Maximum likelihood decoding for linear block codes using Gröbner bases

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E86-A, Issue 3, 2003, Pages 643-651

  Ikegami, Daisuke ^a   Kaji, Yuichi ^a  

^a NARA INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Gr bner basis; Hard decision decoding; Maximum likelihood decoding; Soft decision decoding

Indexed keywords

ALGORITHMS; BINARY CODES; BLOCK CODES; ERROR CORRECTION; FAST FOURIER TRANSFORMS; INTEGER PROGRAMMING; MATRIX ALGEBRA; POLYNOMIALS; SIGNAL TO NOISE RATIO;

BINARY LINEAR BLOCK CODES; CONTI-TRAVERSO ALGORITHM; GROBNER BASES; HARD-DECISION DECODING; MAXIMUM LIKELIHOOD DECODING; SOFT-DECISION DECODING;

DECODING;

EID: 0038035690     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. T. Becker, V. Weispfenning, and H. Kredel, Gröbner Bases - A Computational Approach to Commutative Algebra, Springer-Verlag, 1993.
2. A.M. Cohen, H. Cuypers, and H. Sterks, eds., Some Tapas of Computer Algebra. Algorithms and Computation in Mathematics, vol.4, Springer-Verlag, 1999.
3. P. Conti and C. Traverso, "Buchberger algorithm and integer programming," Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-9), ed. H.F. Mattson, T. Mora, and T.R.N. Rao, LNCS, no.539, pp. 130-139, Springer-Verlag, Oct. 1991.
4. D. Cox, J. Little, and D. O'Shea, Ideals, Varieties and Algorithms - An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd edition, Springer-Verlag, 1998.
5. D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry, Springer-Verlag, 1998.
6. M. de Boer and R. Pellikaan, "Gröbner bases for decoding," in [2], chapter 11, pp. 206-275.
7. J. C. Faugère, P. Gianni, D. Lazard, and T. Mora, "Efficient computation of zero-dimensional Gröbner bases by change of ordering," Journal of Symbolic Computation, vol.16, no.4, pp.329-344, Oct. 1993.
8. J. Fitzgerald, Applications of Gröbner bases to linear codes, Ph. D. Thesis, Louisiana State Univ., 1996.
9. T. Fujiwara, H. Yamamoto, T. Kasami, and S. Lin, "A trellis-based recursive maximum likelihood decoding algorithm for linear codes," IEEE Trans. Inf. Theory, vol.44, no.2, pp.714-729, March 1998.
10. Y.S. Han, C.R.P. Hartman, and C.C. Chen, "Efficient priority-first search maximum-likelihood soft-decision decoding of linear block codes," IEEE Trans. Inf. Theory, vol.39, no.5, pp. 1514-1523, Sept. 1993.
11. Y. Kaji, H. Tokushige, and T. Kasami, "An improved search algorithm for the adaptive and recursive MLD algorithm," 2001 IEEE International Symposium on Information Theory, Washington, D.C., p.344, June 2001.
12. A. Lafourcade and A. Vardy, "Optimum sectionalization of a trellis," IEEE Trans. Inf. Theory, vol.42, no.3, pp.689-702, May 1996.
13. S. Lin, T. Kasami, T. Fujiwara, and M. Fossorier, Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes, Kluwer Academic Publishers, 1998.
14. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, 9th edition, North-Holland Mathematical Library, vol.16, North-Holland, 1996.
15. H. Ohsugi, D. Ikegami, T. Kitamura, and T. Hibi, "Gröbner bases of certain zero-dimensional ideals arising in coding theory," to appear in Advances in Applied Mathematics, 2003.
16. B. Strumfels, Gröbner Bases and Convex Polytopes, University Lecture, vol.8, American Mathematical Society, 1996.