Location of Repository

On Analytic Properties of Entropy Rate of Discrete Random Sources

By Alexander Schönhuth

Abstract

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its analytic properties relative to some reasonable topology. A canonical choice of a topology is that of the norm of total variation as it immediately arises with the idea of a discrete random source as a probability measure on sequence space. It is shown that entropy rate is Lipschitzian relative to this topology, which, by well known facts, is close to differentiability. An application of this theorem leads to a simple and elementary proof of the existence of entropy rate of random sources with finite evolution dimension. This class of sources encompasses arbitrary hidden Markov sources and quantum random walks

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.2135
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://arxiv.org/pdf/0804.2469... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.