Reed-Solomon List Decoding From a System-Theoretic Perspective

IEEE Transactions on Information Theory

Volumn 50, Issue 2, 2004, Pages 259-271+412

  Kuijper, Margreta ^a   Polderman, Jan Willem ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Behaviors; Bivariate interpolation; List decoding; Reed Solomon (RS) codes; System theory

Indexed keywords

CODES (SYMBOLS); DECODING; DIFFERENCE EQUATIONS; INTERPOLATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; SYSTEM THEORY;

BIVARIATE INTERPOLATION; LIST DECODING; REED-SOLOMON (RS) CODES;

INFORMATION THEORY;

EID: 10744231899     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2003.822593     Document Type: Review

References (36)

1. M. Sudan, "Decoding of Reed-Solomon codes beyond the error correction bound," J. Compl., vol. 13, pp. 180-193, 1997.
2. _, "Decoding of Reed-Solomon codes beyond the error correction diameter," in Proc. 35th Allerton Conf. Communication, Control, and Computing, 1997.
3. V. Guruswami and M. Sudan, "Improved decoding of Reed-Solomon and algebraic-geometric codes," IEEE Trans. Inform. Theory, vol. 45, pp. 1757-1768, Sept. 1999.
4. W. Feng and R. E. Blahut, "Some results on the sudan algorithm," in Proc. IEEE Int. Symp. Information Theory (ISIT'98), Cambridge, MA, Aug. 1998, p. 57.
5. G.-L. Feng, "A generalization of the Welch-Berlekamp algorithm for weighted curve fitting with application to the sudan decoding procedure," in Proc. 13th Symp. Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes (AAECC), HI, 1999, pp. 88-89.
6. T. Høholdt and R. R. Nielsen, "Decoding hermitian codes with Sudan's algorithm," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds. New York: Springer-Verlag, 1999, pp. 260-270.
7. R. R. Nielsen, "A class of Sudan-decodable codes," IEEE Trans. Inform. Theory, vol. 46, pp. 1564-1572, July 2000.
8. R. Nielsen and T. Høholdt, "Decoding Reed-Solomon codes beyond half the minimum distance," in Coding Theory, Cryptography and Related Areas, J. Buchmann, T. Høholdt, T. Stichtenoth, and H. Tapia-Recillas, Eds. Berlin, Germany: Springer-Verlag, 2000, pp. 221-236.
9. R. M. Roth and G. Ruckenstein, "Efficient decoding of Reed-Solomon codes beyond half the minimum distance," IEEE Trans. Inform. Theory, vol. 46, pp. 246-258, Jan. 2000.
10. R. Koetter and A. Vardy, "Algebraic soft-decision decoding of Reed-Solomon codes," in Proc. 2000 IEEE Int. Symp. Information Theory (ISIT'00), Sorrento, Italy, June 2000, p. 61.
11. _, "Algebraic soft-decision decoding of Reed-Solomon codes," IEEE Trans. Inform. Theory, submitted for publication.
12. _, "Decoding of Reed-Solomon codes for additive cost functions," in Proc. 2002 IEEE Int. Symp. Information Theory (ISIT'02), Lausanne, Switzerland, 2002, p. 313.
13. M. Kuijper, "The Berlekamp-Massey algorithm, error-correction, keystreams and modeling," in Dynamical Systems, Control, Coding Computer Vision: New trends, Interfaces, and Interplay. ser. Progress in Systems and Control Theory, G. Picci and D. Gilliam, Eds. Basel, Switzerland: Birkhäuser, 1999, pp. 321-342.
14. _, "Algorithms for decoding and interpolation," in Codes, Systems, and Graphical Models, ser. The IMA Volumes in Mathematics and its Applications, B. Marcus and J. Rosenthal, Eds. Berlin, Germany: Springer-Verlag, 2001, vol. 123, pp. 265-282.
15. J. Feigenbaum, G. D. Forney, B. H. Marcus, R. J. McEliece, and A. Vardy, "Introduction to the special issue on codes and complexity," IEEE Trans. Inform. Theory, vol. 42, pp. 1649-1657, Nov. 1996.
