2011 Fiscal Year Final Research Report
Construction of and applications for optimal spreading sequences based on ultra discrete dynamical systems
| Project/Area Number |
21560392
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Communication/Network engineering
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 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 |
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| Research Abstract |
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.
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