標題: | Deterministic Extractors for Independent-Symbol Sources |
作者: | Lee, Chia-Jung Lu, Chi-Jen Tsai, Shi-Chun 資訊工程學系 Department of Computer Science |
關鍵字: | Independent-symbol sources;min-entropy;pseudo-randomness;randomness extractors |
公開日期: | 1-十二月-2010 |
摘要: | In this paper, we consider the task of deterministically extracting randomness from sources consisting of a sequence of n independent symbols from {0, 1}(d). The only randomness guarantee on such a source is that the whole source has min-entropy k. We give an explicit deterministic extractor which extract Omega(log k - log log(1/epsilon)) bits with error epsilon, for any, n, d, k is an element of N and epsilon is an element of (0, 1). For sources with a larger min-entropy, we can extract even more randomness. When k >= n(1/2+gamma), for any constant gamma is an element of (1, 1/2), we can extract m = k - O(d log(1/epsilon)) bits with any error epsilon >= 2(-Omega(n gamma)). When k >= log(c) n, for some constant c > 0 , we can extract m = k - (1/epsilon)(O(1)) bits with any error epsilon >= k(-Omega(1)). Our results generalize those of Kamp and Zuckerman and Gabizon et al. which only work for bit-fixing sources (with d = 1 and each bit of the source being either fixed or perfectly random). Moreover, we show the existence of a nonexplicit deterministic extractor which can extract m = k - O(log(1/epsilon)) bits whenever k = omega(d + log(n/epsilon)). Finally, we show that even to extract from bit-fixing sources, any extractor, seeded or not, must suffer an entropy loss k - m = Omega(log(1/epsilon)). This generalizes a lower bound of Radhakrishnan and Ta-Shma on extracting from general sources. |
URI: | http://dx.doi.org/10.1109/TIT.2010.2079012 http://hdl.handle.net/11536/26303 |
ISSN: | 0018-9448 |
DOI: | 10.1109/TIT.2010.2079012 |
期刊: | IEEE TRANSACTIONS ON INFORMATION THEORY |
Volume: | 56 |
Issue: | 12 |
起始頁: | 6501 |
結束頁: | 6512 |
顯示於類別: | 期刊論文 |