Related papers: Assisted Common Information: Further Results
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…
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each…
We establish the rate region of an extended Gray-Wyner system for 2-DMS $(X,Y)$ with two additional decoders having complementary causal side information. This extension is interesting because in addition to the operationally significant…
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…
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…
In this paper, we revisit the discrete lossy Gray-Wyner problem. In particular, we derive its optimal second-order coding rate region, its error exponent (reliability function) and its moderate deviations constant under mild conditions on…
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…
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…
Nonconvex optimization plays a key role in multi-user information theory and related fields, but it is usually difficult to solve. The rate region of the Gray--Wyner source coding system (or almost equivalently, the mutual information…
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 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 coding problem over the Gray-Wyner network is studied from the second-order coding rates perspective. A tilted information density for this network is introduced in the spirit of Kostina-Verd\'u, and, under a certain regularity…
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…
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…
Examined in this paper, is the Gray and Wyner achievable lossy rate region for a tuple of correlated multivariate Gaussian random variables (RVs) $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}$ and $X_2 : \Omega \rightarrow {\mathbb R}^{p_2}$…
The problem of preserving privacy when a multivariate source is required to be revealed partially to multiple users is modeled as a Gray-Wyner source coding problem with K correlated sources at the encoder and K decoders in which the kth…
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 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…
Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel…