Capacity Sensitivity in Additive Non-Gaussian Noise Channels

Malcolm Egan 1 Samir M. Perlaza 1 Vyacheslav Kungurtsev 2
1 SOCRATE - Software and Cognitive radio for telecommunications
CITI - CITI Centre of Innovation in Telecommunications and Integration of services, Inria Grenoble - Rhône-Alpes
Abstract : In this paper, a new framework based on the notion of \textit{capacity sensitivity} is introduced to study the capacity of continuous memoryless point-to-point channels. The capacity sensitivity reflects how the capacity changes with small perturbations in any of the parameters describing the channel, even when the capacity is not available in closed-form. This includes perturbations of the cost constraints on the input distribution as well as on the channel distribution. The framework is based on continuity of the capacity, which is shown for a class of perturbations in the cost constraint and the channel distribution. The continuity then forms the foundation for obtaining bounds on the capacity sensitivity. As an illustration, the capacity sensitivity bound is applied to obtain scaling laws when the support of additive α-stable noise is truncated.
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Malcolm Egan, Samir M. Perlaza, Vyacheslav Kungurtsev. Capacity Sensitivity in Additive Non-Gaussian Noise Channels. IEEE International Symposium on Information Theory (ISIT), Jun 2017, Aachen, Germany. ⟨hal-01522950⟩

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