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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 1998 Volume 34, Issue 4, Pages 23–38 (Mi ppi422)

This article is cited in 3 papers

Methods of Signal Processing

Upper and Lower Bounds and Asymptotics of Optimal Filtering Error of a Stationary Process with a Small Information Rate

M. S. Pinsker, V. V. Prelov


Abstract: Upper and lower bounds are obtained for the mean-square error of the optimal (nonlinear) filtering of a discrete-time stationary process $X=\{X_j\}$ from the observations $Y=\{Y_j\}$, where $Y=X+Z$ and $Z=\{Z_j\}$ is a sequence of i.i.d. random variables. These bounds are linear functions of the information rate $\overline I(X;Y)$. It is shown that the lower bound is asymptotically tight in the case where both $\overline I(X;Y)$ and the peak power of the signal $X$ tend to zero. The situations where $X_n$ is estimated from either the observations $\{Y_j, j\leq n-1\}$ or the observations $\{Y_j, j\leq n\}$ are both considered.

UDC: 621.391.1:519.28

Received: 30.10.1997


 English version:
Problems of Information Transmission, 1998, 34:4, 309–321

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© Steklov Math. Inst. of RAS, 2025