Algorithmic complexity of $\beta$-expansions and application to A/D conversion

Valentin Abadie; Helmut Boelcskei

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arXiv · 2405.03816

Algorithmic complexity of $\beta$-expansions and application to A/D conversion

Valentin Abadie·Helmut Boelcskei

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Abstract

We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $\beta$-expansions. These relationships allow to develop intuitions on the complexity behavior of $\beta$-expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on $\beta$-expansions. Our last contribution is to solve these problems.

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Valentin Abadie, Helmut Boelcskei. 2024-05-06. Algorithmic complexity of $\beta$-expansions and application to A/D conversion. https://arxiv.org/abs/2405.03816

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