A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Highly resilient correctors for polynomials
Information Processing Letters
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Linear-time encodable/decodable codes with near-optimal rate
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
Efficient and secure evaluation of multivariate polynomials and applications
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
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Ever since the birth of coding theory almost 60 years ago, researchers have been pursuing the elusive goal of constructing the "best codes," whose encoding introduces the minimum possible redundancy for the level of noise they can correct. In this article, we survey recent progress in list decoding that has led to efficient error-correction schemes with an optimal amount of redundancy, even against worst-case errors caused by a potentially malicious channel. To correct a proportion ρ(say 20%) of worst-case errors, these codes only need close to a proportion ρ of redundant symbols. The redundancy cannot possibly be any lower information theoretically. This new method holds the promise of correcting a factor of two more errors compared to the conventional algorithms currently in use in diverse everyday applications.