2017 Fiscal Year Final Research Report
Analyses and design of variable-to-fixed length data compression algorithms focused on the relationship with the sequentially hypothesis testing and the sufficient statistic
| Project/Area Number |
15K06088
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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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| Research Field |
Communication/Network engineering
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| Research Institution | Shonan Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2015-10-21 – 2018-03-31
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| Keywords | データ圧縮 / 十分統計量 / ユニバーサル符号 |
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| Outline of Final Research Achievements |
In this research we aim for the construction of the methods of analyses and design of variable-to-fixed length lossless data compression algorithms using some methods of mathematical statistics. Specifically, some relationships between the sufficient statistic and the universality of lossless source codes are investigated.
At first, the sufficient statistic is extended to the asymptotically sufficient statistic, and some asymptotically sufficient statistics are extracted from the existing lossless data compression algorithms. Then two-step algorithms are constructed. In their algorithms, asymptotically sufficient statistics are encoded in the first step. In the second step, the index of the given data sequence in the set of sequences which generates the same statistic as the given data sequence.
The asymptotic optimalities of the two step codes are proved using the zero-rateness and the asymptotic sufficiency of the statistics encoded in the first step of the two-step codes.
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| Free Research Field |
情報理論
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