超離散力学系に基づく最適拡散符号の実現とその応用

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Author: 藤崎, 礼志ほか

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Publication date: 2012-04-01

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Note (General)：: 金沢大学理工研究域電子情報通信学系本研究では,超離散力学系に基づく最適拡散符号を実現し, SSMA通信システムに応用するために,以下の結果を得た. i) SSMA通信システムの性能評価に関するYaoの問題に対して,確率解析の立場から,完全な解答を与えた. ii)最適な位相シフトフリー拡散符号を実現す...

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Material Type: 文書・図像類
Title: 超離散力学系に基づく最適拡散符号の実現とその応用
Author/Editor: 藤崎, 礼志
Fujisaki, Hiroshi
Author Heading: 藤崎, 礼志
Fujisaki, Hiroshi
Publication Date: 2012-04-01
Publication Date (W3CDTF): 2012-04-01
Alternative Title: Construction of and applications for opyimal spreading sequences based on ultra discrete dynamical systems
Periodical title: 平成23(2011)年度科学研究費補助金基盤研究(C) 研究成果報告書 = 2011 Fiscal Year Final Research Report
No. or year of volume/issue: 2009-2011
Volume: 2009-2011
Pages: 4p.-
Text Language Code: jpn
Subject Heading: 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
Target Audience: 一般
Note (General): 金沢大学理工研究域電子情報通信学系
本研究では,超離散力学系に基づく最適拡散符号を実現し, SSMA通信システムに応用するために,以下の結果を得た. i) SSMA通信システムの性能評価に関するYaoの問題に対して,確率解析の立場から,完全な解答を与えた. ii)最適な位相シフトフリー拡散符号を実現する区分的線形マルコフ変換を含む,区分的単調増加マルコフ変換を考え,それらが離散化された変換に基づく最大周期列を全て生成するような,有界単調真理値表アルゴリズムを与えた.典型例として,アルゴリズムを全てのde Bruijn系列の生成に応用した. iii) NLFSR系列の内, de Bruijn系列の自己相関特性の下界を理論的に導出することに成功した.
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.
出典：研究課題「超離散力学系に基づく最適拡散符号の実現とその応用」課題番号21560392（KAKEN：科学研究費助成事業データベース（国立情報学研究所））（https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-21560392/21560392seika/）を加工して作成
DOI: 10.24517/00052548
Access Restrictions: 限定公開
Related Material: https://kaken.nii.ac.jp/search/?qm=80304757
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21560392/
https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-21560392/21560392seika/
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 金沢大学 : 金沢大学学術情報リポジトリKURA