Asymptotic Representation of the Capacity of a Continuous Channel with Small Nonadditive Noise

An information channel described by a conditional probability density function $g_\varepsilon(x|y)$ is investigated, where $y$ is the value of the channel output signal, $x$ is the input signal value, and $\varepsilon$ is a parameter that suitably characterizes the noise power. Asymptotic expressions are derived for the capacity of the given channel as $\varepsilon$ tends to zero, with various constraints on the conditional density and on the input signal. The asymptotically optimal distribution functions for the input signal are also determined.