Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Efficient Checking of Computations
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
"Soft-decision" decoding of Chinese remainder codes
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Better Lower Bounds for Locally Decodable Codes
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
A Geometric Approach to Information-Theoretic Private Information Retrieval
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On Matrix Rigidity and Locally Self-Correctable Codes
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Local List Decoding with a Constant Number of Queries
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Nonlinear codes from algebraic curves improving the Tsfasman-Vladut-Zink bound
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
Locally Decodable Codes
Query-Efficient Locally Decodable Codes of Subexponential Length
Computational Complexity
Locally decodable codes: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Public key locally decodable codes with short keys
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
SIAM Journal on Computing
From irreducible representations to locally decodable codes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Local correctability of expander codes
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
Locally decodable codes are error-correcting codes that admit efficient decoding algorithms; any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a code and the locality/efficiency of its decoding algorithms has been well studied, and it has widely been suspected that nontrivial locality must come at the price of low rate. A particular setting of potential interest in practice is codes of constant rate. For such codes, decoding algorithms with locality O(kε) were known only for codes of rate exp(1/ε), where k is the length of the message. Furthermore, for codes of rate 1/2, no nontrivial locality has been achieved. In this paper we construct a new family of locally decodable codes that have very efficient local decoding algorithms, and at the same time have rate approaching 1. We show that for every ε 0 and α 0, for infinitely many k, there exists a code C which encodes messages of length k with rate 1 - α, and is locally decodable from a constant fraction of errors using O(kε) queries and time. The high rate and local decodability are evident even in concrete settings (and not just in asymptotic behavior), giving hope that local decoding techniques may have practical implications. These codes, which we call multiplicity codes, are based on evaluating high degree multivariate polynomials and their derivatives. Multiplicity codes extend traditional multivariate polynomial based codes; they inherit the local-decodability of these codes, and at the same time achieve better tradeoffs and flexibility in their rate and distance.