Related papers: A Vector Generalization of Costa's Entropy-Power I…
We give a counterexample to the vector generalization of Costa's entropy power inequality (EPI) due to Liu, Liu, Poor and Shamai. In particular, the claimed inequality can fail if the matix-valued parameter in the convex combination does…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…
This paper first focuses on deriving an alternative approach for proving an extremal entropy inequality (EEI), originally presented in [11]. The proposed approach does not rely on the channel enhancement technique, and has the advantage…
The extremal inequality approach plays a key role in network information theory problems. In this paper, we propose a novel monotone path construction in product probability space. The optimality of Gaussian distribution is then established…
Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…
Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable…
The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
This article addresses the issue of the proof of the entropy power inequality (EPI), an important tool in the analysis of Gaussian channels of information transmission, proposed by Shannon. We analyse continuity properties of the mutual…
This paper gives improved R\'{e}nyi entropy power inequalities (R-EPIs). Consider a sum $S_n = \sum_{k=1}^n X_k$ of $n$ independent continuous random vectors taking values on $\mathbb{R}^d$, and let $\alpha \in [1, \infty]$. An R-EPI…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to…
Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for…
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: $$f(\sqrt{a}\,X + \sqrt{1-a}\,Y) \ge a f(X) + (1-a) f(Y) \quad \forall…
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…
In this study, the quantum R\'{e}nyi entropy power inequality of order $p>1$ and power $\kappa$ is introduced as a quantum analog of the classical R\'{e}nyi-$p$ entropy power inequality. To derive this inequality, we first exploit the…
This paper presents outerbounds for the two-user Gaussian fading broadcast channel. These outerbounds are based on Costa's entropy power inequality (Costa-EPI) and are formulated mathematically as a feasibility problem. For classes of the…