Capacity in the Case of Transmission by Smooth Surfaces in Multiparametric Gaussian White Noise

The author computes the asymptotic behavior of the capacity of a channel with multiparametric Gaussian white noise when the signal is a smooth periodic function of many variables. Constraints are imposed on the average power of the signal and its partial derivatives. The derivatives may be of different order $\beta_T$ in different directions. It is shown that when the noise intensity $\varepsilon^2$ tends to zero, the capacity increases as $\varepsilon^{-2/(\gamma+1)}$, where $\gamma=(\sum\beta_i^{-1})^{-1}$.