Capacity of Uniform Noise Channels Under Average Input Power Constraints

Yihan Zhang

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arXiv · 2607.14352

Capacity of Uniform Noise Channels Under Average Input Power Constraints

Yihan Zhang

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Abstract

The foundational work of Shannon (1948) identified the capacity of an additive noise channel under an average input power constraint as a mutual information maximization problem over input densities subject to a second moment constraint. However, a quantitative understanding of the channel capacity is significantly lacking even for very simple noise distributions beyond Gaussians. In particular, it is a long standing question to determine the capacity of channels with noise uniformly distributed over a centered interval. This paper settles this question by precisely characterizing the capacity and the corresponding capacity achieving input and output distributions of such channels. A key observation en route to these results is a certain periodization identity for the output density of a uniform noise channel which in turn allows for applications of Fourier analytic techniques.

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Yihan Zhang. 2026-07-15. Capacity of Uniform Noise Channels Under Average Input Power Constraints. https://arxiv.org/abs/2607.14352

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