Development of high performance error-correcting codes by using dynamical systems, Groebner basis, and sheaf cohomology

2015 Fiscal Year Final Research Report

• Project/Area Number: 24684007
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University (2015); Kyushu University
• 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)
• Project Period (FY): 2012-04-01 – 2016-03-31
• 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

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.

Free Research Field

応用トポロジー