An Almost Sure Recurrence Theorem with Distortion for Stationary Ergodic Sources

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概要

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• Let {X_k}^∞_<k=-∞> be a stationary and ergodic information source, where each X_k takes values in a standard alphabet A with a distance function d : A × A → [0,∞) defined on it. For each sample sequence X = (..., x_<-1>, x_0, x_1,...) and D > 0 let the approximate D-match recurrence time be defined by R_n(X, D) = min{m ≧ n : d_n(X^n_1 ,X^<m+n>_<m+1_>) ≦ D}, where X^j_i denotes the string x_ix_<i+1>...x_j and d_n : A^n × A^n → [0,∞) is a metric of A^n induced by d for each n. Let R(D) be the rate distortion function of the source {X_k}^∞_<k=-∞> relative to the fidelity criterion {d_n}. Then it is shown that lim sup_<n→∞> 1/nlog R_n(X,D) ≦ R(D/2)a.s.

• 1997-11-25

著者

• Kanaya Fumio

  Shonan Institute Of Technology

• Muramatsu Jun

  Ntt

関連論文

• An Almost Sure Recurrence Theorem with Distortion for Stationary Ergodic Sources
• A Universal Data-Base for Data Compression
• Dual Quantity of the Distortion-Complexity and a Universal Data-Base for Fixed-Rate Data Compression with Distortion (Special Section on Information Theory and Its Applications)

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