Evaluating the channel capacity is one of many key problems in information theory. In this work, we derive rather-mild sufficient conditions under which the capacity of continuous channels is  finite  and  achievable . These conditions are derived for generic, memoryless, and possibly nonlinear additive noise channels. The results are based on a novel sufficient condition that guarantees the convergence of differential entropies under point-wise convergence of probability density functions. Perhaps surprisingly, the finiteness of channel capacity holds for the majority of setups, including those where inputs and outputs have possibly infinite second-moments.
['Jihad Fahs', 'Ibrahim C. Abou-Faycal']
On the Finiteness of the Capacity of Continuous Channels