On the Pless-construction and ML decoding of the (48, 24, 12) quadratic residue code

IEEE Transactions on Information Theory

Volumn 49, Issue 6, 2003, Pages 1527-1535

  Esmaeili, Morteza ^a   Aaron Gulliver, T ^b   Khandani, Amir K ^c  

^a ISFAHAN UNIVERSITY OF TECHNOLOGY   (Iran)

^b UNIVERSITY OF VICTORIA   (Canada)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Linear block codes; Maximum likelihood decoding; Trellis diagram

Indexed keywords

CODES (SYMBOLS); DECODING; GRAPH THEORY;

QUADRATIC RESIDUE CODES;

INFORMATION THEORY;

EID: 0038380323     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2003.811930     Document Type: Article

References (28)

1. E. F. Assmus, Jr. and J. D. Key, Designs and Their Codes: Cambridge University Press, 1993.
2. L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inform. Theory, vol. 20, pp. 284-287, Mar. 1974.
3. A. R. Calderbank, G. D. Forney, Jr., and A. Vardy, "Minimal tail-biting trellises: The Golay code and more," IEEE Trans. Inform. Theory, vol. 45, pp. 1435-1455, July 1999.
4. G. Charbit, H. Manoukian, and B. Honary, "Array codes over rings and their trellis decoding," IEE Proc. Commun., vol. 143, no. 5, pp. 241-246, Oct. 1996.
5. J. H. Conway and N. J. A. Sloane, "Decoding techniques for codes and lattices, including the Golay code and the Leech lattice," IEEE Trans. Infor. Theory, vol. 32, pp. 41-50, Jan. 1986.
6. R. Diestel, Graph Theory, Second ed: Springer, 2000.
7. M. Esmaeili and A. K. Khandani, "Acyclic Tanner graph and maximum-likelihood decoding of linear block codes," IEE Proc. Commun., vol. 147, no. 6, pp. 322-332, Dec. 2000.
8. M. Esmaeili, T. A. Gulliver, and N. P. Secord, "Quasicyclic structure of Reed-Muller codes and their smallest regular trellis diagram," IEEE Trans. Inform. Theory, vol. 43, no. 3, pp. 1040-1052, May 1997.
9. T. Etzion, A. Trachtenberg, and A. Vardy, "Which codes have cycle-free Tanner graphs?," IEEE Trans. Inform. Theory, vol. 45, pp. 2173-2181, Sept. 1999.
10. G. D. Forney, Jr., "The Viterbi algorithm," Proc. IEEE, vol. 61, pp. 268-278, 1973.
11. M. Fossorier and S. Lin, "Computationally efficient soft decision decoding of linear block codes based on ordered statistics," IEEE Trans. Inform. Theory, vol. 42, pp. 738-750, 1996.
12. _, "Generalized coset decoding," IEEE Trans. Commun., vol. 45, pp. 393-395, Apr. 1997.
13. _, "Chase-type and GMD coset decodings," IEEE Trans. Commun., vol. 48, pp. 345-350, Mar. 2000.
14. G. D. Forney, Jr., "Coset codes part II: Binary lattices and related codes," IEEE Trans. Inform. Theory, vol. 34, pp. 1152-1187, Sept. 1988.
15. B. Honary, G. Markarian, and M. Darnell, "Low-complexity trellis decoding of linear block codes," IEE Proc. Commun., vol. 142, pp. 201-209, Aug. 1995.
16. B. Honary, L. Kaya, G. Markarian, and M. Darnell, "Maximum-likelihood decoding of array codes with trellis structure," IEE Proc. Commun, vol. 140, pp, 340-346, Oct. 1993.
17. G. B. Horn and F. R. Kschischang, "On the intractability of permuting a block code to minimize trellis complexity," IEEE Trans. Inform. Theory, vol. 42, pp. 2042-2047, Nov. 1996.
18. R. Johannesson and P. Stahl, "A note on type II convolutional codes," IEEE Trans. Inform. Theory, vol. 46, pp. 1510-1514, July 2000.
19. F. R. Kschischang and V. Sorokine, "On the trellis structure of block codes," IEEE Trans. Inform. Theory, vol. 41, pp. 1924-1937, Nov. 1995.
20. A. Lafourcade and A. Vardy, "Optimal sectionalization of a trellis," IEEE Trans. Inform. Theory, vol. 42, pp. 689-703, May 1996.
21. V. Pless, "Decoding the Golay code," IEEE Trans. Inform. Theory, vol. 32, pp. 561-567, July 1986.
22. M. Ran and J. Snyders, "Constrained designs for maximum likelihood soft decoding of RM(2, m) and the extended Golay codes," IEEE Trans. Commun., vol. 43, pp. 812-820, Feb./March/April 1995.
23. R. A. Silverman and M. Balser, "Coding for a constant data rate source," IRE Trans. Inform. Theory, vol. 4, pp. 50-63, Sept. 1954.
24. V. Sidorenko, O. Markarian, and B. Honary, "Minimal trellis design for linear codes based on the Shannon product," IEEE Trans. Inform. Theory, vol. 42, pp. 2048-2053, Nov. 1996.
25. J. Snyders and Y. Be'ery, "Maximum likelihood soft decoding of binary block codes and decoders for the Golay codes," IEEE Trans. Inform. Theory, vol. 35, pp. 963-975, Sept. 1989.
26. A. Vardy and Y. Be'ery, "More efficient soft decoding of the Golay codes," IEEE Trans. Inform. Theory, vol. 37, pp. 667-672, May 1991.
27. J. K. Wolf, "Maximum likelihood decoding of Linear block codes using a trellis," IEEE Trans. Inform. Theory, vol. 24, pp. 76-80, Jan. 1978.
28. J. Yuan, C. S. Chen, and S. Ma, "Two-level decoding of (32, 16, 8) quadratic residue code," IEE Proc. I, vol. 140, pp. 409-414, Dec. 1993.