The censored channel is the cascade of an additive noise channel with a clipping operator that restricts the signal to the interval [0; 1]. In this paper, after discussing the generality of the considered model, the mutual information of the censored channel is proven to be a continuous function of the input probability distribution whenever the probability density of the noise is bounded. Moreover, there is an input-distribution of bounded support that achieves capacity for a class of noise distributions with bounded support. For a more general class of noise distributions, the capacity can be approximated arbitrarily close using only input-distributions of bounded support. This support is determined only based on the noise distribution and the desired approximation error. These results constitute a first step for characterization of the capacity of censored channels.
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