On likelihood-ratios, mutual information and estimation error for the additive Gaussian channel
نویسنده
چکیده
This paper considers the model of an arbitrary distributed signal x observed in additive 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 w are derived. These results are applied to prove an extended version of a recently derived relation between the mutual information I(x, y) and the minimal mean square error. The derivation of the presented results is based on the Malliavin calculus.
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تاریخ انتشار 2004