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On Extracting Common Random Bits From Correlated Sources

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2 Author(s)
Andrej Bogdanov ; Department of Computer Science and Engineering and Institute for Theoretical Science and Communications, Chinese University of Hong Kong ; Elchanan Mossel

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).

Published in:

IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 10 )