Better Condensers and New Extractors from Parvaresh-Vardy Codes

Amnon Ta-Shma, Christopher Umans
2012 2012 IEEE 27th Conference on Computational Complexity  
We give a new construction of condensers based on Parvaresh-Vardy codes [1]. Our condensers have entropy rate (1−α) for subconstant α (in contrast to [2] which required constant α) and suffer only sublinear entropy loss. Known extractors can be applied to the output to extract all but a subconstant fraction of the minentropy. The resulting (k, ε) extractor E : {0, 1} n × {0, 1} d → {0, 1} m has output length m = (1 − α)k with α = 1/poly log(n), and seed length d = O(log n), when ε ≥ 1/2 log β n
more » ... hen ε ≥ 1/2 log β n for any constant β < 1. Thus we achieve the same "world-record" extractor parameters as [3] , with a more direct construction. 1 One only needs to set δ = log 1−β n and ε = 2 − log β n in Step 3 in the proof of their Theorem 20.
doi:10.1109/ccc.2012.25 dblp:conf/coco/Ta-ShmaU12 fatcat:67aabtaxundcdk6cbvhciardc4