电子学报 ›› 2012, Vol. 40 ›› Issue (10): 2127-2132.DOI: 10.3969/j.issn.0372-2112.2012.10.038

• 科研通信 • 上一篇    下一篇

基于母函数的非线性反馈函数及其子序列研究

吕虹1, 张爱雪2, 方俊初2, 解建侠1, 李炳荣2, 戚鹏1   

  1. 1. 安徽建筑工业学院电子与信息学院, 安徽合肥 230022;
    2. 安徽工程大学电气工程学院, 安徽芜湖 241000
  • 收稿日期:2011-10-13 修回日期:2012-06-16 出版日期:2012-10-25
  • 作者简介:吕 虹 女,1959年10月出生于,安徽怀宁人,硕士,教授,研究方向信号处理,检测技术、EDA技术等. E-mail:lvhong176@163.com 张爱雪 女,1977年出生于山东郓城,安徽工程大学电气工程学院讲师,主要研究方向为信息信号处理、嵌入式系统等. 方俊初 男,1974年4月出生,安徽六安人,硕士,讲师,研究领域涉及信号处理,电子技术,电子系统设计、检测技术等.
  • 基金资助:
    国家自然科学基金(No.61071001)

Study of the Non-Linear Feedback Functions and a Class Subsequence Based on the Root-Functions

LV Hong1, ZHANG Ai-xue2, FANG Jun-chu2, XIE Jian-xia1, LI Bing-rong2, QI Peng1   

  1. 1. Department of Electronic and Information Engineering, Anhui Institute of Architecture and Industry, Hefei, Anhui 230022, China;
    2. Department of Electrical Engineering, Anhui polytechnic University, Wuhu, Anhui 241000, China
  • Received:2011-10-13 Revised:2012-06-16 Online:2012-10-25 Published:2012-10-25
  • Supported by:
    National Natural Science Foundation of China (No.61071001)

摘要: 针对非线性最大长度移位寄存器反馈函数难以构造问题,本文提出了一种基于母函数构造非线性最大长度移位寄存器反馈函数方法.首先,我们阐述了母函数模3分类法,证明了各类母函数新的特征状态集,提取了母函数的特征式;其次,根据特征式对母函数的筛分特性合成了非线性m子序列移位寄存器反馈函数;最后,分析了该移位寄存器生成的伪随机序列,对其自相关值和线性复杂度进行了大量搜索.结果一致表明该序列不仅具有良好的周期特性、平衡特性、游程特性,还具有尖锐的自相关特性和理想的线性复杂度.

关键词: 非线性, 反馈函数, 合成, 筛分, 模3, 特征式, 伪随机序列

Abstract: To solve the problem of constructing feedback functions of non-linear maximal length shift registers (NMLSR),the method to construct the feedback functions for NMLSR was proposed based on root function.First of all,we expatiated the classification method of the root functions modulo 3,proveded the characteristic state sets of the root functions and extracted the eigenfunctions of the root functions.Secondly,we synthesized the feedback function for the nonlinear m subsequence shift register according to the filter of the eigenfunctions on the root functions.Finally,we conducted a great number of calculations and analyses for new type sequences generated from the nonlinear m subsequence shift registers.The results show unanimously that the nonlinear m subsequences dose not only possess better period property,balance property and run-path property,but also the sharp autocorrelation property and the ideal linear complexity.

Key words: nonlinear, feedback function, synthesize, filter, modulo 3, eigenfunction, pseudo-random sequence

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