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A 2Source AlmostExtractor for Linear Entropy Anup Rao #,1

Summary: A 2­Source Almost­Extractor for Linear Entropy
Anup Rao #,1
School of Mathematics, Institute for Advanced Study
Abstract. We give an explicit construction of a function that is almost
a 2­source extractor for linear entropy, it is a condenser where the output
has almost full entropy. Given 2 sources with entropy #n, the output of
the condenser is a distribution on m­bit strings that is #­close to having
min­entropy m- poly(log(1/#), 1/#), where here m is linear in n.
1 Introduction
This paper is about constructing e#ciently computable 2­source extractors.
These are e#ciently computable functions of the type Ext : {0, 1} n
× {0, 1} n
{0, 1} m with the property that for any 2 independent distributions X,Y , each
with entropy 1 k, the output Ext(X, Y ) is close to uniform. Another way to view
this object is as a coloring of the edges of the N ×N complete bipartite graph
with M colors that guarantees that in every K×K complete bipartite subgraph,
every set of colors is hit with roughly the right frequency.
This problem was first suggested in the work of Chor and Goldreich [CG88]


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle


Collections: Computer Technologies and Information Sciences