On the Finiteness of the Capacity of Continuous Channels

Jihad Fahs; Ibrahim Abou-Faycal

doi:10.1109/tcomm.2015.2503403

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arXiv · 1504.03814

On the Finiteness of the Capacity of Continuous Channels

Jihad Fahs·Ibrahim Abou-Faycal

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Abstract

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 is finite and achievable. These conditions are derived for generic, memoryless and possibly non-linear 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.

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Jihad Fahs, Ibrahim Abou-Faycal. 2015-04-15. On the Finiteness of the Capacity of Continuous Channels. https://doi.org/10.1109/tcomm.2015.2503403

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