Entropy, Derivation Operators and Huffman Trees
Information Theory
2021-07-26 v1 math.IT
Abstract
We build a theory of binary trees on finite multisets that categorifies, or operationalizes, the entropy of a finite probability distribution. Multisets operationalize probabilities as the event outcomes of an experiment. Huffman trees operationalize the entropy of the distribution of these events. We show how the derivation property of the entropy of a joint distribution lifts to Huffman trees.
Cite
@article{arxiv.2107.11208,
title = {Entropy, Derivation Operators and Huffman Trees},
author = {Simon Burton},
journal= {arXiv preprint arXiv:2107.11208},
year = {2021}
}