Algorithmic complexity of $\beta$-expansions and application to A/D conversion
Information Theory
2025-05-28 v3 math.IT
Abstract
We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and -expansions. These relationships allow to develop intuitions on the complexity behavior of -expansions, and raise problems related to compressibility of binary sequences generated in the context of A/D conversion relying on -expansions. Our last contribution is to solve these problems.
Cite
@article{arxiv.2405.03816,
title = {Algorithmic complexity of $\beta$-expansions and application to A/D conversion},
author = {Valentin Abadie and Helmut Boelcskei},
journal= {arXiv preprint arXiv:2405.03816},
year = {2025}
}