Capacity-Achieving Input Distribution in Per-Sample Zero-Dispersion Model of Optical Fiber

The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint.Comment: 18 pages; Submitted for review to the IEEE Transactions on Information Theor

On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models with Input Cost Constraints

We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the noise probability density function, one which dictates the type of the optimal input. In Layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cut-off rate equal to the logarithm of the noise PDF evaluated at the input-output function. Furthermore, we prove a converse statement that says whenever the cost grows slower than the cut-off rate, the optimal input has necessarily an unbounded support. In addition, we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties. We argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cut-off rate. Our results are valid for any cost function that is super-logarithmic. They summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models, such as Gaussian mixtures, generalized-Gaussians and heavy-tailed noise models, that we state along with numerical computations.Comment: Accepted for publication in the IEEE Transactions on Information Theory with minor modifications on the current versio