Limits to list decoding reed-solomon codes

IEEE Transactions on Information Theory

Volumn 52, Issue 8, 2006, Pages 3642-3649

  Guruswami, Venkatesan ^a   Rudra, Atri ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bose Chaudhuri hocquenghem (BCH) codes; Johnson bound; List decoding; List recovering; Reed solomon codes

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; DECODING; POLYNOMIALS;

BOSE-CHAUDHURI-HOCQUENGHEM (BCH) CODES; JOHNSON BOUND; LIST DECODING; LIST RECOVERING; REED-SOLOMON CODES;

CODES (SYMBOLS);

EID: 33746600750     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.878164     Document Type: Article

References (18)

1. V. Guruswami and A. Rudra, "Limits to list decoding Reed-Solomon codes," in Proc. 37th ACM Symp. Theory Comput. (STOC), 2005.
2. M. Sudan, "Decoding of Reed-Solomon codes beyond the error-correction bound," J. Complexity, vol. 13, no. 1, pp. 180-193, 1997.
3. V. Guruswami and M. Sudan, "Improved decoding of Reed-Solomon and algebraic-geometric codes," IEEE Trans. Inf. Theory, vol. 45, pp. 1757-1767, 1999.
4. R. Koetter and A. Vardy, "Algebraic soft-decision decoding of Reed-Solomon codes," IEEE Trans. Inf. Theory, vol. 49, no. 11, pp. 2809-2825, 2003.
5. V. Guruswami and M. Sudan, Extensions to the Johnson Bound 2000 [Online]. Available: http://theory.1cs.mit.edu/madhu/papers.html, Manuscript
6. V. Guruswami and P. Indyk, "Expander-based constructions of efficiently decodable codes," in Proc. 42nd Annu. Symp. Found. Comput. Sci. (FOCS), 2001, pp. 658-667.
7. A. Ta-Shma and D. Zuckerman, "Extractor Codes," in Proc. 33rd Annu. ACM Symp. Theory Comput., Jul. 2001, pp. 193-199.
8. F. Parvaresh and A. Vardy, "Correcting errors beyond the Guruswami-Sudan radius in polynomial time," in Proc. 46th Annu. Symp. Found. Comput. Sci. (FOCS), 2005.
9. V. Guruswami and A. Rudra, "Explicit capacity-achieving list-decodable codes," in Proc. 38th ACM Symp. Theory Comput. (STOC), 2006, to Appear.
10. J. Justesen and T. Høholdt, "Bounds on list decoding of MDS codes," IEEE Trans. Inf. Theory, vol. 47, no. 4, pp. 1604-1609, May 2001.
11. Q. Cheng and D. Wan, "On the list and bounded distance decodability of Reed-Solomon codes," in Proc. 45th Annu. Symp. Found. Comput. Sci. (FOCS), 2004.
12. I. Dumer, D. Micciancio, and M. Sudan, "Hardness of approximating the minimum distance of a code," IEEE Trans. Inf. Theory, vol. 49, no. 1, pp. 22-37, Jan. 2003.
13. C. Xing, "Nonlinear codes from algebraic curves improving the Tsfasman-Vladut-Zink bound," IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 1653-1657, Jul. 2003.
14. V. Guruswami, J. Håstad, M. Sudan, and D. Zuckerman, "Combinatorial bounds for list decoding," IEEE Trans. Inf. Theory, vol. 48, pp. 1021-1035, May 2002.
15. E. Ben-Sasson, S. Kopparty, and J. Radhakrishnan, "The list-decoding radius for Reed-Solomon codes," in Proc. AMS Sectional Meet., Lincoln, NE, Oct. 2005.
16. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error- Correcting Codes. North-Holland, Amsterdam: Elsevier, 1981.
17. E. Berlekamp, Algebraic Coding Theory. New York: McGraw-Hill, 1968.
18. A. Granville, The Arithmetic Properties of Binomial Coefficients [Online]. Available: http://www.cecm.sfu.ca/organics/Papers/granville 1996