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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.03816 |
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| _version_ | 1866912396299206656 |
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| author | Abadie, Valentin Boelcskei, Helmut |
| author_facet | Abadie, Valentin Boelcskei, Helmut |
| contents | We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $β$-expansions. These relationships allow to develop intuitions on the complexity behavior of $β$-expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on $β$-expansions. Our last contribution is to solve these problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithmic complexity of $β$-expansions and application to A/D conversion Abadie, Valentin Boelcskei, Helmut Information Theory We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $β$-expansions. These relationships allow to develop intuitions on the complexity behavior of $β$-expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on $β$-expansions. Our last contribution is to solve these problems. |
| title | Algorithmic complexity of $β$-expansions and application to A/D conversion |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.03816 |