On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel
<|reference_start|>On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel: 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.<|reference_end|>
@article{zakai2004on,
    title={On mutual information, likelihood-ratios and estimation error for the
  additive Gaussian channel},
    author={Moshe Zakai},
    journal={IEEE Trans. on Information Theory, Vol. 51(9), pp. 3017-3024,
  Sept. 2005},
    year={2004},
    doi={10.1109/TIT.2005.853297},
    archivePrefix={arXiv},
    eprint={math/0409548},
    primaryClass={math.PR cs.IT math.IT math.ST stat.TH}
}