On the epsilon-entropy and the rate-distortion function of certain non-Gaussian processes
J Binia, M Zakai, J Ziv - IEEE Transactions on Information …, 1974 - ieeexplore.ieee.org
Let\xi=\{\xi (t), 0\leq t\leq T\} be a process with covariance function K (s, t) and E\int_0^ T\xi^ 2
(t) dt<\infty. It is proved that for every\varepsilon> 0 the\varepsilon-entropy H_
{\varepsilon}(\xi) satisfies\begin {equation} H_ {\varepsilon}(\xi_g)-\mathcal {H} _
{\xi_g}(\xi)\leq H_ {\varepsilon}(\xi)\leq H_ {\varepsilon}(\xi_g)\end {equation} where\xi_g is a
Gaussian process with the covarianee K (s, t) and\mathcal {H} _ {\xi_g}(\xi) is the entropy of
the measure induced by\xi (in function space) with respect to that induced by\xi_g. It is also …
(t) dt<\infty. It is proved that for every\varepsilon> 0 the\varepsilon-entropy H_
{\varepsilon}(\xi) satisfies\begin {equation} H_ {\varepsilon}(\xi_g)-\mathcal {H} _
{\xi_g}(\xi)\leq H_ {\varepsilon}(\xi)\leq H_ {\varepsilon}(\xi_g)\end {equation} where\xi_g is a
Gaussian process with the covarianee K (s, t) and\mathcal {H} _ {\xi_g}(\xi) is the entropy of
the measure induced by\xi (in function space) with respect to that induced by\xi_g. It is also …
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