On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel

Details On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel

2004-09-28

arxiv.org/abs/math/0409548v2

IEEE Trans. on Information Theory, Vol. 51(9), pp. 3017-3024, Sept. 2005

Mathematics

Probability

21 pages, to appear in the IEEE Transactions on Information Theory

Scientific paper

This paper considers the model of an arbitrary distributed signal x observed through an added independent white Gaussian noise w, y=x+w. New relations between the minimal mean square error of the non-causal estimator and the likelihood ratio between y and \omega are derived. This is followed by an extended version of a recently derived relation between the mutual information I(x;y) and the minimal mean square error. These results are applied to derive infinite dimensional versions of the Fisher information and the de Bruijn identity. The derivation of the results is based on the Malliavin calculus.

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