Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mutual Information and Minimum Mean-square Error in Gaussian Channels   This paper deals with arbitrarily distributed finite-power input signals
observed through an additive Gaussian noise channel. It shows a new formula
that connects the input-output mutual information and the minimum mean-square
error (MMSE) achievable by optimal estimation of the input given the output.
That is, the derivative of the mutual information (nats) with respect to the
signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input
statistics. This relationship holds for both scalar and vector signals, as well
as for discrete-time and continuous-time noncausal MMSE estimation. This
fundamental information-theoretic result has an unexpected consequence in
continuous-time nonlinear estimation: For any input signal with finite power,
the causal filtering MMSE achieved at SNR is equal to the average value of the
noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is
chosen uniformly distributed between 0 and SNR.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an