List Error-Correction with Optimal Information Rate (Invited Talk)
ICITS '08 Proceedings of the 3rd international conference on Information Theoretic Security
Error correction up to the information-theoretic limit
Communications of the ACM - Being Human in the Digital Age
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Artin automorphisms, cyclotomic function fields, and folded list-decodable codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
List Decoding of Binary Codes---A Brief Survey of Some Recent Results
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Guest column: from randomness extraction to rotating needles
ACM SIGACT News
The existence of concatenated codes list-decodable up to the hamming bound
IEEE Transactions on Information Theory
Data stream algorithms for codeword testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Algorithms and theory of computation handbook
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Optimal error correction for computationally bounded noise
IEEE Transactions on Information Theory
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
SIAM Journal on Computing
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
Root lifting techniques and applications to list decoding
ACM Communications in Computer Algebra
Optimal rate list decoding via derivative codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
List decoding subspace codes from insertions and deletions
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
A novel elementary construction of matching vectors
Information Processing Letters
Folded codes from function field towers and improved optimal rate list decoding
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A general construction for 1-round δ-RMT and (0, δ)-SMT
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
Fuzzy vault for multiple users
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Optimally robust private information retrieval
Security'12 Proceedings of the 21st USENIX conference on Security symposium
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
Power series solutions of singular (q)-differential equations
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
ℓ2/ℓ2-Foreach sparse recovery with low risk
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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In this paper, we present error-correcting codes that achieve the information-theoretically best possible tradeoff between the rate and error-correction radius. Specifically, for every 0 < R < 1 and epsiv < 0, we present an explicit construction of error-correcting codes of rate that can be list decoded in polynomial time up to a fraction (1- R - epsiv) of worst-case errors. At least theoretically, this meets one of the central challenges in algorithmic coding theory. Our codes are simple to describe: they are folded Reed-Solomon codes, which are in fact exactly Reed-Solomon (RS) codes, but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Given the ubiquity of RS codes, this is an appealing feature of our result, and in fact our methods directly yield better decoding algorithms for RS codes when errors occur in phased bursts. The alphabet size of these folded RS codes is polynomial in the block length. We are able to reduce this to a constant (depending on epsiv) using existing ideas concerning ldquolist recoveryrdquo and expander-based codes. Concatenating the folded RS codes with suitable inner codes, we get binary codes that can be efficiently decoded up to twice the radius achieved by the standard GMD decoding.