Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels

• DOI: 10.48550/arxiv.2501.11636
• Publication Date: 2025-01-20
• Authors: Holger Boche; Andrea Grigorescu; Rafael F. Schaefer; H. Vincent Poor
• Keywords: Characterization

This paper studies the computability of secrecy capacity fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically or not. To address this question, concept Turing machines is used, which establishes fundamental performance limits digital computers. It shown that certain computable continuous fading probability distribution functions yield capacities are non-computable numbers. Additionally, we assess capacity's classification within arithmetical hierarchy, revealing absence achievability and converse bounds.