Asymptotic Behavior of the Capacity of a Continuous Channel with Large Smooth Noise

The article investigates the asymptotic behavior of the capacity of a memoryless channel with independent additive noise, under the assumption that the average signal power of the input tends to zero. It is assumed that the distribution density of the noise is a smooth function. It is shown that the order of the asymptotic form of the capacity depends strongly on whether there exists a set of nonzero measure on which the distribution density of the noise becomes zero. If there is no such set, the order of the asymptotic form depends on the rate of decrease of the noise distribution density at infinity.