IEEE Transactions on Information Theory
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)
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
Better binary list decodable codes via multilevel concatenation
IEEE Transactions on Information Theory
On the list-decodability of random linear codes
Proceedings of the forty-second ACM symposium on Theory of computing
IEEE Transactions on Information Theory - Part 1
Combinatorial bounds for list decoding
IEEE Transactions on Information Theory
Limits to List Decoding Reed–Solomon Codes
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
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It is proven that binary linear concatenated codes with an outer algebraic code (specifically, a foalded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve, with high probability, the optimal tradeoff between rate and list-decoding radius. In particular, for any 0 0, there exist concatenated codes of rate at least 1 - H(ρ) - Ζ that are (combinatorially) list-decodable up to a ρ fraction of errors. (The Hamming bound states that the best possible rate for such codes cannot exceed 1 - H (ρ), and standard random coding arguments show that this bound is approached by random codes with high probability.) A similar result, with better list size guarantees, holds when the outer code is also randomly chosen. The methods and results extend to the case when the alphabet size is any fixed prime power q ≥ 2.