Date of this Version
IEEE Transactions on Information Theory
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).
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
Bogdanov, A., & Mossel, E. (2011). On Extracting Common Random Bits From Correlated Sources. IEEE Transactions on Information Theory, 57 (10), 6351-6355. http://dx.doi.org/10.1109/TIT.2011.2134067
Date Posted: 27 November 2017
This document has been peer reviewed.