Universal codes of the natural numbers
Logic in Computer Science
2015-07-01 v2 Information Theory
math.IT
Abstract
A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense. As an application, we prove that the existence of a scale of codes (a well-ordered set of codes which contains a code better than any given code) is independent of ZFC.
Keywords
Cite
@article{arxiv.1308.1600,
title = {Universal codes of the natural numbers},
author = {Yuval Filmus},
journal= {arXiv preprint arXiv:1308.1600},
year = {2015}
}
Comments
11 pages