Title :
Coincidence of 1- and 2-dimensional entropies
Author :
Burke, Neil ; Enns, John
Author_Institution :
Fac. of Math., Cambridge Univ., Cambridge, UK
fDate :
June 29 2014-July 4 2014
Abstract :
We compare the entropy of a 1-dimensional shift space, or constrained system, to that of its 2-dimensional version. In particular we study when these entropies are equal. This leads to the introduction of a class of shifts with periodically varying constraints called interleavings of full shifts. We prove that an irreducible sofic shift has the same entropy in 1 and 2 dimensions if and only if it is of this class. We also explore some consequences in higher dimensions.
Keywords :
entropy; graph theory; set theory; 1D entropies; 1D shift space; 2D entropies; constrained system; irreducible sofic shift; Educational institutions; Eigenvalues and eigenfunctions; Encoding; Entropy; Sections;
Conference_Titel :
Information Theory (ISIT), 2014 IEEE International Symposium on
Conference_Location :
Honolulu, HI
DOI :
10.1109/ISIT.2014.6874816
