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首页> 外文期刊>IEEE Transactions on Information Theory >On Mutual Information, Likelihood Ratios, and Estimation Error for the Additive Gaussian Channel
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On Mutual Information, Likelihood Ratios, and Estimation Error for the Additive Gaussian Channel

机译：加性高斯信道的互信息，似然比和估计误差

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摘要

This paper considers the model of an arbitrarily 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 noncausal estimator and the likelihood ratio between$y$and$w$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. A comparison between the causal and noncausal estimation errors yields a restricted form of the logarithmic Sobolev inequality. The derivation of the results is based on the Malliavin calculus.
机译：本文考虑了通过添加独立的白高斯噪声$ w，y = x + w $观察到的任意分布信号$ x $的模型。推导了非因果估计量的最小均方误差与y和w之间的似然比之间的新关系。这之后是互信息$ I（x; y）$与最小均方误差之间的最近派生关系的扩展版本。这些结果可用于导出Fisher信息和de Bruijn身份的无穷大形式。因果和非因果估计误差之间的比较产生对数Sobolev不等式的受限形式。结果的推导基于Malliavin微积分。

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