%0 Generic %1 citeulike:1059774 %A Guo, Dongning %A Shamai, Shlomo %A Verdu, Sergio %D 2004 %K information mutual %T Mutual Information and Minimum Mean-square Error in Gaussian Channels %U http://arxiv.org/abs/cs/0412108 %X 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.

@misc{citeulike:1059774, abstract = {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.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Guo, Dongning and Shamai, Shlomo and Verdu, Sergio}, biburl = {https://www.bibsonomy.org/bibtex/2d63c8184126a86dc7ac9a82a456f8f8c/a_olympia}, citeulike-article-id = {1059774}, description = {citeulike}, eprint = {cs/0412108}, interhash = {17a517a27b5865afe9ddd573f0bc6153}, intrahash = {d63c8184126a86dc7ac9a82a456f8f8c}, keywords = {information mutual}, month = Dec, priority = {2}, timestamp = {2007-08-18T13:22:32.000+0200}, title = {Mutual Information and Minimum Mean-square Error in Gaussian Channels}, url = {http://arxiv.org/abs/cs/0412108}, year = 2004 }