Grassmannian Frames with Applications to Coding and Communication

Grassmannian Frames with Applications to Coding and Communication

13 Jan 2003 | Thomas Strohmer and Robert Heath
The paper introduces the concept of Grassmannian frames, which are frames that minimize the maximal correlation among their elements within a given class of uniform frames. The authors analyze finite-dimensional Grassmannian frames, derive bounds on the minimal achievable correlation, and show that optimal finite Grassmannian frames coincide with uniform tight frames. They also explore connections to graph theory, equiangular line sets, and coding theory to construct explicit examples of Grassmannian frames. The concept is extended to infinite-dimensional frames, and the authors discuss their connection to uniform tight frames generated by group-like unitary systems. An example of a Grassmannian Gabor frame is provided, and the applications of Grassmannian frames in wireless communication and multiple description coding are discussed. The paper highlights the importance of Grassmannian frames in various areas of mathematics and engineering, including spherical codes, algebraic geometry, and coding theory.The paper introduces the concept of Grassmannian frames, which are frames that minimize the maximal correlation among their elements within a given class of uniform frames. The authors analyze finite-dimensional Grassmannian frames, derive bounds on the minimal achievable correlation, and show that optimal finite Grassmannian frames coincide with uniform tight frames. They also explore connections to graph theory, equiangular line sets, and coding theory to construct explicit examples of Grassmannian frames. The concept is extended to infinite-dimensional frames, and the authors discuss their connection to uniform tight frames generated by group-like unitary systems. An example of a Grassmannian Gabor frame is provided, and the applications of Grassmannian frames in wireless communication and multiple description coding are discussed. The paper highlights the importance of Grassmannian frames in various areas of mathematics and engineering, including spherical codes, algebraic geometry, and coding theory.
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Understanding GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION