Asymptotic Behavior of the Capacity of a Continuous Channel with a Large Amount of Noise

We consider a channel with independent additive noise, whose output signal $\eta=\xi+\zeta$, where $\xi$ is the input signal and $\zeta$ is the noise. Assuming that the average power of the input signal tends to zero $M|\xi|^2\leq\varepsilon\to 0$, and with certain conditions imposed on the distribution density of the noise, we determine the asymptotic behavior of the channel capacity. We also obtain the form of the asymptotically optimum distribution at the channel input.