马尔可夫链产生均匀随机数的非渐近与渐近分析
Uniform Random Number Generation from Markov Chains: Non-Asymptotic and Asymptotic Analyses
摘要：
本文给出了带/不带边信息的随机数生成的非渐近可积性和逆界。我们的边界是有效的计算在这个意义上的计算复杂性不依赖于块的长度。我们还刻画了大偏差区和中等偏差区的渐近行为，这意味着我们的边界是渐近紧在这些地区。我们还显示了这些问题的二阶速率，并推导出表征二阶速率的方差的单字母形式。此外，我们解决这些问题的含糊率。
英文摘要：
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length. We also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds, which implies that our bounds are asymptotically tight in those regimes. We also show the second order rates of those problems, and derive single letter forms of the variances characterizing the second order rates. Further, we address the equivocation rates for these problems.
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。
