Information theory in random fields

  • Toby Berger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 311)


A random field is a family of random variables with a multidimensional parameter set. Random fields provide mathematical models for distributed sources of information. Channels that link an input and an output random field also are of interest.

First, we describe in detail a celebrated result of random field theory to the effect that a random field has the Markov property if and only if it is a Gibbs state with a nearest neighbor potential. Next we lower bound the zero-error capacity of a certain binary random field channel by developing an efficient zero-error coding scheme. Finally, we consider algorithms for computing the stationary distribution of a time evolution mechanism. These algorithms, which have long been employed in mathematical statistical mechanics, also play a central role in simulated annealing.


Simulated Annealing Random Field Input Pattern Markov Random Field Channel System 


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  1. [1]
    C. J. Preston, Gibbs States on Countable Sets, Cambridge Tracts, Cambridge University Press, 1974.Google Scholar
  2. [2]
    B. Hajek and T. Berger, ”A Decomposition Theorem for Binary Markov Random Fields, Annals of Probability, vol. 15, no. 3, pp. 1112–1125, July 1987.Google Scholar
  3. [3]
    S. Kirkpatrick, et al., Optimization by Simulated Annealing, Science, vol. 220, pp. 671–679, 1983.Google Scholar
  4. [4]
    B. Hajek, Cooling Schedules for Simulated Annealing, preprint, University of Illinois, Coordinated Science Laboratory, submitted to Mathematics of Operations Research.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Toby Berger
    • 1
    • 2
  1. 1.Department Systems at Connunications CNRS UA 820E.N.S.TParis Cedex 13France
  2. 2.School of Electrical Engineeering and Center for Applied MathematicsCornell UniversityIthaca

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