超離散カオス力学系に基づく最適相関最大周期列の効率的生成と多元接続通信への応用

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Author: 藤崎, 礼志ほか

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Publication date: 2021-06-03

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Note (General)：: 出版タイプ： AM金沢大学理工研究域電子情報通信学系超離散カオス力学系に基づく最大周期列の効率的生成とその多元接続通信への応用に関して次の結果を得た．(i)Sawadaらのアルゴリズムで生成されるde Bruijn 系列の自己相関特性を明らかにし，良好な自己相関特性を有するde Bruijn 系列の...

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Material Type: 規格・テクニカルリポート類
Title: 超離散カオス力学系に基づく最適相関最大周期列の効率的生成と多元接続通信への応用
Author/Editor: 藤崎, 礼志
Fujisaki, Hiroshi
Author Heading: 藤崎, 礼志
Fujisaki, Hiroshi
Publication Date: 2021-06-03
Publication Date (W3CDTF): 2021
Alternative Title: Efficient generation of full-length sequences with optimal correlation based on discretized chaotic transformations and its applications to multiple access communication systems
Periodical title: 令和2(2020)年度科学研究費補助金基盤研究(C) 研究成果報告書 = 2020 Fiscal Year Final Research Report
No. or year of volume/issue: 2018-04-01 - 2021-03-31
Volume: 2018-04-01 - 2021-03-31
Pages: 7p.-
Subject Heading: 超離散力学系
マルコフ連鎖
最大周期列
記号力学系
非対称2進数系(ABS)
Target Audience: 一般
Note (General): 出版タイプ： AM
金沢大学理工研究域電子情報通信学系
超離散カオス力学系に基づく最大周期列の効率的生成とその多元接続通信への応用に関して次の結果を得た．(i)Sawadaらのアルゴリズムで生成されるde Bruijn 系列の自己相関特性を明らかにし，良好な自己相関特性を有するde Bruijn 系列のファミリーを構成した．(ii)Sawadaらのアルゴリズムを拡張し，離散化黄金平均変換に基づく最大周期列を1ビット当たりならし計算量O(1)で生成し，その自己相関特性を明らかにした．(iii)ストリーム型データ圧縮アルゴリズム非対称2進数系(asymmetric binary systems (ABS))が正しく動作するための必要十分条件を与えた．
We have previously defined the discretized Markov transformations and the full-length sequences based on such transformations. De Bruijn sequences can be regarded as the full-length sequences based on the discretized Markov beta-transformation with beta=2. Recently, Sawada et al. proposed an efficient construction of de Bruijn sequence. We modify their construction and apply it to construct a full-length sequence based on the discretized Markov beta-transformation, where beta is the golden mean. We also give correlational properties of not only de Bruijn sequences constructed by Sawada et al. but the full-length sequences constructed in this research, which are based on the discretized golden mean transformation.The stream version of asymmetric binary systems (ABS) is irreducible if it admits an irreducible finite-state Markov chain. For a probability p (0<p<1), where p is irrational, we give a necessary and sufficient condition for the stream version of ABS to be irreducible.
研究課題/領域番号:18K11465, 研究期間(年度):2018-04-01 - 2021-03-31
出典：「超離散カオス力学系に基づく最適相関最大周期列の効率的生成と多元接続通信への応用」研究成果報告書　課題番号18K11465（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-18K11465/18K11465seika/）を加工して作成
DOI: 10.24517/00057768
https://doi.org/10.24517/00057768
Related Material: https://kaken.nii.ac.jp/search/?qm=80304757
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18K11465/
https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-18K11465/18K11465seika/
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