16. M. Kuijper and J. C. Willems, "An algorithm for computing a shortest linear recurrence relation for a sequence of matrices: generalizing the Berlekamp-Massey algorithm," in Proc. 1998 IEEE Int. Symp. Information Theory (ISIT'98), Cambridge, MA, Aug. 1998, p. 441.
17. M. Kuijper, "A system-theoretic derivation of the Welch-Berlekamp algorithm," in Proc. 2000 IEEE Int. Symp. Information Theory, Sorrento, Italy, June 2000, p. 418.
18. _, "Further results on the use of a generalized B-M algorithm for BCH decoding beyond the designed error-correcting capability," in Proc. 13th Symp. Applied Algebra Algebraic Algorithms, and Error-Correcting Codes (AAECC), HI, 1999, pp. 98-99.
19. M. Kuijper and J. C. Willems, "On constructing a shortest linear recurrence relation," IEEE Trans. Automat. Contr., vol. 42, pp. 1554-1558, Nov. 1997.
20. M. Kuijper, M. van Dijk, H. Hollmann, and A. J. Oostveen, "A unifying system-theoretic framework for errors-and-erasures Reed-Solomon decoding," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Lecture Notes in Computer Science), S. Boztas and I. Shparlinski, Eds. Berlin, Germany: Springe-Verlag, 2001, vol. 2227, pp. 343-352.
21. J. C. Willems, "Paradigms and puzzles in the theory of dynamical systems," IEEE Trans. Automat. Contr., vol. 36, pp. 259-294, Mar. 1991.
22. R. E. Blahut, Theory and practice of error control codes. Reading, MA: Addison-Wesley, 1983.
23. M. Kuijper and J. W. Polderman, "A behavioral approach to list decoding," in Proc. 15th Int. Symp. Mathematical Theory of Networks and Systems, D. Gilliam and J. Rosenthal, Eds., IN, 2002.
24. _, "Behavioral models for list decoding," J. Math. Comput. Modeling of Dyn. Syst. (MCMDS), vol. 8, pp. 429-444, 2003.
25. M. Kuijper, "Partial realization and the euclidean algorithm," IEEE Trans. Automat. Contr., vol. 44, pp. 1013-1016, May 1999.
26. R. Koetter and A. Vardy, "A complexity reducing transformation in algebraic list decoding of Reed-Solomon codes," in Proc. 2003 Information Theory Workshopo, Paris, France, 2003.
27. H. Hasse, "Theorie der höheren Differentiale in einem algebraischen Funktionkörper mit volkommenen Konstantenkörper bei beliebiger Charakteristik," J. Reine Angew. Math., vol. 175, pp. 50-54, 1936.
28. G. Castagnoli, J. L. Massey, P. A. Schoeller, and N. v. Seemann, "On repeated-root cyclic codes," IEEE Trans. Inform. Theory, vol. 37, pp. 50-54, Jan. 1991.
29. R. Lidl and H. Niederreiter, Finite Fields, 2 ed. Cambridge, U.K.: Cambridge Univ. Press, 1997.
30. J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory: a Behavioral Approach, ser. Texts in Applied Mathematics. New York: Springer-Verlag, 1997, vol. 26.
31. M. Kuijper, First-Order Representations of Linear Systems, ser. Systems and Control: Foundations and Applications. Boston, MA: Birkhäuser, 1994.
32. J. M. Schumacher, "Transformations of linear systems under external equivalence," Linear Alg. its Applic., vol. 102, pp. 1-33, 1988.
33. W. A. Wolovich, Linear multivariable systems. New York: Springer-Verlag, 1974.
34. G. D. Forney Jr, "Minimal bases of rational vector spaces, with applications to multivariable linear systems," SIAM J. Control, vol. 13, pp. 493-520, 1975.
35. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
36. J. C. Willems, "From time series to linear system. Part II: Exact modeling," Automatica, vol. 22, pp. 675-694, 1986.