Geometric approach to sampling and communication

2010/02/15 by Emil Saucan, Saucan, Emil, Eli Appleboim +3
Computer Science · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.CV #cs.IT #math.DG #math.IT

paper · pdf · doi:10.48550/arxiv.1002.2959

19 pages, submitted for publication

arxiv created 2010/02/15 · arxiv updated 2010/02/26

Abstract

Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive method to determine the quantizing dimension in Zador's theorem is provided. A geometric version of Shannon's Second Theorem is introduced. Applications to Pulse Code Modulation and Vector Quantization of Images are addressed.

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