Statistics Papers

Document Type

Journal Article

Date of this Version

10-2011

Publication Source

IEEE Transactions on Information Theory

Volume

57

Issue

10

Start Page

6351

Last Page

6355

DOI

10.1109/TIT.2011.2134067

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).

Keywords

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

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Date Posted: 27 November 2017

This document has been peer reviewed.