Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929683102171136 |
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| author | Boche, Holger Grigorescu, Andrea Schaefer, Rafael F. Poor, H. Vincent |
| author_facet | Boche, Holger Grigorescu, Andrea Schaefer, Rafael F. Poor, H. Vincent |
| contents | This paper studies the computability of the secrecy capacity of fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically or not. To address this question, the concept of Turing machines is used, which establishes fundamental performance limits of digital computers. It is shown that certain computable continuous fading probability distribution functions yield secrecy capacities that are non-computable numbers. Additionally, we assess the secrecy capacity's classification within the arithmetical hierarchy, revealing the absence of computable achievability and converse bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels Boche, Holger Grigorescu, Andrea Schaefer, Rafael F. Poor, H. Vincent Information Theory This paper studies the computability of the secrecy capacity of fast-fading wiretap channels from an algorithmic perspective, examining whether it can be computed algorithmically or not. To address this question, the concept of Turing machines is used, which establishes fundamental performance limits of digital computers. It is shown that certain computable continuous fading probability distribution functions yield secrecy capacities that are non-computable numbers. Additionally, we assess the secrecy capacity's classification within the arithmetical hierarchy, revealing the absence of computable achievability and converse bounds. |
| title | Characterization of the Arithmetic Complexity of the Secrecy Capacity of Fast-Fading Gaussian Channels |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.11636 |