Guest column: error-correcting codes and expander graphs
ACM SIGACT News
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
Euclidean Sections of $\ell_1^N$ with Sublinear Randomness and Error-Correction over the Reals
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Error correction up to the information-theoretic limit
Communications of the ACM - Being Human in the Digital Age
On the design and alphabet size of Roth-Skachek nearly MDS expander codes
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
Approaching Blokh-Zyablov error exponent with linear-time encodable/decodable codes
IEEE Communications Letters
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Capacity achieving codes from randomness conductors
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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
Algorithms and theory of computation handbook
Hardness amplification within NP against deterministic algorithms
Journal of Computer and System Sciences
Efficient reductions for non-signaling cryptographic primitives
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
Linear time decoding of regular expander codes
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Linear-time decoding of regular expander codes
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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We present an explicit construction of linear-time encodable and decodable codes of rate r which can correct a fraction (1-r-ε)/2 of errors over an alphabet of constant size depending only on ε, for every 00. The error-correction performance of these codes is optimal as seen by the Singleton bound (these are "near-MDS" codes). Such near-MDS linear-time codes were known for the decoding from erasures; our construction generalizes this to handle errors as well. Concatenating these codes with good, constant-sized binary codes gives a construction of linear-time binary codes which meet the Zyablov bound, and also the more general Blokh-Zyablov bound (by resorting to multilevel concatenation). Our work also yields linear-time encodable/decodable codes which match Forney's error exponent for concatenated codes for communication over the binary symmetric channel. The encoding/decoding complexity was quadratic in Forney's result, and Forney's bound has remained the best constructive error exponent for almost 40 years now. In summary, our results match the performance of the previously known explicit constructions of codes that had polynomial time encoding and decoding, but in addition have linear-time encoding and decoding algorithms.