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Universally Typical Sets for Ergodic Sources of Multidimensional Data

By Tyll Krueger, Guido Montufar, Ruedi Seiler and Rainer Siegmund-Schultze

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 one-dimensional discrete-time 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 $h_0$.Comment: 15 pages, 1 figure. To appear in Kybernetika. This replacement corrects typos and slightly strengthens the main theore

Topics: Computer Science - Information Theory, 94A24, 62D05, 94A08
Year: 2013
OAI identifier: oai:arXiv.org:1105.0393
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