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.
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Kieffer, J. A Catalog of Self-Affine Hierarchical Entropy Functions. Algorithms 2011, 4, 307-333.
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.