Journal ArticleDOI
List decoding of algebraic-geometric codes
M.A. Shokrollahi,H. Wasserman +1 more
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This work designs algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code.Abstract:
We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields. For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are included.read more
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Book
List Decoding of Error-Correcting Codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: This thesis presents a detailed investigation of list decoding, and proves its potential, feasibility, and importance as a combinatorial and algorithmic concept and presents the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate.
Journal ArticleDOI
List decoding: algorithms and applications
TL;DR: The list-decoding problem, the algorithms that have been developed, and a diverse collection of applications within complexity theory are described.
Proceedings ArticleDOI
Expander-based constructions of efficiently decodable codes
Venkatesan Guruswami,Piotr Indyk +1 more
TL;DR: Several novel constructions of codes are presented which share the common thread of using expander (or expander-like) graphs as a component and enable the design of efficient decoding algorithms that correct a large number of errors through various forms of "voting" procedures.
Journal ArticleDOI
Linear-time encodable/decodable codes with near-optimal rate
Venkatesan Guruswami,Piotr Indyk +1 more
TL;DR: An explicit construction of linear-time encodable and decodable codes of rate r which can correct a fraction of errors over an alphabet of constant size depending only on /spl epsiv/, for every 00.
Journal ArticleDOI
Combinatorial bounds for list decoding
TL;DR: This work presents a polynomial time constructible asymptotically good family of binary codes of rate /spl Omega/(/spl epsi//sup 4/) that can be list-decoded in polynometric time from up to a fraction of errors, using lists of size O(/spl Epsi //sup -2/).
References
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Journal ArticleDOI
Decoding of Reed Solomon Codes beyond the Error-Correction Bound
TL;DR: To the best of the knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides error recovery capability beyond the error-correction bound of a code for any efficient code.
Journal ArticleDOI
Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert bound
Proceedings ArticleDOI
Improved decoding of Reed-Solomon and algebraic-geometric codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometric codes is presented, including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed- Solomon codes.
Journal ArticleDOI
A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
TL;DR: In this paper, a tower of function fields is constructed such that the ratioN(Fi)/g(Fi) tends to the Drinfeld-Vladut boundq−1.