Development of high performance error-correcting codes by using dynamical systems, Groebner basis, and sheaf cohomology
| Project/Area Number |
24684007
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University (2015)
Kyushu University |
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Principal Investigator |
Hiraoka Yasuaki 東北大学, 原子分子材料科学高等研究機構, 准教授 (10432709)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥14,300,000 (Direct Cost: ¥11,000,000、Indirect Cost: ¥3,300,000)
Fiscal Year 2015: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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| Keywords | 近似最尤推定復号 / 位相的データ解析 / パーシステントホモロジー / 一般化MacWilliams恒等式Mac / 最尤推定復号 / 一般化MacWilliams恒等式 / 有理写像 / グレブナー基底 / MacWilliams恒等式 |
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| Outline of Final Research Achievements |
We generalized the encode-decode duality theorem into polynomial maps. The key idea is to represent maximum likelihood decoding as generalized MacWilliams identity. We also studied numerical experiments and found that the performance of the proposed method is quite better than conventional methods. For the subject on network coding and sheaf cohomology, we studied a formulation using quiver representations. We derived an algorithm for indecomposable decompositions on several explicit examples, and studied the structure on representation category.
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Report
(5 results)
Research Products
(12 results)
