The additive white Gaussian noise (AWGN) channel is one of the central models in information theory. Under an average-power constraint, its capacity is achieved by a Gaussian input, providing a particularly elegant connection between the statistical structure of the noise and the optimal signaling strategy.

Many practical communication channels, however, exhibit noise that is not well described by a single Gaussian distribution. For example, impulsive noise can occasionally produce disturbances that are much stronger than those predicted by an ordinary Gaussian model. A natural way to capture such behavior is through a Gaussian-mixture noise model, in which the noise distribution is a weighted mixture of Gaussian components with different variances. Such models arise in the study of impulsive and non-Gaussian noise in communication systems.

For Gaussian-mixture noise, however, the situation is considerably more subtle [1]. In general, a Gaussian input is no longer optimal, and the capacity-achieving distribution can exhibit a discrete structure with a finite number of mass points [2]. Understanding why this happens and how the optimal distribution depends on the noise and power constraints is the main focus of this project. 

The student should develop the necessary information-theoretic background and study the capacity formulation for additive Gaussian-mixture noise channels. The main theoretical reference is the work of Vu et al., which establishes structural properties of the capacity-achieving input distribution. The student should understand the main arguments, including the assumptions under which the characterization is obtained and the implications for the form of the optimal input. A numerical investigation [3] is not required, but constitutes a bonus component. 

[1] J. G. Smith, “The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels,” Information and Control, 1971.

[2] H. V. Vu, N. H. Tran, M. C. Gursoy, T. Le-Ngoc, and S. I. Hariharan, “Capacity-Achieving Input Distributions of Additive Quadrature Gaussian Mixture Noise Channels,” IEEE Transactions on Communications, vol. 63, no. 10, pp. 3607–3620, 2015.

[3] Y. Dou, X. Niu, B. Bai, W. Han, and Y. Geng, “Computing Gaussian Mixture Inputs for Channels with Additive Gaussian Mixture Noises," 2025 Asia Pacific Workshop on Data Science and Information Theory, 2025.

Voraussetzungen