On the Asymptotic Behaviors of the Recurrence Time with Fidelity Criterion for Discrete Memoryless Sources and Memoryless Gaussian Sources

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概要

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• The asymptotic behavior of the recurrence time with fidelity criterion is discussed. Let X={X_i}^∞_<i=0> be a source and Y={Y_i}^<-1>_<i=-∞> a database. For a Δ>0 and an integer ι>0 define N^<[B]>_l(Y, X, Δ)as the minimum integer N satisfying d_l(X^<ι-1>_0, Y^<-Nι-1>_<-(N+1)l>)≦Δ subject to a fidelity criterion d_ι. In this paper the following two i.i.d. cases are considered:(A)X_i 〜 P and Y_i 〜 Q, where P and Q are probability distributions on a finite alphabet, and(B)X_i 〜 N(0, 1)and Y_i 〜 N(0, 1). In case(A)it is proved that 1/ι log_2N^<[B]>_ι(Y, X, Δ)almost surely converges to a certain constant determined by P, Q and Δ as ι → ∞. The Kac's lemma plays an important role in the proof on the convergence. In case(B)it is shown that there is a quantity related to 1/ι log_2N^<[B]>_ι(Y, X, Δ)that converges to the rate-distortion bound in almost sure sense.

• 社団法人電子情報通信学会の論文
• 1998-05-25

著者

• Koga H

  Univ. Tsukuba Tsukuba‐shi Jpn

• Arimoto Suguru

  College Of Science And Engineering Ritsumeikan University

• Koga Hiroki

  Graduate School Of Systems And Information Engineering University Of Tsukuba

関連論文

• On the Asymptotic Behaviors of the Recurrence Time with Fidelity Criterion for Discrete Memoryless Sources and Memoryless Gaussian Sources
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