%0 Journal Article
%T A Catalog of Self-Affine Hierarchical Entropy Functions
%A John Kieffer
%J Algorithms
%D 2011
%I MDPI AG
%R 10.3390/a4040307
%X For fixed k ¡Ý 2 and fixed data alphabet of cardinality m, the hierarchical type class of a data string of length n = k j for some j ¡Ý 1 is formed by permuting the string in all possible ways under permutations arising from the isomorphisms of the unique finite rooted tree of depth j which has n leaves and k children for each non-leaf vertex. Suppose the data strings in a hierarchical type class are losslessly encoded via binary codewords of minimal length. A hierarchical entropy function is a function on the set of m-dimensional probability distributions which describes the asymptotic compression rate performance of this lossless encoding scheme as the data length n is allowed to grow without bound. We determine infinitely many hierarchical entropy functions which are each self-affine. For each such function, an explicit iterated function system is found such that the graph of the function is the attractor of the system.
%K types
%K type classes
%K lossless compression
%K hierarchical entropy
%K self-affine functions
%K iterated function systems
%U http://www.mdpi.com/1999-4893/4/4/307