Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors for a constant number of polynomially small min-entropy independent sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
Deterministic extractors for independent-symbol sources
IEEE Transactions on Information Theory
Extracting Kolmogorov complexity with applications to dimension zero-one laws
Information and Computation
On obtaining pseudorandomness from error-correcting codes
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Deterministic extractors for independent-symbol sources
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Generalized strong extractors and deterministic privacy amplification
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
IH'12 Proceedings of the 14th international conference on Information Hiding
| Hi-index | 0.06 |
On an input probability distribution with some (min-)entropy an extractor outputs a distribution with a (near) maximum entropy rate (namely the uniform distribution). A natural weakening of this concept is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). We construct efficient explicit condensers. The condenser constructions combine (variants or more efficient versions of) ideas from several works, including the block extraction scheme of Nisan and Zuckerman (1996), the observation made by Srinivasan and Zuckerman (1994) and Nisan and Ta-Schma (1999) that a failure of the block extraction scheme is also useful, the recursive "win-win" case analysis of Impagliazzo et al. (1999, 2000), and the error correction of random sources used by Trevisan (1999). As a natural byproduct, (via repeated iterating of condensers), we obtain new extractor constructions. The new extractors give significant qualitative improvements over previous ones for sources of arbitrary min-entropy; they are nearly optimal simultaneously in the main two parameters-seed length and output length. Specifically, our extractors can make any of these two parameters optimal (up to a constant factor), only at a poly-logarithmic loss in the other. Previous constructions require polynomial loss in both cases for general sources. We also give a simple reduction converting "standard" extractors (which are good for an average seed) to "strong " ones (which are good for mast seeds), with essentially the same parameters.