2020 Fiscal Year Final Research Report
Efficient generation of full-length sequences with optimal correlation based on discretized chaotic transformations and its applications to multiple access communication systems
| Project/Area Number |
18K11465
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 61040:Soft computing-related
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | 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) |
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| Outline of Final Research Achievements |
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.
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| Free Research Field |
情報工学
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| Academic Significance and Societal Importance of the Research Achievements |
de Bruijn 系列は暗号解読，衛星通信，ゲノム解析に応用されているが，位数nのde Bruijn 系列の自己相関関数は，時刻t=0に値1を取り，0<t<|n|において値0を取るという零相関帯を有すること，それ以外については上下界しか知られていない．相関特性は学術のみならず応用上も重要な統計量であるので，研究成果(i),(ii)は擬似乱数，系列の専門分野に留まらず，de Bruijn 系列を応用する分野にも貢献した．ストリーム型ABSは，アップル社オープンソースデータ圧縮アルゴリズムに採用される程，実用上優れた性能を有する．研究成果(iii)はそれをデータ圧縮として利用する人々に貢献した．
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