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.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
J. L. Massey, “Foundation and methods of channel encoding,” in Proc. Int. Conf. Inform. Theory and Systems, vol. 65, (Berlin), Sept. 1978.
G. D. Forney, Jr., “Coset codes II: Binary lattices and related codes,” IEEE Trans. on Inform. Theory, vol. 34, pp. 1152–1187, Sep. 1988.
D. J. Muder, “Minimal trellises for block codes,” IEEE Trans. on Inform. Theory, vol. 34, pp. 1049–1053, Sept. 1988.
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.
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.
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.
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.
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.
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.
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.
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.
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.
R. J. McEliece, “On the BCJR trellis for linear block codes,” IEEE Trans. on Inform. Theory, vol. 42, 1996. To appear.
A. Lafourcade and A. Vardy, “Asymptotically good codes have infinite trellis complexity,” IEEE Trans. on Inform. Theory, vol. 41, pp. 555–559, March 1995.
M. Esmaeli, T. A. Gulliver, and N. P. Secord, “Trellis complexity of linear block codes via atomic codewords.” Preprint, 1995.
A. Lafourcade and A. Vardy, “Optimal sectionalization of a trellis,” IEEE Trans. on Inform. Theory, vol. 42, 1996.
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.
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.
F. R. Kschischang, “The trellis structure of maximal fixed-cost codes,” IEEE Trans. on Inform. Theory, vol. 42, 1996. To appear.
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.
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.
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.
C.-K. Lee, “Nonminimal trellises for linear block codes,” Master's thesis, University of Toronto, Department of Electrical and Computer Engineering, June 1996.
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.
M. Esmaeili, Graphical Properties of Quasi Cyclic Codes PhD thesis, Ottawa-Carleton Institute of Mathematics and Statistics, 1996.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0025140
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61748-8
Online ISBN: 978-3-540-70647-2
eBook Packages: Springer Book Archive