Grassmannian frames with applications to coding and communication. (English) Zbl 1028.42020
For a given class \({\mathcal F}\) of unit norm frames, a Grassmannian frame is defined as one that minimizes the maximal correlation \({\mathcal M}(\{f_k\})=\max_{k\neq l}|\langle f_k,f_l\rangle|\) among all frames \(\{f_k\}\in {\mathcal F}\). A lower bound on \({\mathcal M}(\{f_k\})\) is given for frames in finite-dimensional spaces, and Grassmannian frames are related to antipodal spherical codes, graph theory, and coding theory. Finally, Grassmannian frames are considered for unitary group-like systems in infinite-dimensional spaces; it is proved that for such a frame, one can find a tight frame with “almost” as small maximal correlation as the given Grassmannian frame; the deviation depends on the redundancy of the given frame.
Reviewer: Ole Christensen (Lyngby)
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 94B60 | Other types of codes |
| 94A05 | Communication theory |
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