Efficiently Extracting Randomness from Imperfect Stochastic Processes

TL;DR

This paper introduces new extractors that efficiently generate nearly optimal random bits from imperfect, correlated sources without prior knowledge of their distribution, improving upon existing methods.

Contribution

We design variable-input, fixed-output length extractors that are efficient, adaptable to unknown sources, and approach the Shannon entropy limit.

Findings

Extractors approach the Shannon entropy limit.

Efficiently handle sources with unknown distributions.

Capable of extracting randomness from correlated processes.

Abstract

We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related interval algorithm proposed by Han and Hoshi has asymptotically optimal performance; however, it assumes that the distribution of the input stochastic process is known. The motivation for our work is the fact that, in practice, sources of randomness have inherent correlations and are affected by measurement's noise. Namely, it is hard to obtain an accurate estimation of the distribution. This challenge was addressed by the concepts of seeded and seedless extractors that can handle general random sources with unknown distributions. However, known seeded and seedless extractors provide extraction efficiencies that are substantially smaller than Shannon's entropy limit. Our main contribution is the design of extractors that have a variable input-length and a fixed output length, are efficient in the consumption of symbols from the source, are capable of generating random bits from general stochastic processes and approach the information theoretic upper bound on efficiency.