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Published May 2013 | public
Book Section - Chapter

Frames From Groups: Generalized Bounds And Dihedral Groups

Abstract

The problem of designing low coherence matrices and lowcorrelation frames arises in a variety of fields, including compressed sensing, MIMO communications and quantum measurements. The challenge is that one must control the n/2 pairwise inner products of the columns of the matrix. In this paper, we follow the group code approach of David Slepian, which constructs frames using unitary group representations and which in general reduces the number of distinct inner products to n-1. We examine representations of cyclic groups as well as generalized dihedral groups, and we expand upon previous results which bound the coherence of the resulting frames.

Additional Information

© 2013 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech's Lee Center for Advanced Networking. The first author was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024