Zero-Error Capacity of Continuous Memoryless Channels with a Small Input Signal

We examine a continuous memoryless channel given by an arbitrary transition function $Q(x,B)$, $\in X$, $B\in\mathscr{Y}$, whose signal space at the input is a $k$-dimensional Euclidean space $\mathbf{R}^k$, while the signal space at the output is an arbitrary measurable space $(Y,\mathscr{Y})$. The asymptotic behavior of the zero-error capacity of such a channel under the assumption that the input signal power tends to zero is investigated.