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Canadian Workshop on Information Theory

CWIT 1995: Information Theory and Applications II pp 111–129Cite as

Non-minimal trellises for linear block codes

  • Decoding Methods and Techniques
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1133))

Abstract

The technique of atomic span modification is used to construct non-minimal trellises for linear block codes. Non-minimal trellises may have properties like regularity and vertex localization that make the corresponding trellis-based decoding algorithms better-suited for VLSI or multiprocessor implementation. A simple class of “universal” trellises with a regular structure is defined, from which soft decision decoders can be built by parallel combination of identical trellis search processors. Coset decoding is proposed as a general soft-decision decoding technique for multiprocessor implementation, and algorithms for selecting a sub-code to achieve large speedup are described.

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References

  1. G. D. Forney, Jr., “Review of random tree codes.” Nasa Ames Research Center, Appendix A of Final Report on Contract NAS2-3637, NASA CR73176, Dec. 1967.

    Google Scholar 

  2. G. D. Forney, Jr., “Trellises old and new,” in Communications and Cryptography: Two Sides of One Tapestry (R. E. Blahut, D. J. Costello, Jr., U. Maurer, and T. Mittelholzer, eds.), pp. 115–128, Kluwer Academic Publishers, 1994.

    Google Scholar 

  3. L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. on Inform. Theory, vol. 20, pp. 284–287, Mar. 1974.

    Google Scholar 

  4. J. K. Wolf, “Efficient maximum-likelihood decoding of linear block codes using a trellis,” IEEE Trans. on Inform. Theory, vol. IT-24, pp. 76–80, 1978.

    Google Scholar 

  5. J. L. Massey, “Foundation and methods of channel encoding,” in Proc. Int. Conf. Inform. Theory and Systems, vol. 65, (Berlin), Sept. 1978.

    Google Scholar 

  6. G. D. Forney, Jr., “Coset codes II: Binary lattices and related codes,” IEEE Trans. on Inform. Theory, vol. 34, pp. 1152–1187, Sep. 1988.

    Google Scholar 

  7. D. J. Muder, “Minimal trellises for block codes,” IEEE Trans. on Inform. Theory, vol. 34, pp. 1049–1053, Sept. 1988.

    Google Scholar 

  8. T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes,” IEEE Trans. on Inform. Theory, vol. 39, pp. 242–245, Jan. 1993.

    Google Scholar 

  9. T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On complexity of trellis structure of linear block codes,” IEEE Trans. on Inform. Theory, vol. 39, pp. 1057–1064, May 1993.

    Google Scholar 

  10. G. D. Forney, Jr. and M. D. Trott, “The dynamics of group codes: State spaces, trellis diagrams and canonical encoders,” IEEE Trans. on Inform. Theory, vol. 39, pp. 1491–1513, Sept. 1993.

    Google Scholar 

  11. F. R. Kschischang and V. Sorokine, “On the trellis structure of block codes,” IEEE Trans. on Inform. Theory, vol. 41, pp. 1924–1937, Nov. 1995.

    Google Scholar 

  12. V. Sorokine, F. R. Kschischang, and V. Durand, “Trellis-based decoding of binary linear block codes,” Lecture Notes in Computer Science, vol. 793, pp. 270–286, 1994.

    Google Scholar 

  13. Y. Berger and Y. Be'ery, “Bounds on the trellis size of linear block codes,” IEEE Trans. on Inform. Theory, vol. 39, pp. 203–209, Jan. 1993.

    Google Scholar 

  14. A. D. Kot and C. Leung, “On the construction and dimensionality of linear block code trellises,” in Proc. 1993 IEEE Int. Symp. on Inform. Theory, (San Antonio, TX), p. 291, Jan. 17–22, 1993.

    Google Scholar 

  15. G. D. Forney, Jr., “Dimension/length profiles and trellis complexity of linear block codes,” IEEE Trans. on Inform. Theory, vol. 40, pp. 1741–1752, Nov. 1994.

