On the Many Faces of Block Codes

  • Kaustubh Deshmukh
  • Priti Shankar
  • Amitava Dasgupta
  • B. Sundar Rajan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)

Abstract

Block codes are first viewed as finite state automata represented as trellises. A technique termed subtrellis overlaying is introduced with the object of reducing decoder complexity. Necessary and sufficient conditions for subtrellis overlaying are next derived from the representation of the block code as a group, partitioned into a subgroup and its cosets. Finally a view of the code as a graph permits a combination of two shortest path algorithms to facilitate efficient decoding on an overlayed trellis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inform. Theory 20(2), March 1974, pp 284–287.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A.R. Calderbank, G. David Forney, Jr., and Alexander Vardy, Minimal Tail-Biting Trellises: The Golay Code and More, IEEE Trans. Inform. Theory 45(5) July 1999, pp 1435–1455.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    G.D. Forney, Jr., Coset codes II: Binary lattices and related codes, IEEE Trans. Inform. Theory 36(5), Sept. 1988, pp 1152–1187.CrossRefMathSciNetGoogle Scholar
  4. 4.
    G.D. Forney, Jr. and M.D. Trott, The dynamics of group codes:State spaces, trellis diagrams and canonical encoders, IEEE Trans. Inform. Theory 39(5) Sept 1993, pp 1491–1513.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Y.S. Han, C.R.P. Hartmann, and C.C. Chen, Efficient Priority-First Search Maximum-Likelihood Soft-Decision Decoding of Linear Block Codes, IEEE Trans. Inform. Theory 39(5), Sept. 1993, pp 714–729.CrossRefMathSciNetGoogle Scholar
  6. 6.
    P.E. Hart, N.J. Nilsson, and B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Trans. Solid-State Circuits SSC-4, 1968, pp 100–107.Google Scholar
  7. 7.
    F.R. Kschischang and V. Sorokine, On the trellis structure of block codes, IEEE Trans. Inform Theory 41(6), Nov 1995, pp 1924–1937.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    F.R. Kschischang, The trellis structure of maximal fixed cost codes, IEEE Trans. Inform Theory 42(6), Nov. 1996, pp 1828–1837.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Lind and M. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995.Google Scholar
  10. 10.
    F.J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1981.Google Scholar
  11. 11.
    J.L. Massey, Foundations and methods of channel encoding, in Proc. Int. Conf. on Information Theory and Systems 65(Berlin, Germany) Sept 1978.Google Scholar
  12. 12.
    R.J. McEliece, On the BCJR trellis for linear block codes, IEEE Trans. Inform Theory 42, 1996, pp 1072–1092MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    D.J. Muder, Minimal trellises for block codes, IEEE Trans. Inform Theory 34(5), Sept 1988, pp 1049–1053.CrossRefMathSciNetGoogle Scholar
  14. 14.
    Amitava Dasgupta, Priti Shankar, Kaustubh Deshmukh, and B.S. Rajan, On Viewing Block Codes as Finite Automata, Technical Report IISc-CSA-1999-7, Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India, November, 1999.Google Scholar
  15. 15.
    A. Vardy, Trellis structure of codes, in Handbook of Coding Theory, R.A. Brualdi, W.C. Huffman, V.S. Pless, Eds., Vol.2, Chap. 24, Elsevier, 1998.Google Scholar
  16. 16.
    A.J. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Trans. Inform Theory 13, April 1967, pp 260–269.MATHCrossRefGoogle Scholar
  17. 17.
    N. Wiberg, H.-A. Loeliger and R. Kotter, Codes and iterative decoding on general graphs, Euro. Trans. Telecommun.,6 pp 513–526, Sept 1995.CrossRefGoogle Scholar
  18. 18.
    J.C. Willems, Models for Dynamics, in Dynamics Reported, 2, U. Kirchgraber and H.O. Walther, Eds. New York: Wiley, 1989, pp 171–269.Google Scholar
  19. 19.
    J.K. Wolf, Efficient maximum-likelihood decoding of linear block codes using a trellis, IEEE Trans. Inform Theory 24(1), January 1978, pp 76–80.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kaustubh Deshmukh
    • 1
  • Priti Shankar
    • 2
  • Amitava Dasgupta
    • 2
  • B. Sundar Rajan
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology BombayMumbaiIndia
  2. 2.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia
  3. 3.Department of Electrical Communication EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations