An extension of entropy power inequality for dependent random variables

Asgari, Fatemeh; Alamatsaz, Mohammad Hossein

doi:10.1080/03610926.2020.1813305

Cited by 2 publications

(2 citation statements)

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“…However, there are several real situations, such as in radar and sonar systems, in which the noise is highly dependent on the transmitted signal [11]. It was illustrated in [16] that, under some assumptions, Shannon’s EPI can hold for weakly dependent random variables; [3] extended the EPI to dependent random variables with arbitrary distibutions; and [10] provided certain conditions under which the conditional EPI can hold for dependent summands as well.…”

Section: Introductionmentioning

confidence: 99%

Costa’s concavity inequality for dependent variables based on the multivariate Gaussian copula

Asgari

Alamatsaz

2023

J. Appl. Probab.

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An extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.

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Section: Introductionmentioning

confidence: 99%

Costa’s concavity inequality for dependent variables based on the multivariate Gaussian copula

Asgari

Alamatsaz

2023

J. Appl. Probab.

Self Cite

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“…The entropy power inequality (EPI) which is viewed as the fundamental property of differential entropy is investigated extensively. More recently, the differential entropy is used as a tool to study uncertainty relations based on entropy power [13][14][15]. Consider a bipartite quantum system with its Hilbert space C m ⊗ C n (m n).…”

Section: Introductionmentioning

confidence: 99%