Name
Abstract | ||
|---|---|---|
We give new constructions of randomness extractors and lossless condensers that are optimal to within constant factors in both the seed length and the output length. For extractors, this matches the parameters of the current best known construction (LRVW03); for lossless condensers, the previous best constructions achieved optimality to within a constant factor in one parameter only at the expense of a polynomial loss in the other. Our constructions are based on the Parvaresh-Vardy codes (PV05), and our proof technique is in- spired by the list-decoding algorithm for those codes. The main object we construct is a condenser that loses only the entropy of its seed plus one bit, while condensing to entropy rate 1 ¡ ® for any desired constant ® > 0. This construction is simple to describe, and has a short and completely self-contained analysis. Our other results only require, in addition, stan dard uses of randomness-efficient hash functions (to obtain a lossless condenser) or expander walks (to obtain an extractor). Our techniques also show for the first time that a natural cons truction based on univariate polynomials (i.e., Reed-Solomon codes) yields a condenser that retains a 1 ¡ ® fraction of the source min-entropy, for any desired constant ® > 0, while condensing to constant entropy rate and using a seed length that is optimal to within constant factors. |
Year | Venue | DocType |
|---|---|---|
2006 | Electronic Colloquium on Computational Complexity (ECCC) | Journal |
Volume | Issue | Citations |
13 | 134 | 2 |
PageRank | References | Authors |
0.44 | 23 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| V. Guruswami | 1 | 3205 | 247.96 |
| Christopher Umans | 2 | 879 | 55.36 |
| Salil P. Vadhan | 3 | 4676 | 234.84 |