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- W2098392316 abstract "Suppose Alice and Bob receive strings of unbiased independent but noisy bits from some random source. They wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating. How many such bits can they extract? The trivial strategy of outputting the first <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$k$</tex> </formula> bits yields an agreement probability of <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex Notation=TeX>$(1-varepsilon)^{k}<2^{-1.44kvarepsilon}$</tex></formula> , where <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$varepsilon$</tex> </formula> is the amount of noise. We show that no strategy can achieve agreement probability better than <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$2^{-kvarepsilon/(1-varepsilon)}$</tex> </formula> ." @default.
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- W2098392316 date "2011-10-01" @default.
- W2098392316 modified "2023-10-05" @default.
- W2098392316 title "On Extracting Common Random Bits From Correlated Sources" @default.
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- W2098392316 doi "https://doi.org/10.1109/tit.2011.2134067" @default.
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