Expander-Based Constructions of Efficiently Decodable Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Concatenated codes can achieve list-decoding capacity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
List Decoding of Binary Codes---A Brief Survey of Some Recent Results
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
The existence of concatenated codes list-decodable up to the hamming bound
IEEE Transactions on Information Theory
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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A polynomial time construction of binary codes with the currently best known tradeoff between rate and error-correction radius is given. Specifically, linear codes over fixed alphabets are constructed that can be list decoded in polynomial time up to the so-called Blokh-Zyablov bound. The work builds upon earlier work by the authors where codes list decodable up to the Zyablov bound (the standard product bound on distance of concatenated codes) were constructed. The new codes are constructed via a (known) generalization of code concatenation called multilevel code concatenation. A probabilistic argument, which is also derandomized via conditional expectations, is used to show the existence of inner codes with a certain nested list decodability property that is appropriate for use in multilevel concatenated codes. A "level-by-level" decoding algorithm, which crucially uses the list recovery algorithm for the outer folded Reed-Solomon codes, enables list decoding up to the designed distance bound, aka the Blokh-Zyablov bound, for multilevel concatenated codes.