On the Capacity of Censored Channels

Conference: SCC 2017 - 11th International ITG Conference on Systems, Communications and Coding
02/06/2017 - 02/09/2017 at Hamburg, Germany

Proceedings: ITG-Fb. 268: SCC 2017

Pages: 6Language: englishTyp: PDF

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Authors:
Behboodi, Arash; Alirezaei, Gholamreza; Mathar, Rudolf (Institute for Theoretical Information Technology, RWTH Aachen University, 52056 Aachen, Germany)

Abstract:
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.