Capacity Bounds for Additive Symmetric $\alpha $ -Stable Noise Channels

Impulsive noise features in many modern communication systems-ranging from wireless to molecular-and is often modeled by the α-stable distribution. At present, the capacity of α-stable noise channels is not well understood, with the exception of Cauchy noise (α = 1) with a logarithmic constraint and Gaussian noise (α = 2) with a power constraint. In this paper, we consider additive symmetric α-stable noise channels with α ∈ (1, 2]. We derive bounds for the capacity with an absolute moment constraint. We then compare our bounds with a numerical approximation via the Blahut-Arimoto algorithm, which provides insight into the effect of noise parameters on the bounds. In particular, we find that our lower bound is in good agreement with the numerical approximation for α near 2.