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arXiv · 2307.11690

Redundancy of information: lowering dimension

Jun Le Goh·Joseph S. Miller·Mariya I. Soskova·Linda Westrick
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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.

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Jun Le Goh, Joseph S. Miller, Mariya I. Soskova, Linda Westrick. 2023-07-21. Redundancy of information: lowering dimension. https://arxiv.org/abs/2307.11690

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