Group theoretic approach to the design of codes suitable for flash memories
| Project/Area Number |
15K00021
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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 |
Theory of informatics
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| Research Institution | Sophia University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ランク変調 / フラッシュメモリ / 多重集合 / 支配集合 / 群論 / 置換行列 / ランク変調符号 / 制約符号化 / 群の作用 / 対称群 |
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| Outline of Final Research Achievements |
In this study, we have developed a method to analyze the characteristics of the set of states associated with flash memories. This method utilizes an action of the group of permutation matrices that represents the state transition of memory.
Most of conventional studies considered the set of memory states as the group of permutation on {1,2,...,n} and investigated its characteristics. On the other hand, we focus not on the set of memory states itself but on the fact that the set of all permutation matrices corresponding to the state transitions becomes a group.
Then we have provided a concrete example of flash codes whose maximum possible number of rewriting and the capacity is well-balanced. Moreover, we have succeeded to develop the upper bound on the capacity of flash memories under the condition that the rewriting cost is fixed.
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Report
(4 results)
Research Products
(6 results)
