An upper bound on the capacity of censored channels

In this paper, we consider a channel which is linear over the interval [0, 1] and is censored to the left by zero and to the right by one. Examples of this channel type are radio frequency amplifiers which amplify only up to certain thresholds. In the baseband, this channel is a model for censoring symbols whenever they exceed given thresholds. One-bit quantization may be seen as an extreme case when the right censoring bound converges to the left one. Determining mutual information and capacity of this channel is a fundamental information theoretic problem which seems to be unsolved in general. One reason seems to be that the output distribution has two mass points at the bounds of the censoring interval and can be continuous within the linear region. In this paper, we provide a compact formula for mutual information of this channel. Furthermore, an upper bound for the capacity of this channel is given. Finally, selected numerical results for additive uniformly distributed and Gaussian noise are presented to evaluate the accuracy of the bound.