Related papers: On Wyner's Common Information in the Gaussian Case
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…
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 propose two novel extensions of the Wyner common information optimization problem. Each relaxes one fundamental constraints in Wyner's formulation. The \textit{Variational Wyner Common Information} relaxes the matching constraint to the…
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…
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 Gray and Wyner lossy source coding for a simple network for sources that generate a tuple of jointly Gaussian random variables (RVs) $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}$ and $X_2 : \Omega \rightarrow {\mathbb R}^{p_2}$, with…
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…
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…
A new bimodal generative model is proposed for generating conditional and joint samples, accompanied with a training method with learning a succinct bottleneck representation. The proposed model, dubbed as the variational Wyner model, is…
We introduce a novel relaxation of combinatorial discrepancy called Gaussian discrepancy, whereby binary signings are replaced with correlated standard Gaussian random variables. This relaxation effectively reformulates an optimization…
Explicit constructions of polar codes and polar lattices for both lossless and lossy Gray-Wyner problems are studied. Polar codes are employed to extract Wyner's common information of doubly symmetric binary source; polar lattices are then…
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…
We analyse the common information problem for the generalised Gray-Wyner problem. We aim to explore the problem and solution in relation to the non-orthogonality among the source decoders' components. We consider a simple networked control…
We present a closed form expression for the information matrix associated with the Wiener model identification problem under the assumption that the input signal is a stationary Gaussian process. This expression holds under quite generic…
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…
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 establish the first known upper bound on the exact and Wyner's common information of $n$ continuous random variables in terms of the dual total correlation between them (which is a generalization of mutual information). In particular, we…
We consider the problem of source coding subject to a fidelity criterion for the Gray-Wyner network that connects a single source with two receivers via a common channel and two private channels. The pareto-optimal trade-offs between the…
We study a generalized version of Wyner's common information problem (also coined the distributed source simulation problem). The original common information problem consists in understanding the minimum rate of the common input to…
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…