Grassmannian Frames with Applications to Coding and Communications
Thomas Strohmer and Robert
W. Heath Jr
Applied and Computational Harmonic Analysis, Vol. 14, Issue 3, pp. 257-275, May 2003.
For a given class F of uniform frames of fixed redundancy we define
a Grassmannian frame as one that minimizes the maximal correlation among all frames F. We first analyze
finite-dimensional Grassmannian frames. Using links to packings in Grassmannian
spaces and antipodal spherical codes we derive bounds on the minimal achievable
correlation for Grassmannian frames. These bounds yield a simple condition under
which Grassmannian frames coincide with uniform tight frames. We exploit
connections to graph theory, equiangular line sets, and coding theory in order
to derive explicit constructions of Grassmannian frames. Our findings extend
recent results on uniform tight frames. We then introduce infinite-dimensional
Grassmannian frames and analyze their connection to uniform tight frames for
frames which are generated by group-like unitary systems. We derive an example
of a Grassmannian Gabor frame by using connections to sphere packing theory.
Finally we discuss the application of Grassmannian frames to wireless
communication and to multiple description coding.
Grassmannian packing, frame theory, tight-frames
Preprint is available as a .IEEE Xplore . The final version appears at Applied and Computational Harmonic Analysis.