Frames from groups: Generalized bounds and dihedral groups

The problem of designing low coherence matrices and low-correlation frames arises in a variety of fields, including compressed sensing, MIMO communications and quantum measurements. The challenge is that one must control the (n over 2) pairwise inner products of the columns of the matrix. In this paper, we follow the group code approach of David Slepian [1], 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.