Information rates in certain stationary non-Gaussian channels in weak-signal transmission (Q1276928)

Let \(\xi= \{\xi_j\}\) and \(\zeta= \{\zeta_j\}\) be independent discrete-time second-order stationary processes obtained by means of an invertible linear transformation \(L\) from a stationary entropy-regular process \(X= \{X_j\}\) and a sequence of i.i.d. random variables \(Z= \{Z_j\}\) such that \(\xi= LX\) and \(\zeta= LZ\). Under the assumption that the Fisher information \(J(Z_1)\) exists and some additional assumptions on the properties of the linear transformation \(L\) and on the density function of \(Z_1\), it is shown that the following equality for the information rate \(\overline{I} (\varepsilon \xi,\varepsilon \xi+\zeta)\) holds: \(\overline{I} (\varepsilon \xi,\varepsilon \xi+\zeta)= \frac 12 J(Z_1) (\text{var } X_1)^2+ o(\varepsilon^2)\), \(\varepsilon \to 0\). This result is a generalization of the corresponding results where \(\xi\) was assumed to be Gaussian.