Universally Typical Sets for Ergodic Sources of Multidimensional Data
Abstract
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual onedimensional discretetime setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to 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 one and whose cardinality grows at most at exponential rate $h_0$.
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 arXiv:
 arXiv:1105.0393
 Bibcode:
 2011arXiv1105.0393K
 Keywords:

 Computer Science  Information Theory;
 94A24;
 62D05;
 94A08
 EPrint:
 15 pages, 1 figure. To appear in Kybernetika. This replacement corrects typos and slightly strengthens the main theorem