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FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
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FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
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APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
IEEE Transactions on Information Theory - Part 1
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IEEE Transactions on Information Theory
Limits to List Decoding Reed–Solomon Codes
IEEE Transactions on Information Theory
List Decoding of Binary Codes---A Brief Survey of Some Recent Results
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Better binary list decodable codes via multilevel concatenation
IEEE Transactions on Information Theory
Efficient list decoding of explicit codes with optimal redundancy
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
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We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve the list-decoding capacity with high probability. In particular, for any 0 0, there exist concatenated codes of rate at least 1 -- H(ρ) -- ε that are (combinatorially) list-decodable up to a fraction ρ of errors. (The best possible rate, aka list-decoding capacity, for such codes is 1 -- H(ρ), and is achieved by random codes.) A similar result, with better list size guarantees, holds when the outer code is also randomly chosen. Our methods and results extend to the case when the alphabet size is any fixed prime power q ≥ 2. Our result shows that despite the structural restriction imposed by code concatenation, the family of concatenated codes is rich enough to include capacity achieving list-decodable codes. This provides some encouraging news for tackling the problem of constructing explicit binary list-decodable codes with optimal rate, since code concatenation has been the preeminent method for constructing good codes over small alphabets.