Linear-time list decoding in error-free settings (extended abstract)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3142, Issue , 2004, Pages 695-707

  Guruswami, Venkatesan ^a   Indyk, Piotr ^b  

^a University of Washington   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CLUSTERING ALGORITHMS; CODES (SYMBOLS); DECODING; ENCODING (SYMBOLS); POLYNOMIAL APPROXIMATION; RECOVERY; REED-SOLOMON CODES;

DECODING COMPLEXITY; ENCODING/DECODING; EXPLICIT CONSTRUCTIONS; EXTENDED ABSTRACTS; LINEAR-TIME ALGORITHMS; LIST DECODING; LIST-DECODABLE CODES; POLYNOMIAL-TIME;

POLYNOMIALS;

EID: 35048819116     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-27836-8_59     Document Type: Article

References (15)

1. Andres Albanese, Johannes Blomer, Jeff Edmonds, Michael Luby, and Madhu Sudan. Priority encoding transmission. IEEE Transactions on Information Theory, 42(6):1737-1744, November 1996.
2. Michael Alekhnovich. Linear diophantine equations over polynomials and soft decoding of Reed-Solomon codes. Proceedings of the Symposium on Foundations of Computer Science, pages 439-448, 2002.
3. Noga Alon, Jehoshua Bruck, Joseph Naor, Moni Naor, and Ronny Roth. Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs. IEEE Transactions on Information Theory, 38:509-516, 1992.
4. Noga Alon, Jeff Edmonds, and Michael Luby. Linear time erasure codes with nearly optimal recovery. In Proceedings of the 36th IEEE Symposium on Foundations of Computer Science, pages 512-519, 1995.
5. Sigal Ar, Richard J. Lipton, Ronitt Rubinfeld, and Madhu Sudan. Reconstructing algebraic functions from mixed data. SIAM Journal on Computing, 28(2):487-510, 1999.
6. Peter Elias. Zero error capacity under list decoding. Quarterly Progress Report ,Research Laboratory of Electronics, MIT, 48:88-90, 1958.
7. G. L. Feng. Two fast algorithms in the Sudan decoding procedure. Proceedings of the 37th Annual Allerton Conference on Communication, Control and Computing, pages 545-554, 1999.
8. Venkatesan Guruswami. List decoding from erasures: Bounds and code constructions. IEEE Transactions on Information Theory, 49(11):2826-2833, 2003.
9. Venkatesan Guruswami and Piotr Indyk. Near-optimal linear-time codes for unique decoding and new list-decodable codes over smaller alphabets. Proceedings of the Symposium on Theory of Computing, pages 812-821, 2002.
10. Venkatesan Guruswami and Piotr Indyk. Linear-time encodable and list-decodable codes. Proceedings of the Symposium on Theory of Computing, pages 126-135, 2003.
11. Venkatesan Guruswami and Madhu Sudan. Improved decoding of Reed-Solomon and algebraic-geometric codes. IEEE Transactions on Information Theory, 45:1757-1767, 1999.
12. Alex Lubotzky, R. Phillips, and Peter Sarnak. Ramanujan graphs. Combinatorial, 8(3):261-277, 1988.
13. Daniel Spielman. Linear-time encodable and decodable error-correcting codes. IEEE Transactions on Information Theory, 42(6):1723-1732, 1996.
14. Madhu Sudan. Decoding of Reed-Solomon codes beyond the error-correction bound. Journal of Complexity, 13(1):180-193, 1997.
15. Gillés Zémor. On expander codes. IEEE Transactions on Information Theory, 47(2):835-837, 2001.