    Google Scholar 

  16. F. R. Kschischang and G. B. Horn, “A heuristic for ordering a linear block code to minimize trellis state complexity,” in Proc. 32nd Annual Allerton Conf. on Communication, Control, and Computing, Allerton Park, Illinois, pp. 75–84, Sept. 1994.

    Google Scholar 

  17. R. J. McEliece, “On the BCJR trellis for linear block codes,” IEEE Trans. on Inform. Theory, vol. 42, 1996. To appear.

    Google Scholar 

  18. A. Lafourcade and A. Vardy, “Asymptotically good codes have infinite trellis complexity,” IEEE Trans. on Inform. Theory, vol. 41, pp. 555–559, March 1995.

    Google Scholar 

  19. M. Esmaeli, T. A. Gulliver, and N. P. Secord, “Trellis complexity of linear block codes via atomic codewords.” Preprint, 1995.

    Google Scholar 

  20. A. Lafourcade and A. Vardy, “Optimal sectionalization of a trellis,” IEEE Trans. on Inform. Theory, vol. 42, 1996.

    Google Scholar 

  21. H. T. Moorthy, S. Lin, and G. T. Uehara, “Good trellises for IC implementation of Viterbi decoders for linear block codes.” Submitted to IEEE Trans. on Commun., 1995.

    Google Scholar 

  22. J. H. Conway and N. J. A. Sloane, “Lexicographic codes: Error-correcting codes from Game Theory,” IEEE Trans. on Inform. Theory, vol. IT-32, pp. 337–348, May 1986.

    Google Scholar 

  23. F. R. Kschischang, “The trellis structure of maximal fixed-cost codes,” IEEE Trans. on Inform. Theory, vol. 42, 1996. To appear.

    Google Scholar 

  24. J. H. Conway and N. J. A. Sloane, “Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice,” IEEE Trans. on Inform. Theory, vol. 32, pp. 41–50, 1986.

    Google Scholar 

  25. T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On the structural complexity of the l-section minimal trellis diagram for binary linear block codes,” IEICE Transactions, vol. E76-A, pp. 1411–1421, 1993.

    Google Scholar 

  26. A. Vardy and Y. Be'ery, “More efficient soft decoding of the Golay codes,” IEEE Trans. on Inform. Theory, vol. 37, pp. 667–672, 1991.

    Google Scholar 

  27. C.-K. Lee, “Nonminimal trellises for linear block codes,” Master's thesis, University of Toronto, Department of Electrical and Computer Engineering, June 1996.

    Google Scholar 

  28. H. T. Moorthy, S. Lin, and G. T. Uehara, “Trellises with parallel structure for block codes with constraint on maximum state space dimension,” in Proc. 1995 IEEE Int. Symp. Inform. Theory (Whistler, B.C., Canada), p. 127, 1995.

    Google Scholar 

  29. M. Esmaeili, Graphical Properties of Quasi Cyclic Codes PhD thesis, Ottawa-Carleton Institute of Mathematics and Statistics, 1996.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, Canada

    Ryan Chi-Kong Lee & Rank R. Kschischang

Authors
  1. Ryan Chi-Kong Lee
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  2. Rank R. Kschischang
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Editor information

Jean-Yves Chouinard Paul Fortier T. Aaron Gulliver

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© 1996 Springer-Verlag Berlin Heidelberg

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Lee, R.CK., Kschischang, R.R. (1996). Non-minimal trellises for linear block codes. In: Chouinard, JY., Fortier, P., Gulliver, T.A. (eds) Information Theory and Applications II. CWIT 1995. Lecture Notes in Computer Science, vol 1133. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025140

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  • DOI: https://doi.org/10.1007/BFb0025140

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61748-8

  • Online ISBN: 978-3-540-70647-2

  • eBook Packages: Springer Book Archive

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