Redundancy of information: lowering dimension
Logic
2023-08-08 v2
Abstract
Let At denote the set of infinite sequences of effective dimension t. We determine both how close and how far an infinite sequence of dimension s can be from one of dimension t, measured using the Besicovitch pseudometric. We also identify classes of sequences for which these infima and suprema are realized as minima and maxima. When t < s, we find d(X,At) is minimized when X is a Bernoulli p-random, where H(p)=s, and maximized when X belongs to a class of infinite sequences that we call s-codewords. When s < t, the situation is reversed.
Keywords
Cite
@article{arxiv.2307.11690,
title = {Redundancy of information: lowering dimension},
author = {Jun Le Goh and Joseph S. Miller and Mariya I. Soskova and Linda Westrick},
journal= {arXiv preprint arXiv:2307.11690},
year = {2023}
}
Comments
28 pages, 3 figures