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GLOBECOM
2007
IEEE

Volume Growth and General Rate Quantization on Grassmann Manifolds

9 years 19 days ago
Volume Growth and General Rate Quantization on Grassmann Manifolds
—The Grassmann manifold Gn,p (L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space Ln , where L is either R or C. This paper considers an unequal dimensional quantization in which a source in Gn,q (L) is quantized through a code in Gn,p (L), where p and q are not necessarily the same. The analysis for unequal dimensional quantization is based on the volume of a metric ball in Gn,q (L) whose center is in Gn,p (L). Our chief result is to show that as n, p, q and the square radius approach infinity with constant ratios, the volume of a metric ball “grows” as exp −n2 V (1 + o (1)) for a computable constant V ≥ 0. This result is stronger than our previous volume formula which is only valid when the radius is at most one. The tools behind the present result include large deviation techniques and equilibrium measure ideas from potential theory. Based on the volume growth formula, the rate distortion tradeoff is precisely quantified in...
Wei Dai, Brian Rider, Youjian Liu
Added 02 Jun 2010
Updated 02 Jun 2010
Type Conference
Year 2007
Where GLOBECOM
Authors Wei Dai, Brian Rider, Youjian Liu
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