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

摘要

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]_ι(Y, X, Δ) as the minimum integer N satisfying d_ι(X~ι-1_0, Y~-Nι-1_-(N + 1)ι) ≤ 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, ad (B) X_i ～ N(0, 1) and Y_i ～ N(0, 1).