Belongie. Enhanced Decoding for the Galileo S-Band Mission. JPL TDA Progress Report, Volume 42–114, August 1993.Google Scholar
  20. [For66]
    G. D. Forney Jr.. Concatenated Codes. Cambridge: MIT Press, 1966.Google Scholar
  21. [HH89]
    J. Hagenauerand, P. Hoeher. A Viterbi Algorithm with Soft-Decision Outputs and Its Applications. In Proceedings of the IEEE 1989 Global Communications Conference, Dallas, Texas, pg. 47.1.1–47.1.7, November 1989.Google Scholar
  22. [HOP96]
    J. Hagenauer, E. Offer, and L. Papke. Iterative decoding of binary block and convolutional codes. IEEE Transactions on Information Theory, IT-42:429–445, 1996.zbMATHCrossRefGoogle Scholar
  23. [HRP94]
    J. Hagenauer, P. Robertson, and L. Papke. Iterative (turbo) decoding of systematic convolutional codes with the map and sova algorithms. In ITG Conference on Source and Channel Coding, pages 1–9, Frankfurt, Germany, October 1994.Google Scholar
  24. [HOP94]
    J. Hagenauer, E. Offer, and L. Papke. Matching Viterbi Decoders and Reed-Solomon Decoders in Concatenated Systems. Reed-Solomon Codes and Their Applications, (S. B. Wicker and V. K. Bhargava ed.), Piscataway: IEEE Press, pp. 242–271, 1994.Google Scholar
  25. [KW98a]
    S Kim and S.B. Wicker. A Connection Between the Baum-Welch Algorithm and Turbo Decoding. Proceedings of the 1998 Information Theory Workshop, Killarney, Ireland, June 22–26, pp. 12–13, 1998.Google Scholar
  26. [Lee 77]
    L. N. Lee. Concatenated Coding Systems Employing a Unit-Memory Convolutional Code and a Byte-Oriented Decoding Algorithm. IEEE Transactions on Communications, COM-25:1064–1074, 1977.zbMATHCrossRefGoogle Scholar
  27. [LDJC83]
    S. Lin and D. J. Costello, Jr.. Error Control Coding: Fundamentals and Applications. Englewood Cliffs: Prentice Hall, 1983.Google Scholar
  28. [MS86]
    R. J. McEliece and L. Swanson. On the Decoder Error Probability for Reed-Solomon Codes. IEEE Transactions on Information Theory. IT-32(5):701–703, 1986.MathSciNetzbMATHCrossRefGoogle Scholar
  29. [MS94]
    R. J. McEliece and L. Swanson. Reed-Solomon Codes and the Exploration of the Solar System. In Reed-Solomon Codes and Their Applications (ed. S. B. Wicker and V. K. Bhargava). Piscataway: IEEE Press, 1994, pp. 25–40.Google Scholar
  30. [MDB81]
    R. L. Miller, L. J. Deutsch, and S. A. Butman. On the Error Statistics of Viterbi Decoding and the Performance of Concatenated Codes. JPL Publication 81–9, September 1, 1981.Google Scholar
  31. [Paa90]
    E. Paaske. Improved Decoding for a Concatenated Coding System Recommended by CCSDS. IEEE Transactions on Communications, COM-38:1138–1144, 1990.CrossRefGoogle Scholar
  32. [Paa91]
    E. Paaske. Efficient Methods for Improving Coding Gains in Concatenated Coding Systems. Abstracts, International Symposium on Information Theory, Budapest, Hungary, p. 297, June 1991.Google Scholar
  33. [PSC96]
    L. C. Perez, J. Seghers, and D. J. Costello Jr.. A distance spectrum interpretation of turbo codes. IEEE Transactions onlnformation Theory, IT-42(6):1698–1709, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  34. [Rob94]
    P. Robertson. Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes. In Globcom Conference, pages 1298–1303, 1994.Google Scholar
  35. [VonB92]
    D. C. L. von Berg and S. G. Wilson. Improved Concatenated Coding for Deep Space Probes. Proceedings of the International Symposium on Information Theory, San Antonio, Texas, p. 381, January 1993.Google Scholar
  36. [WW96]
    X.-A. Wang and S. B. Wicker. Generalized Soft Decision Decoding for Concatenated Systems. IEEE Transactions onlnformation Theory, IT-42(2):543–553, 1996zbMATHCrossRefGoogle Scholar
  37. [Wic94]
    S. B. Wicker and V. K. Bhargava (editors). Reed-Solomon Codes and Their Applications. Piscataway: IEEE Press, 1994.zbMATHGoogle Scholar
  38. [Wic95]
    S. B. Wicker. Error Control Systems for Digital Communications and Storage. Englewood Cliffs: Prentice Hall, 1995.Google Scholar
  39. [Wic98]
    S. B. Wicker. Deep Space Applications, Coding Theory Handbook. (V. Pless and W. Huffman, ed.) Amsterdam: Elsevier, 1998.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Chris Heegard
    • 1
    • 2
  • Stephen B. Wicker
    • 2
  1. 1.Alantro Communications, Inc.USA
  2. 2.Cornell UniversityUSA

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