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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
86/2014

Sequential Recurrence-Based Multidimensional Universal Source Coding of Lempel-Ziv Type

Tyll Krüger, Guido Montúfar, Ruedi Seiler and Rainer Siegmund-Schultze

Abstract

We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every realization of any finite-alphabet ergodic process on $\mathbb{Z}_{\geq0}^d$ to the entropy, in the limit.

Received:
19.08.14
Published:
20.08.14
MSC Codes:
68P30

Related publications

Preprint
2014 Repository Open Access
Tyll Krüger, Guido Montúfar, Ruedi Seiler and Rainer Siegmund-Schultze

Sequential recurrence-based multidimensional universal source coding of Lempel-Ziv type