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arXiv · 1601.07059

Permutation codes, source coding and a generalisation of Bollobás-Lubell-Yamamoto-Meshalkin and Kraft inequalities

Kristo Visk·Ago-Erik Riet
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Abstract

We develop a general framework to prove Kraft-type inequalities for prefix-free permutation codes for source coding with various notions of permutation code and prefix. We also show that the McMillan-type converse theorem in most of these cases does not hold, and give a general form of a counterexample. Our approach is more general and works for other structures besides permutation codes. The classical Kraft inequality for prefix-free codes as well as results about permutation codes follow as corollaries of our main theorem and main counterexample.

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Kristo Visk, Ago-Erik Riet. 2016-01-26. Permutation codes, source coding and a generalisation of Bollobás-Lubell-Yamamoto-Meshalkin and Kraft inequalities. https://arxiv.org/abs/1601.07059

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