Self-testing/correcting with applications to numerical problems
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Designs and their codes
Highly resilient correctors for polynomials
Information Processing Letters
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth 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
Efficient Checking of Computations
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects 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
Local List Decoding with a Constant Number of Queries
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
IEEE Transactions on Information Theory - Part 1
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
Error exponents of expander codes
IEEE Transactions on Information Theory
A recursive approach to low complexity codes
IEEE Transactions on Information Theory
Concatenated codes: serial and parallel
IEEE Transactions on Information Theory
Distance properties of expander codes
IEEE Transactions on Information Theory
Locally Decodable Codes
Share Conversion and Private Information Retrieval
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Query-Efficient Locally Decodable Codes of Subexponential Length
Computational Complexity
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In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the codeword can be recovered with high probability by reading Nε symbols from the corrupted codeword, where N is the block-length of the code. Expander codes, introduced by Sipser and Spielman, are formed from an expander graph G=(V,E) of degree d, and an inner code of block-length d over an alphabet Σ. Each edge of the expander graph is associated with a symbol in Σ. A string in ΣE will be a codeword if for each vertex in V, the symbols on the adjacent edges form a codeword in the inner code. We show that if the inner code has a smooth reconstruction algorithm in the noiseless setting, then the corresponding expander code has an efficient local-correction algorithm in the noisy setting. Instantiating our construction with inner codes based on finite geometries, we obtain a novel locally decodable codes with constant rate. This provides an alternative to the multiplicity codes of Kopparty, Saraf and Yekhanin (STOC '11) and the lifted codes of Guo, Kopparty and Sudan (ITCS '13).