Geometric approach to sampling and communication

TL;DR

This paper explores the connections between classical and geometric sampling theories, introduces a geometric version of Shannon's theorem, and applies these concepts to coding, communication, and image quantization.

Contribution

It provides a constructive method for quantizing dimension in Zador's theorem and introduces a geometric perspective to Shannon's Second Theorem.

Findings

A new geometric approach to sampling and communication.

A constructive method for quantizing dimension in Zador's theorem.

Applications demonstrated in Pulse Code Modulation and image vector quantization.

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.