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Foundations and Trends in Communications and Information Theory
Bit-Interleaved Coded Modulation
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Temporal privacy in wireless sensor networks: Theory and practice
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Gaussian process regressors for multiuser detection in DS-CDMA systems
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Power allocation for block-fading channels with arbitrary input constellations
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An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel
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An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Secrecy capacity region of the Gaussian multi-receiver wiretap channel
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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Mismatched estimation and relative entropy
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Directed information and causal estimation in continuous time
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On optimal precoding in linear vector Gaussian channels with arbitrary input distribution
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Directed information, causal estimation, and communication in continuous time
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Linear precoding for mutual information maximization in MIMO systems
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Capacity bounds for peak-constrained multiantenna wideband channels
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ICC'09 Proceedings of the 2009 IEEE international conference on Communications
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Noncoherent capacity of underspread fading channels
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Outage exponents of block-fading channels with power allocation
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Automatica (Journal of IFAC)
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Mismatched estimation and relative entropy
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| Hi-index | 755.87 |
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.