On Minimum Attainable Mean-Square Error in Transmission of a Parameter over a Channel with White Gaussian Noise

The article considers the problem of asymptotically optimal $(A\to\infty)$ choice of signals for transmission of a parameter over a channel with white Gaussian noise, with a constraint on the signal energy $A$. The quality criterion $e_\alpha(A)$ is the absolute moment of degree a $\alpha\geq 2$ of the magnitude of the error. The logarithmically exact asymptotic form of $e_\alpha(A)$ for $\alpha\geq 2$ is obtained.