Related papers: Wyner's Common Information: Generalizations and A …
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…
The two most prevalent notions of common information (CI) are due to Wyner and Gacs-Korner and both the notions can be stated as two different characteristic points in the lossless Gray-Wyner region. Although the information theoretic…
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 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…
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…
Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a…
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…
The classical Gray and Wyner source coding for a simple network for sources that generate a tuple of multivariate, correlated Gaussian random variables $(Y_1,Y_2)$ is re-examined using the geometric approach of Gaussian random variables,…
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…
Many computer vision tasks share substantial overlapping information, yet conventional codecs tend to ignore this, leading to redundant and inefficient representations. The Gray-Wyner network, a classical concept from information theory,…
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…
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…
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…
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…
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…
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 give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that…
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 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…