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TR03-085 | 28th November 2003 00:00
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#### On the (Im)possibility of Non-interactive Correlation Distillation

TR03-085
Authors:

Ke Yang
Publication: 8th December 2003 20:38

Downloads: 2149

Keywords:

**Abstract:**
We study the problem of non-interactive correlation distillation

(NICD). Suppose Alice and Bob each has a string, denoted by

$A=a_0a_1\cdots a_{n-1}$ and $B=b_0b_1\cdots b_{n-1}$,

respectively. Furthermore, for every $k=0,1,...,n-1$, $(a_k,b_k)$ is

independently drawn from a distribution $\noise$, known as the ``noise

mode''. Alice and Bob wish to ``distill'' the correlation

non-interactively, i.e., they wish to each apply a function to their

strings, and output one random bit, denoted by $X$ and $Y$, such that

$\prob[X=Y]$ can be made as close to 1 as possible. The problem is,

for what noise model can they succeed? This problem is related to

various topics in computer science, including information

reconciliation and random beacons. In fact, if NICD is indeed possible

for some general class of noise models, then some of these topics

would, in some sense, become straightforward corollaries.

We prove two negative results on NICD for various noise models.

We prove that for these models, it is impossible to distill the

correlation to be arbitrarily close to 1. We also give an example

where Alice and Bob can increase their correlation with one bit of

communication (in this case they need to each output two bits). This

example, which may be of its own interest, demonstrates that even the

smallest amount of communication is provably more powerful than no

communication.

An extended abstract of this paper is to appear in the Latin American

Theoretical INformatics (LATIN 2004), Buenos Aires, Argentina, 2004.