Empirical Study of Extractors from Reed-Solomon Codes

• Main Authors: Sung-Tsu Wang, 王頌袓
• Other Authors: Shi-Chun Tsai
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/72454985132698764012

碩士 === 國立交通大學 === 資訊工程系 === 91 === Since Trevisan shows the connection between extractors and codes in [tre99], Ta-Shma, Zuckerman and Shaltiel construct extractors by encoding the weak random source using the Reed-Muller codes [tszs01] [su01]. In this thesis, we study the possibility of constructing extractors by Reed-Solomon codes. In our experiments, we focus on the "bounded segment source". The bounded segment source consists of several segments of equal length, and in each segment, there are some bits fixed as 0. We make each segment in length $\lceil p\rceil$, where p is a prime. We consider two kinds of bit fixing in each segment. One is with the most significant bits fixed, and the other is with every other bit interleaved in the segment. Using the Reed-Solomon codes to encode the bounded segment source, we perform three types of constructions to the encoded polynomial. For each construction, we do three experiments. The first is to check the number of constraints required for the interpolation of the encoded polynomial. The second is to make statistical analyses to the randomness of the ith digit under given i-1 previous digits. The third is to calculate the statistical distance between the induced distribution of our constructions and the uniform distribution. We find that if the output length is under a threshold depending on the field, the output sequence is very close to random.