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A 2-Source Almost-Extractor for Linear Entropy School of Mathematics, Institute for Advanced Study

Summary: A 2-Source Almost-Extractor 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 2-source 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 m-bit strings that is -close to having
min-entropy m - poly(log(1/), 1/), where here m is linear in n.
1 Introduction
This paper is about constructing efficiently computable 2-source extractors.
These are efficiently 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 entropy1
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,


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


Collections: Computer Technologies and Information Sciences