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
20/2011
Universally Typical Sets for Ergodic Sources of Multidimensional Data
Tyll Krüger, Guido Montúfar, Ruedi Seiler and Rainer Siegmund-Schultze
Abstract
We lift important results of the theory of samples of discrete ergodic information sources to the multidimensional setting. We use the technique of packings and coverings with multidimensional windows in entropy estimation and universal lossless compression. In particular, we construct sequences of multidimensional array sets which, in the limit, build the generated samples of any ergodic source of entropy rate below an $h_{0}$ with probability 1 and whose cardinality grows at most at exponential rate $h_{0}$. Thereby we extrapolate mathematical framework relevant for universal source coding of multi-dimensionally correlated data.
