RAID: high-performance, reliable secondary storage
ACM Computing Surveys (CSUR)
Journal of Combinatorial Theory Series A
Communication complexity
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)
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Randomness-efficient oblivious sampling
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Hard-disk drives: the good, the bad, and the ugly
Communications of the ACM - One Laptop Per Child: Vision vs. Reality
Locally Testable Codes Require Redundant Testers
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Error-correcting codes for semiconductor memory applications: a state-of-the-art review
IBM Journal of Research and Development
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tolerant locally testable codes
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
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
Efficiently decodable error-correcting list disjunct matrices and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Streaming algorithms for recognizing nearly well-parenthesized expressions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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Motivated by applications in storage systems and property testing, we study data stream algorithms for local testing and tolerant testing of codes. Ideally, we would like to know whether there exist asymptotically good codes that can be local/tolerant tested with one-pass, poly-log space data stream algorithms. We show that for the error detection problem (and hence, the local testing problem), there exists a one-pass, log-space data stream algorithm for a broad class of asymptotically good codes, including the Reed-Solomon (RS) code and expander codes. In our technically more involved result, we give a one-pass, O(e log2n)-space algorithm for RS (and related) codes with dimension k and block length n that can distinguish between the cases when the Hamming distance between the received word and the code is at most e and at least a ċ e for some absolute constant a 1. For RS codes with random errors, we can obtain e ≤ O(n/k). For folded RS codes, we obtain similar results for worst-case errors as long as e ≤ (n/k)1-ε for any constant ε 0. These results follow by reducing the tolerant testing problem to the error detection problem using results from group testing and the list decodability of the code. We also show that using our techniques, the space requirement and the upper bound of e ≤ O(n/k) cannot be improved by more than logarithmic factors.