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Summary
This summary is machine-generated.

This study provides upper bounds for the rate-distortion function (RDF) of Gaussian vectors and develops coding strategies to achieve them. These methods simplify the computation for Gaussian autoregressive (AR) sources.

Keywords:
Gaussian vectorautoregressive (AR) sourcediscrete Fourier transform (DFT)rate-distortion function (RDF)source coding

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Area of Science:

  • Information Theory
  • Signal Processing
  • Statistical Modeling

Background:

  • The rate-distortion function (RDF) is a fundamental concept in information theory, quantifying the theoretical limit of lossy compression for a data source.
  • Gaussian vectors and autoregressive (AR) processes are widely used models in signal processing and statistics due to their tractable mathematical properties.

Purpose of the Study:

  • To establish achievable upper bounds for the rate-distortion function (RDF) of Gaussian vectors.
  • To introduce novel coding strategies that attain these RDF bounds.
  • To reduce the computational complexity associated with coding Gaussian asymptotically wide sense stationary (AWSS) autoregressive (AR) sources.

Main Methods:

  • Derivation of upper bounds for the RDF of general Gaussian vectors.
  • Development and analysis of coding schemes designed to approach these bounds.
  • Investigation of conditions ensuring an AR process meets the asymptotically wide sense stationary (AWSS) criteria.

Main Results:

  • The paper successfully derives upper bounds for the RDF of Gaussian vectors.
  • Novel coding strategies are proposed and shown to achieve these bounds.
  • The proposed strategies demonstrably reduce the computational complexity for coding Gaussian AWSS AR sources.
  • Sufficient conditions for AR processes to be classified as AWSS are provided.

Conclusions:

  • The established RDF upper bounds and associated coding strategies offer a significant advancement in the efficient compression of Gaussian vector data.
  • The work provides a practical method for simplifying computations in the processing of Gaussian AWSS AR sources.
  • The identified conditions for AWSS AR processes contribute to a deeper theoretical understanding and practical application in signal modeling.