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)<sup>k</sup> <; 2<sup>-1.44kε</sup>, where ε is the amount of noise. We show that no strategy can achieve agreement probability better than 2<sup>-kε/(1-ε)</sup>. 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)<sup>-1/2</sup> · 2<sup>-kε/(1-ε)</sup>.
IEEE Transactions on Information Theory 11/2011; · 3.01 Impact Factor