Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Limits to list decoding Reed-Solomon codes
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
The unified theory of pseudorandomness: guest column
ACM SIGACT News
Decodability of group homomorphisms beyond the johnson bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The complexity of the matroid–greedoid partition problem
Theoretical Computer Science
List decoding tensor products and interleaved 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)
Extracting Computational Entropy and Learning Noisy Linear Functions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
List decoding and pseudorandom constructions
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Noise-resilient group testing: limitations and constructions
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
A lower bound on list size for list decoding
IEEE Transactions on Information Theory
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
A lower bound on list size for list decoding
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Reconstructive dispersers and hitting set generators
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
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We study error-correcting codes for highly noisy channels. For example, every received signal in the channel may originate from some half of the symbols in the alphabet. Our main conceptual contribution is an equivalence between error-correcting codes for such channels and extractors. Our main technical contribution is a new explicit error-correcting code based on Trevisan's extractor that can handle such channels, and even noisier ones. Our new code has polynomial-time encoding and polynomial-time soft-decision decoding. We note that Reed-Solomon codes cannot handle such channels, and our study exposes some limitations on list decoding of Reed-Solomon codes. Another advantage of our equivalence is that when the Johnson bound is restated in terms of extractors, it becomes the well-known Leftover Hash Lemma. This yields a new proof of the Johnson bound which applies to large alphabets and soft decoding. Our explicit codes are useful in several applications. First, they yield algorithms to extract many hardcore bits using few auxiliary random bits. Second, they are the key tool in a recent scheme to compactly store a set of elements in a way that membership in the set can be determined by looking at only one bit of the representation. Finally, they are the basis for the recent construction of high-noise, almost-optimal rate list-decodable codes over large alphabets.