从不完全随机过程中有效提取随机性
Efficiently Extracting Randomness from Imperfect Stochastic Processes
摘要：
我们研究了从非理想随机过程中提取指定数量的随机比特的问题。Han和Hoshi提出的相关区间算法具有渐近最优性能，但它假设输入随机过程的分布是已知的。我们工作的动机是，在实践中，随机性的来源具有内在的相关性，并受到测量噪声的影响。也就是说，很难获得分布的准确估计。这个挑战是解决的种子和无籽提取器，可以处理一般的随机源未知分布的概念。然而，已知的有籽和无籽提取器提供的提取效率远小于香农的熵极限。我们的主要贡献是设计的提取器，有一个可变的输入长度和一个固定的输出长度，是有效的消费的符号从源，能够产生随机比特从一般的随机过程和方法的信息理论上界的效率。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
