Construction of and applications for optimal spreading sequences based on ultra discrete dynamical systems

基于超离散动力系统的最优扩频序列的构建及应用

• 批准号: 21560392
• 负责人: FUJISAKI Hiroshi
• 金额: $ 3万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21560392/
• 关键词: 超離散力学系; 最大周期列; de Bruijn系列; 記号力学系; スペクトル拡散符号; de Brui jn系列

In this research we constructed optimal spreading sequences based on ultra discrete dynamical systems. For their applications, we considered asynchronous spread spectrum multiple access communication systems with spreading sequences of Markov chains. The main results in the three-year study are summarized as follows. i) By refinement of the large deviations analysis, we obtained exact asymptotic analyses of bit error probabilities in such systems. Comparing theoretical expressions of bit error probabilities with experimental results, we confirmed that for too small numbers of users compared to the lengths of spreading sequences, the central limit asymptotic analyses became invalid, but for large deviations asymptotic analyses turned out to be relevant. ii) We considered discretized piecewise-monotone-increasing Markov transformations and gave an algorithm, called the bounded monotone truth-table algorithm, for generating all full-length sequences which were based on the discretized transformations. The algorithm was applicable to generation of all de Bruijn sequences. iii) We gave a novel lower bound of the minimum values of the normalized auto-correlation functions for de Bruijn sequences.

本研究基于超离散动力系统构造最优扩频序列。对于它们的应用，我们考虑了具有马尔可夫链扩频序列的异步扩频多址通信系统。三年研究的主要结果总结如下。i）通过对大偏差分析的改进，我们得到了这种系统中误码概率的精确渐近分析。误码率的理论表达式与实验结果相比，我们证实，对于太小的用户数相比，扩频序列的长度，中心极限渐近分析变得无效，但大偏差渐近分析原来是相关的。ii）考虑了离散分段单调递增Markov变换，给出了一种生成基于离散变换的所有全长序列的算法，称为有界单调真值表算法。该算法适用于所有de Bruijn序列的生成。（3）给出了de Bruijn序列的归一化自相关函数的最小值的一个新的下界。

项目成果

On Invariant Measures for the Fibonacci Dyck Shift

关于斐波那契戴克平移的不变测度

• 发表时间: 2012
• 作者: 高博昭;上原秀幸;大平孝;Hiroshi Fujisaki
• 通讯作者: Hiroshi Fujisaki

On Embeddings of Shifts of Finite Type into the Golden-Mean-Dyck Shift

关于有限类型平移嵌入到中庸戴克平移中

• 发表时间: 2011
• 期刊: Proc.of the 2010 International Symposium on Information Theory and its Applications
• 作者: Hiroshi Fujisaki;Hiroshi Fujisaki;Hiroshi Fujisaki
• 通讯作者: Hiroshi Fujisaki

On Embeddings of Shiftis of FiniteType into the Golden-Mean-DyckShi shift

将有限类型的 Shiftis 嵌入到 Golden-Mean-DyckShi 移位中

• 发表时间: 2011
• 作者: Nanao;S.;Masuyama;H.;Kasahara;S.;and Takahashi;Y.;Hiroshi Kamabe;Hiroshi Fujisaki
• 通讯作者: Hiroshi Fujisaki

超離散力学系に基づく位相シフトフリーM-相スペクトル拡散符号の実現とその応用

基于超离散动力系统的无相移M相扩频码的实现及其应用

• 发表时间: 2010
• 期刊: 電気通信普及財団研究調査報告書
• 作者: Hiroshi Fujisaki;Hiroshi Fujisaki;Hiroshi Fujisaki;藤崎礼志
• 通讯作者: 藤崎礼志

Performance Analysis of SSMA Communication Systems With Spreading Sequences of Markov Chains: Large Deviations Principle Versus the Central Limit Theorem

• DOI: 10.1109/tit.2011.2110030
• 发表时间: 2011-04
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: H. Fujisaki