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Invited Talk : Four Limits in Probability and Their Operational Meanings in Information Theory

  • KOGA Hiroki
    Faculty of Systems and Information, University of Tsukuba

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  • 招待講演 情報理論における4種類の確率的極限とそれらの操作的意味 (ワイドバンドシステム)
  • 招待講演 情報理論における4種類の確率的極限とそれらの操作的意味
  • ショウタイ コウエン ジョウホウ リロン ニ オケル 4シュルイ ノ カクリツテキ キョクゲン ト ソレラ ノ ソウサテキ イミ

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Abstract

In information-spectrum methods proposed by Han and Verdu, quantities defined by using the ordinary superior/inferior limits in probability have operational meanings in various information-theoretic problems. In this paper we introduce another two nonconventional limits in probability and define four kinds of quantities by using the ordinary and the nonconventional limits. We first show that the four quantities satisfy a certain inequality if a source satisfies a certain property. Next, we discuss operational meanings of the four quantities in fixed-length coding of a general source. We also give applications of the four quantities such that we can give necessary and sufficient conditions that correspond to nonconventional strong converse properties. Finally, we explain a result on the achievable rate region in the optimistic sense of separate coding of two correlated general sources.

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