An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel

Bustin, Ronit; Liu, Ruoheng; Poor, H. Vincent; Shamai, Shlomo

doi:10.1109/isit.2009.5205967

Cited by 103 publications

(101 citation statements)

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“…Recently, the confidential message transmission [10], [26] in the MIMO wireless communication has attracted considerable attention as a practical problem setting (e.g. [7], [17], [18]). Although the key agreement in the context of the wireless communication has also attracted considerable attention recently [6], the key agreement from analog sources has not been studied sufficiently compared to the confidential message transmission.…”

Section: Introductionmentioning

confidence: 99%

Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication

Watanabe

Oohama

2010

IEICE Trans. Fundamentals

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SUMMARYWe investigate the secret key agreement from correlated Gaussian sources in which the legitimate parties can use the public communication with limited rate. For the class of protocols with the one-way public communication, we show a closed form expression of the optimal trade-off between the rate of key generation and the rate of the public communication. Our results clarify an essential difference between the key agreement from discrete sources and that from continuous sources.

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Section: Introductionmentioning

confidence: 99%

Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication

Watanabe

Oohama

2010

IEICE Trans. Fundamentals

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“…The expression in (114) has been used to study MIMO wiretap channels [101], extensions of Costa's EPI [102], and the design of optimal precoders for MIMO Gaussian channels [103]. However, much work is needed to attain the same level of maturity for the gradient expression in (114) as for the original I-MMSE results [8].…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

A View of Information-Estimation Relations in Gaussian Networks

Dytso

Bustin

Poor

et al. 2017

Entropy

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Abstract:Relations between estimation and information measures have received considerable attention from the information theory community. One of the most notable such relationships is the I-MMSE identity of Guo, Shamai and Verdú that connects the mutual information and the minimum mean square error (MMSE). This paper reviews several applications of the I-MMSE relationship to information theoretic problems arising in connection with multi-user channel coding. The goal of this paper is to review the different techniques used on such problems, as well as to emphasize the added-value obtained from the information-estimation point of view.

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“…More generally, [8] applies (11) and Proposition 14 to prove a more general result, originally given in [23].…”

Section: Monotonicitymentioning

confidence: 99%

“…In fact the whole rate-equivocation region can be obtained using the same techniques. Note that the MIMO wiretap channel can be treated similarly [11].…”

Section: A Secrecy Capacity Of the Gaussian Wiretap Channelmentioning

confidence: 99%

“…The preceding information-estimation relationships have found a number of applications, e.g., in nonlinear filtering [1], [3], in multiuser detection [4], in power allocation over parallel Gaussian channels [5], [6], in the proof of Shannon's entropy power inequality (EPI) and its generalizations [2], [7], [8], and in the treatment of the capacity region of several multiuser channels [9]- [11]. Relationships between relative entropy and mean-square error are also found in [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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Estimation in Gaussian Noise: Properties of the Minimum Mean-Square Error

Guo

Shamai

et al. 2011

IEEE Trans. Inform. Theory

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205

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Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signalto-noise ratio (SNR) as well as a functional of the input distribution (of the random variable to be estimated). It is shown that the MMSE is concave in the input distribution at any given SNR. For a given input distribution, the MMSE is found to be infinitely differentiable at all positive SNR, and in fact a real analytic function in SNR under mild conditions. The key to these regularity results is that the posterior distribution conditioned on the observation through Gaussian channels always decays at least as quickly as some Gaussian density. Furthermore, simple expressions for the first three derivatives of the MMSE with respect to the SNR are obtained. It is also shown that, as functions of the SNR, the curves for the MMSE of a Gaussian input and that of a non-Gaussian input cross at most once over all SNRs. These properties lead to simple proofs of the facts that Gaussian inputs achieve both the secrecy capacity of scalar Gaussian wiretap channels and the capacity of scalar Gaussian broadcast channels, as well as a simple proof of the entropy power inequality in the special case where one of the variables is Gaussian.

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An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel

Cited by 103 publications

References 6 publications

Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication

Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication

A View of Information-Estimation Relations in Gaussian Networks

Estimation in Gaussian Noise: Properties of the Minimum Mean-Square Error

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