Authors: Stanković, Stanislav
Astola, Jaakko
Miller, David Michael
Stanković, Radomir 
Title: Heterogeneous decision diagrams for applications in harmonic analysis on finite non-Abelian groups
Journal: Proceedings of The International Symposium on Multiple-Valued Logic
First page: 307
Last page: 312
Conference: 40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010; Barcelona; Spain; 26 May 2010 through 28 May 2010
Issue Date: 12-Aug-2010
ISBN: 978-0-769-54024-5
ISSN: 0195-623X
DOI: 10.1109/ISMVL.2010.63
Abstract: 
Spectral techniques on Abelian groups are a well established tool in diverse fields such as signal processing, switching theory, multi-valued logic and logic design. The harmonic analysis on finite non-Abelian groups is an extension of them, which has also found applications for particular tasks in the same fields. It takes advantages of the peculiar features of the domain groups and their dual objects. Representing unitary irreducible representations, that are kernels of Fourier transforms on non-Abelian groups, in a compact manner is a key task in this area. These representations are usually specified in terms of rectangular matrices with matrix entries. Therefore, the problem of their efficient representations can be viewed as handling large rectangular matrices with matrix-valued entries. Quantum Multiple-valued Decision Diagrams (QMDDs) and Heterogeneous Decision Diagrams (HDDs) have been used for representation of matrices with numerical values, under some restrictions to the order of matrices to be represented. In this paper, we present a generalization of this concept for the representation of rectangular matrices with matrix-valued entries. We also demonstrate an implementation of an XML-based software package aimed at handling such data structures.
Publisher: IEEE

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