Algebraic Soft-Decision Decoding of Reed-Solomon Codes

IEEE Transactions on Information Theory

Volumn 49, Issue 11, 2003, Pages 2809-2825

  Koetter, Ralf ^a   Vardy, Alexander ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Berlekamp Welch algorithm; Guruswami Sudan algorithm; List decoding; Polynomial interpolation; Reed Solomon codes; Soft decision decoding

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); DECISION THEORY; DECODING; INTERPOLATION; POLYNOMIALS; QUADRATURE AMPLITUDE MODULATION;

LIST DECODING; POLYNOMIAL INTERPOLATION; REED-SOLOMON CODES; SOFT-DECISION DECODING;

INFORMATION THEORY;

EID: 0345306775     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2003.819332     Document Type: Article

References (32)

1. D. Augot and L. Pecquet, "A Hensel lifting to replace factorization in list-decoding of algebraic-geometric and Reed-Solomon codes," IEEE Trans. Inform. Theory, vol. 46, pp. 2605-2614, Nov. 2000.
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, Mar. 1974.
3. E. R. Berlekamp, "Bounded distance+1 soft-decision Reed-Solomon decoding," IEEE Trans. Inform. Theory, vol. 42, pp. 704-721, May 1996.
4. 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-24, pp. 384-386, May 1978.
5. E. R. Berlekamp, R. E. Peile, and S. P. Pope, "The application of error control to communications," IEEE Commun. Mag., vol. 25, pp. 44-57, Jan. 1987.
6. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley Interscience, 1991.
7. A. B. Cooper 3rd, "Soft-decision decoding of Reed-Solomon codes," in Reed-Solomon Codes and their Applications, S. B. Wicker and V. K. Bhargava, Eds. New York: IEEE Press, 1994, pp. 108-124.
8. G.-L. Feng, "A fast special factorization algorithm in the Sudan decoding procedure," in Proc. 31st Allerton Conf. Communications, Control, and Computing, Oct. 2000, pp. 593-602.
9. G.-L. Feng and X. Giraud, "Fast algorithms in Sudan decoding procedure for Reed-Solomon codes," IEEE Trans. Inform. Theory, submitted for publication.
10. G. D. Forney Jr., "Generalized minimum distance decoding," IEEE Trans. Inform. Theory, vol. IT-12, pp. 125-131, Apr. 1966.
11. _, Concatenated Codes. Cambridge, MA: MIT Press, 1966.
12. W. J. Gross, F. R. Kschischang, R. Koetter, and P. G. Gulak, "A VLSI architecture for interpolation in soft-decision list decoding of Reed-Solomon codes," Proc. IEEE Workshop on Signal Processing Systems, pp. 39-44, Oct. 2002.
13. _,"Applications of algebraic soft-decision decoding of Reed-Solomon codes," IEEE Trans. Commun., submitted for publication.
14. V. Guruswami and M. Sudan, "Improved decoding of Reed-Solomon and algebraic-geometric codes," IEEE Trans. Inform. Theory, vol. 45, pp. 1757-1767, Sept. 1999.
15. _, "List decoding algorithms for certain concatenated codes," IEEE Trans. Inform. Theory, submitted for publication.
16. R. Koetter, "On Algebraic Decoding of Algebraic-Geometric and Cyclic codes," Ph.D. dissertation. Univ. Linköping, Linköping, Sweden, 1996.
17. _, "Fast generalized minimum distance decoding of algebraic geometric and Reed-Solomon codes," IEEE Trans. Inform. Theory, vol. 42, pp. 721-738, May 1996.
18. F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inform. Theory, vol. 47, pp. 498-519, Feb. 2001.
19. R. R. Nielsen, "Decoding concatenated codes with Sudan's algorithm," IEEE Trans. Inform. Theory, submitted for publication.
20. R. R. Nielsen and T. Høholdt, "Decoding Reed-Solomon codes beyond half the minimum distance," preprint, 1998.
21. V. Olshevsky and A. Shokrollahi. "A displacement structure approach to efficient decoding of Reed-Solomon and algebraic-geometric codes," in Proc. 31th ACM Symp. Theory of Computing (STOC), Atlanta, GA, May 1999, pp. 235-244.
22. A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 1984.
23. V. Ponnampalam and B. S. Vucetic, "Soft decision decoding of Reed-Solomon codes," in Proc. 13th Symp. Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Honolulu, HI, Nov. 1999.
24. S. Ray-Chaudhuri and A. H. Chan, "Bit-level parallel decoding of Reed-Solomon codes." in Proc. 31th Allerton Conf. Communications, Control, and Computing, Sept. 1993.
25. 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.
26. U. Sorger, "A new Reed-Solomon decoding algorithm based on Newton's interpolation," IEEE Trans. Inform. Theory, vol. 39, pp. 358-365, Mar. 1993.
27. M. Sudan, "Decoding of Reed-Solomon codes beyond the error correction bound," J. Complexity, vol. 12, pp. 180-193, 1997.
28. A. Vardy, "Algorithmic complexity in coding theory and the minimum distance problem," in Proc. 29th Symp. Theory of Computing, El Paso, TX, 1997, pp. 92-109.
29. A. Vardy and Y. Be'ery, "Bit-level soft-decision decoding of Reed-Solomon codes," IEEE Trans. Commun., vol. 39, pp. 440-445, Mar. 1991.
30. L. R. Welch and E. R. Berlekamp, "Error Correction for Algebraic Block Codes," U.S. Patent 633 470, Dec. 30, 1986.
31. W. W. Wu, D. Haccoun, R. E. Peile, and Y. Hirata, "Coding for satellite communication," IEEE J. Select. Areas Commun., vol. 5, pp. 724-785, May 1987.
32. X.-W. Wu and P. H. Siegel, "Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes," IEEE Trans. Inform. Theory, vol. 47, pp. 2579-2587. Sept. 2001.