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A Catalog of Self-Affine Hierarchical Entropy Functions
AbstractFor fixed k ≥ 2 and fixed data alphabet of cardinality m, the hierarchical type class of a data string of length n = kj for some j ≥ 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.
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Kieffer, J. A Catalog of Self-Affine Hierarchical Entropy Functions. Algorithms 2011, 4, 307-333.View more citation formats
Kieffer J. A Catalog of Self-Affine Hierarchical Entropy Functions. Algorithms. 2011; 4(4):307-333.Chicago/Turabian Style
Kieffer, John. 2011. "A Catalog of Self-Affine Hierarchical Entropy Functions." Algorithms 4, no. 4: 307-333.