Analysis of Data Conversion for Highly Reliable and Secure Communication/Storage Systems

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K06340
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: The University of Electro-Communications
• Principal Investigator: Yagi Hideki 電気通信大学, 大学院情報理工学研究科, 准教授 (60409737)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 情報理論 / 符号化 / 情報セキュリティ / 乱数生成 / 情報源符号化

Outline of Final Research Achievements

The conversion of a uniformly distributed random number to approximate a given target distribution is generally called random number generation. In this study, we consider the problem of minimizing the size of the value set in which the uniform random number takes while the approximation is done within some precision. This problem is called the problem of resolvability. This study introduces the problem of resolvability based on the idea of variable-length coding, and the minimum resolvability rate is investigated. When the target distribution is a stationary memoryless source or a mixture of such sources, the minimum resolvability can be characterized in a form which does not depend on the length of source sequences. In addition, we extend the approximation measure between two probability distributions in the problem of fixed-length resolvability.

Free Research Field

情報理論

Academic Significance and Societal Importance of the Research Achievements

本研究で導出し可変長のResolvability問題における最小乱数生成レートの公式から，固定長の問題に対する最小乱数生成レートよりも平均的に変換のコストを下げられることを示している．さらにこの結果から，定常無記憶情報源やマルコフ情報源を近似する最小乱数生成レートは，この情報源からの出力系列を符号化する際の最小符号化レートと一致することがわかり，系列長に依存しない形式で最小乱数生成レートの公式が得られる．系列長に依存しない定数オーダの計算量で一様乱数の最少レートを計算することが可能になり，乱数生成アルゴリズムの設計の指針を与える結果と言える．