Suboptimal decoding of linear codes: Partition technique

IEEE Transactions on Information Theory

Volumn 42, Issue 6 PART 1, 1996, Pages 1971-1986

  Dumer, Ilya ^a  

^a University of California Riverside   (United States)

Author keywords

Information subsets; Output matched weights; Shortest paths; Suboptimal decoding; Symmetric channels; Trellis

Indexed keywords

ALGORITHMS; CODING ERRORS; COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTATIONAL COMPLEXITY; INFORMATION THEORY; OPTIMIZATION; PROBABILITY; TRELLIS CODES;

CONCATENATED CODES; DECODING ERROR PROBABILITY; INFORMATION SUBSETS; LINEAR CODES; NEAR MAXIMUM LIKELIHOOD DECODING; PARTITION TECHNIQUE; SUBOPTIMAL DECODING;

DECODING;

EID: 0030286942     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.556688     Document Type: Article

References (43)

1. O. Amrani, B. Be'ery, A. Vardy, F.-W. Sun, and H. C. A. van Tilborg, "The Leech lattice and the Golay codes: Bounded-distance decoding and multilevel constructions," IEEE Trans. Inform. Theory, vol. 40, no. 4, pp. 1030-1043, July 1994.
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. IT-20, pp. 284-287, 1974.
3. A. M. Barg and I. I. Dumer, "The algorithm of cascade decoding with incomplete inspection of code vectors," Probl. Pered. Inform., vol. 22, no. 1, pp. 3-10, 1986 (in Russian).
4. "On computing the weight spectrum of cyclic codes," IEEE Trans. Inform. Theory, vol. 38, pp. 1382-1386, 1992.
5. E. R. Berlekamp, R. J. McEliece, and H. C. A. van Tilborg, "On the inherent intractability of certain coding problems," IEEE Trans. Inform. Theory, vol. IT-29, pp. 384-386, 1978.
6. V. M. Blinovskii, "Lower asymptotic bound on the number of linear code words in a sphere of given radius F," Probl. Pered. Inform., vol. 23, no. 2, pp. 50-53, 1987 (in Russian).
7. E. L. Blokh and V. V. Zyablov, Linear Concatenated Codes. Moscow, Russia: Nauka, 1982 (in Russian).
8. J. Brack and M. Naor, "The hardness of decoding linear codes with preprocessing," IEEE Trans. Inform. Theory, vol. 36, pp. 381-385, 1990.
9. A. R. Calderbank and N, J. A. Sloane, "New trellis codes based on lattices and cosets," IEEE Trans. Inform. Theory, vol. IT-33, pp. 177-195, 1987.
10. D. Chase, "A class of algorithms for decoding block codes with channel measurement information," IEEE Trans. Inform. Theory, vol. IT-18, pp. 170-182, 1972.
11. J. T. Coffey and R. M. F. Goodman, "The complexity of information set decoding," IEEE Trans. Inform. Theory, vol. 36, pp. 1031-1037, 1990.
12. J. T. Coffey, R. M. F. Goodman, and P. G. Farrell, "New approaches to reduced-complexity decoding," Discr. Appl. Math., vol. 33, pp. 43-60, 1991.
13. B. G. Dorsch, "A decoding algorithm for binary block codes and J-ary output channels," IEEE Trans. Inform. Theory, vol. IT-20, pp. 391-394, 1974.
14. I. I. Dumer, "On the complexity of maximum likelihood decoding of the best concatenated codes," Proc. 8 Ail-Union Conf. Coding Theory (Moscow-Kuibyshev, Russia, 1981), vol. 2, pp. 66-69 (in Russian).
15. "Two algorithms for linear codes decoding," Probl. Pered. Inform., vol. 25, no. 1, pp. 24-32, 1989 (in Russian).
16. "On minimum distance decoding of linear codes," Proc. 5th Int. Workshop on Information Theory "Convolutional Codes; Multiuser Comm." (Moscow, Russia, Jan. 1991), pp. 50-52.
17. "Suboptimal decoding of linear codes," CISM Courses and Lectures, vol. 339. New York: Springer-Verlag, 1993, pp. 369-382.
18. J. Eiguren, I. 1. Dumer, and P. G. Farrell, "Recent developments in soft-decision decoding for linear block error-control codes," Communication Theory and Application IL Selected Papers. Ambleside, UK, HW Comm. Ltd., 1994, pp. 2-10.
