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Capacity-achieving distributions for non-Gaussian additive noise channels

We characterize the capacity-achieving distribution for a class of non-Gaussian additive noise channels, when the transmitter is subject to an "average" power constraint. Specifically, we show that if the probability density function of the noise, in addition to satisfying some mild technical conditions, has a tail which decays at a rate slower (resp. faster) than the Gaussian, then the capacity-achieving distribution has bounded (resp. unbounded) support.