The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Mutual Information and Minimum Mean-Square Error in Gaussian Channels
Open accessAbstract
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 SNR is chosen uniformly distributed between 0 and SNR.
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Cites
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A Mathematical Theory of Communication
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Elements of Information Theory
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Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2005) · doi:10.1002/047174882x · Cited by 13,791
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Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications
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Communication In The Presence Of Noise
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Liu, F., Cui, Y., Masouros, C., Xu, J., Han, T. X., Eldar, Y. C., & Buzzi, S. (2022) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2022.3156632 · Cited by 3,857
Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design
Christensen, S. S., Agarwal, R., De Carvalho, E., & Cioffi, J. M. (2008) · IEEE Transactions on Wireless Communications · doi:10.1109/t-wc.2008.070851 · Cited by 1,014
Community Detection and Stochastic Block Models
Abbe, E. (2018) · now publishers, Inc. eBooks · doi:10.1561/9781680834772 · Cited by 544
Foundations of MIMO Communication
Heath Jr, R. W., & Lozano, A. (2018) · Cambridge University Press eBooks · doi:10.1017/9781139049276 · Cited by 426
Gradient of mutual information in linear vector Gaussian channels
Palomar, D. P., & Verdu, S. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.860424 · Cited by 363
Self-citation
Metadata
- Authors
- Guo, D., Shamai, S., & Verdu, S.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2005-04
- Volume
- 51
- Issue
- 4
- Pages
- 1261-1282
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2111616148
- Cited by
- 1,201
- References
- 33
- FWCI
- 53.59
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
