On Extracting Common Random Bits From Correlated Sources

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Statistics Papers
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hamming codes
probability
random codes
hamming weight code
common random noisy bit extraction
correlated sources
first k bits
correlation
entropy
hamming weight
noise
noise measurement
protocols
upper bound
common information
randomness extraction
Computer Sciences
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Bogdanov, Andrej
Mossel, Elchanan
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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 k bits yields an agreement probability of (1-ε)k< 2 −1.44kε, where ε is the amount of noise. We show that no strategy can achieve agreement probability better than 2−kε/(1−ε). On the other hand, we show that when k ≥ 10 + 2(1 − ε)/ε, there exists a strategy which achieves an agreement probability of 0.003(kε)−1/2 · 2−kε/(1−ε).

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2011-10-01
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IEEE Transactions on Information Theory
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