Related papers: A Secret Common Information Duality for Tripartite…
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…
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…
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…
Common information (CI) is ubiquitous in information theory and related areas such as theoretical computer science and discrete probability. However, because there are multiple notions of CI, a unified understanding of the deep…
Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, hence also confined to, several existing interpretations in various source coding problems. This…
We 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…
In the multiterminal secret key agreement problem, a set of users want to discuss with each other until they share a common secret key independent of their discussion. We want to characterize the maximum secret key rate, called the secrecy…
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…
We study the generation of a secret key of maximum rate by a pair of terminals observing correlated sources and with the means to communicate over a noiseless public com- munication channel. Our main result establishes a structural…
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…
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 investigate the secret key agreement from correlated vector 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…
In this paper we consider the problem of generating arbitrary three-party correlations from a combination of public and secret correlations. Two parties -- called Alice and Bob -- share perfectly correlated bits that are secret from a…
Wyner's Common Information and a natural relaxation are studied in the special case of Gaussian random variables. The relaxation replaces conditional independence by a bound on the conditional mutual information. The main contribution is…
We demonstrate the existence of Gaussian multipartite bound information which is a classical analog of Gaussian multipartite bound entanglement. We construct a tripartite Gaussian distribution from which no secret key can be distilled, but…
We show the mutual information between the targets in a Gray-Wyner Network as a bound that separates Wyner's lossy common information and G\'acs-K\"orner lossy common information. The results are a generalization of the lossless case…
We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the…
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…
The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…
Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input. Wyner's "common…