Lossy asymptotic equipartition property for hierarchical data structures

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Abstract

This paper presents a rate-distortion theory for hierarchically networked data structures modelled as tree-indexed multitype process. Specifically, this paper gives a generalized asymptotic equipartition property (AEP) for hierarchical data structures. The proof of our main result uses large deviation principles for suitably defined empirical measures of multitype Galton-Watson trees.

Original languageEnglish
Pages (from-to)1013-1024
Number of pages12
JournalFar East Journal of Mathematical Sciences
Volume101
Issue number5
DOIs
Publication statusPublished - Mar 2017

Keywords

  • Asymptotic equipartition property
  • Empirical measure
  • Perron-Frobenius eigenvalue
  • Perron-Frobenius eigenvector
  • Rate-distortion theory
  • Relative entropy
  • Weak irreducibility

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