Minimum attainable mean-square error in transmission of a parameter over a channel with white Gaussian noise (Q1083421)

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 \(\alpha\geq 2\) of the magnitude of the error. The logarithmically exact asymptotic form of \(e_{\alpha}(A)\) for \(\alpha\geq 2\) is obtained.