Large deviations for coding Markov chains and Gibbs random fields
Amit, Y.; Miller, M.
Information Theory, IEEE Transactions on
Volume 39, Issue 1, Jan 1993 Page(s):109 - 118
Digital Object Identifier 10.1109/18.179348
Summary:Fixed block coding schemes for Gibbs random fields are proposed in
which the empirical expectations of the local interactions of the Gibbs
measure is compared to its expectation with respect to all Gibbs
measures having those interactions. The exponential decay of the error
probabilities is proven and it is shown that the code rates equal the
entropy of the random field. In addition, it is shown that any coding
scheme based on regarding the field as a 1-D sequence of symbols has
rate greater than the entropy of the field. The theory of fixed length
coding is approached from the point of view of large deviations, both
for the calculation of the error exponents or error probabilities and
for the calculation of the encoding rates or the asymptotic
combinatorics of the coding schemes. This approach is also applied to
fixed length coding schemes of Markov sources for which estimates on the
error exponents and on the rates are derived
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