Advertisement

Error Bounds for Tree Codes, Trellis Codes, and Convolutional Codes with Encoding and Decoding Procedures

  • James L. Massey
Part of the International Centre for Mechanical Sciences book series (CISM, volume 216)

Abstract

One of the anomalies of coding theory has been that while block parity-check codes form the subject for the overwhelming majority of theoretical studies, convolutional codes have been used in the majority of practical applications of “error-correcting codes.” There are many reasons for this, not the least being the elegant algebraic characterizations that have been formulated for block codes. But while we may for aesthetic reasons prefer to speculate about linear block codes rather than convolutional codes, it seems to me that an information-theorist can no longer be inculpably ignorant of non-block codes. It is the purpose of these lectures to provide a reasonably complete and self-contained treatment of non-block codes for a reader having some general familiarity with block codes.

Keywords

Error Bound Terminal Node Block Code Convolutional Code Information Digit 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Gallager, R.G., Information Theory and Reliable Communication, John Wiley and Sons, New York, 1968.MATHGoogle Scholar
  2. [2]
    Johannesson, R., “On The Error Probability of General Tree and Trellis Codes with Applications to Sequential Decoding,” Tech. Rpt. No. EE 7316, Dept. of Elec. Engr., Univ. of Notre Dame, Notre Dame, Indiana, U.S.A. December 1973.Google Scholar
  3. [3]
    Viterbi, A.J.,, “Convolutional Codes and Their Performance in Communication Systems,” IEEE Trans. Comm Tech., Vol. COM-19, pp. 751–772, October, 1971.Google Scholar
  4. [4]
    Larsen, K.J., “Short Convolutional Codes with Maximum Free Distance for Rates 1/2, 1/3, and 1/4”, IEEE Trans. Info. Th., Vol. IT-19, pp. 371–372, May, 1973.Google Scholar
  5. [5]
    Johannesson, R., “Robustly-Optimal Rate One-Half Binary Convolutional Codes”, IEEE Trans. Info. Th., Vol. IT-21, pp. 464–468, July 1975.CrossRefGoogle Scholar
  6. [6]
    Wozencraft, J.M., and B. Reiffen, Sequential Decoding, M.I.T. Press, Cambridge, Mass., 1959.Google Scholar
  7. [7]
    Massey, J.L., Threshold Decoding, M.I.T. Press, Cambridge, Mass., 1963.Google Scholar
  8. [8]
    Costello, D.J., Jr., “A Construction Technique for Random-Error-Correcting Convolutional Codes,” IEEE Trans. Info. Th., Vol. IT-15, pp. 631–636, September 1969.CrossRefMathSciNetGoogle Scholar
  9. [9]
    Forney, G. David, Jr., “Cbnvolutional Codes I: Algebraic Structure,” IEEE Trans. Info. Th., Vol. IT-16, pp. 720–738, November, 1970.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Massey J.L., and M.K. Sain, “Inverses of Linear Sequential Circuits,” IEEE Trans. Computers, Vol. C-17, pp. 330–337, April, 1968.CrossRefGoogle Scholar
  11. [11]
    Olson, R.R., “Note on Feedforward Inverses of Linear Sequential Circuits,” IEEE Trans. Computers, Vol. C-19, pp. 1216–1221, December, 1970.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Viterbi, A.J., “Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm,” IEEE Trans. Info. Th., Vol. IT-13, pp. 260–269, April, 1967.CrossRefGoogle Scholar
  13. [13]
    Omura, J.K., “On the Viterbi Decoding Algorithm,” IEEE Trans. Info. Th., Vol. IT-15, pp. 177–179, January, 1969.CrossRefMathSciNetGoogle Scholar
  14. [14]
    Fano, R.M., “A Heuristic Discussion of Probabilistic Decoding,” IEEE Trans. Info. Th., Vol. IT-9, pp. 64–74, April 1963.CrossRefMathSciNetGoogle Scholar
  15. [15]
    Massey, J.L., “Variable-Length Codes and the Fano Metric,” IEEE Trans. Info. Th., Vol. IT-18, pp. 196–198, January, 1972.CrossRefMathSciNetGoogle Scholar
  16. [16]
    Zigangirov, K.Sh., “Some Sequential Decoding Procedures,” Prob. Pederachi Inform., Vol. 2. pp. 13–25, 1966.Google Scholar
  17. [17]
    Jelinek, F., “A Fast Sequential Decoding Algorithm Using a Stack,” IBM J. Res. Dey., Vol. 13, pp. 675–685, November, 1969.CrossRefMATHMathSciNetGoogle Scholar
  18. [18]
    Wozencraft, J.M., and I.M. Jacobs, Principles of Communication Engineering, John Wiley and Sons, New York, 1965.Google Scholar
  19. [19]
    Geist, J.M., “Search Properties of Some Sequential Decoding Algorithms,” IEEE Trans. Info. Th., Vol. IT-19, pp. 519–526, July, 1973.CrossRefMathSciNetGoogle Scholar
  20. [20]
    Geist, J.M., “A, Empirical Comparison of Two Sequential Decoding Algorithms,” IEEE Trans. Comm. Techn., Vol. COM-19, pp. 415–419, August, 1971.CrossRefGoogle Scholar
  21. [21]
    Van De Meeberg, L., “A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding,” IEEE Trans. Info. Th., Vol. IT-20, pp. 389–391, May, 1974.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1975

Authors and Affiliations

  • James L. Massey
    • 1
  1. 1.University of Notre DameNotre DameUSA

Personalised recommendations