19. G. S. Evseev, "On the complexity of decoding linear codes," Probl Pered. Inform., vol. 19, no. 1, pp. 3-8, 1983 (in Russian).
20. G. D. Forney, Jr., "Final report on a coding system design for advanced solar missions," Contract NAS2-3637, NASA Ames Res. Ctr, Moffet Field, CA, Dec. .1967.
21. "Coset codes II: Binary lattices and related codes," IEEE Trans. Inform. Theory, vol. 34, pp. 1152-1187, 1988.
22. "Dimension/length profiles and trellis complexity of linear block codes," IEEE Trans. Inform. Theory, vol. 40, pp. 1741-1752, 1992.
23. G. D. Forney, Jr., and M. D. Trott, "The dynamics of group codes: State spaces, trellis diagrams and canonical encoders," IEEE Trans. Inform. Theory, vol. 39, pp. 1491-1513, 1993.
24. M. P. C. Fossorier and S. Lin, "Soft-decision decoding of linear block codes based on ordered statistics," IEEE Trans. Inform. Theory, vol. 41, pp. 1379-1396, 1995.
25. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
26. Y. S. Han, C. R. P. Hartmann, and C. C. Chen, "Efficient priority-search maximum-likelihood soft-decision decoding of linear block codes," IEEE Trans. Inform. Theory, vol. 39, pp. 1514-1523, 1993.
27. D. E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, vol. 2. Reading, MA: Addison-Wesley, 1969.
28. E. A. Krouk, "A bound on the decoding complexity of linear block codes," Probl. Pered. Inform., vol. 25, no. 3, pp. 103-106, 1989 (in Russian).
29. B. D. Kudryashov and T. G. Zakharova, "Block codes from convolutional codes," Probl. Pered. Inform., vol. 25, no. 2, pp. 98-102, 1989 (in Russian).
30. B. D. Kudryashov, "Soft decision decoding for block codes obtained from convolutional codes," Lecture Notes in Computer Science, vol. 573. New York: Springer-Verlag, 1992, pp. 113-119.
31. A. Lafourcade and A. Vardy, "Optimal sectionalization of a trellis," IEEE Trans. Inform. Theory, vol. 42, no. 3, pp. 689-703, May 1996.
32. "Lower bounds on trellis complexity of block codes," IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1938-1952, Nov. 1995.
33. L. Levitin and C. Hartmann, "A new approach to the general minimum distance decoding problem: The zero-neighbors algorithm," IEEE Trans. Inform. Theory, vol. IT-31, pp. 378-384, 1985.
34. A. Lobstein, "The hardness of solving subset sum with preprocessing," IEEE Trans. Inform. Theory, vol. 36, pp. 943-946, 1990.
35. J. L. Massey, "Foundations and methods of channel coding," Proc. Int. Con/, on Information Theory and Systems, NTG-Fachberichte, vol. 65, pp. 148-157, 1978.
36. R. J. McEliece, "On the BCJR trellis for linear block codes," IEEE Trans. Inform. Theory, vol. 42, no. 4, pp. 1072-1092, July 1996.
37. D. J. Muder, "Minimal trellises for block codes," IEEE Trans. Inform. Theory, vol. 34, pp. 1049-1053, 1988.
38. J. Snyders and Y. Be'ery, "Maximum likelihood soft decoding of binary block codes and decoders for the Golay code," IEEE Trans. Inform. Theory, vol. 35, pp. 963-975, 1989.
39. T. Takata, Y. Yamashita, T. Fujiwara, T. Kasami, and S. Lin, "Suboptimum decoding of decomposable block codes," IEEE Trans. Inform. Theory, vol. 40, no. 5, pp. 1392-1405, Sept. 1994.
40. C. Thommesen, "The existence of binary linear concatenated codes with Reed-Solomon outer codes which asymptotically meet the Gilbert-Varshamov bound," IEEE Trans. Inform. Theory, vol. IT-29, pp. 850-853, 1983.
41. A. Vardy and Y. Be'ery, "Maximum likelihood .soft decision decoding of BCH codes," IEEE Trans. Inform. Theory, vol. 40, no. 2, pp. 546-554, Mar. 1994.
42. J. K. Wolf, "Efficient maximum likelihood decoding of linear codes using a trellis," IEEE Trans. Inform. Theory, vol. IT-24, pp. 76-80, 1978.
43. V. V. Zyablov and V. R, Sidorenkö, "Bounds on complexity of trellis decoding of linear codes," Probl. Pered. Inform., vol. 29, no. 3, pp. 3-9, 1993 (in Russian).