相关论文: A short proof of the G\'acs--K\"orner theorem
A short, information-theoretic proof of the Kac--Bernstein theorem, which is stated as follows, is presented: For any independent random variables $X$ and $Y$, if $X+Y$ and $X-Y$ are independent, then $X$ and $Y$ are normally distributed.
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
We propose a notion of common information that allows one to quantify and separate the information that is shared between two random variables from the information that is unique to each. Our notion of common information is defined by an…
We take a closer look at the structure of bivariate dependency induced by a pair of predictor random variables $(X_1, X_2)$ trying to synergistically, redundantly or uniquely encode a target random variable $Y$. We evaluate a recently…
This paper generalizes Wyner's definition of common information of a pair of random variables to that of $N$ random variables. We prove coding theorems that show the same operational meanings for the common information of two random…
An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general…
Consider two correlated sources $X$ and $Y$ generated from a joint distribution $p_{X,Y}$. Their G\'acs-K\"orner Common Information, a measure of common information that exploits the combinatorial structure of the distribution $p_{X,Y}$,…
In this paper we generalize the notion of common information of two dependent variables introduced by G\'acs & K\"orner. They defined common information as the largest entropy rate of a common random variable two parties observing one of…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
We explore the duality between the simulation and extraction of secret correlations in light of a similar well-known operational duality between the two notions of common information due to Wyner, and G\'acs and K\"orner. For the inverse…
We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…
This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity…
We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…
A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…
The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random…
In literature, different common informations were defined by G\'acs and K\"orner, by Wyner, and by Kumar, Li, and Gamal, respectively. In this paper, we define two generalized versions of common informations, named approximate and exact…
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of…
We presented assisted common information as a generalization of G\'acs-K\"orner (GK) common information at ISIT 2010. The motivation for our formulation was to improve upperbounds on the efficiency of protocols for secure two-party sampling…