on Information Theory

Paper ID | O.4.4 | ||

Paper Title | Characterization of Conditional Independence and Weak Realizations of Multivariate Gaussian Random Variables: Applications to Networks |
||

Authors | Charalambos D. Charalambous, University of Cyprus, Cyprus; Jan H. van Schuppen, Van Schuppen Control Research, Netherlands | ||

Session | O.4: Multi-terminal Source Coding II | ||

Presentation | Lecture | ||

Track | Source Coding |
||

Manuscript | Click here to download the manuscript | ||

Virtual Presentation | Click here to watch in the Virtual Symposium | ||

Abstract | 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 respect to square-error distortion at the two decoders is re-examined using (1) Hotelling's geometric approach of Gaussian RVs-the canonical variable form, and (2) van Putten's and van Schuppen's parametrization of joint distributions ${\bf P}_{X_1, X_2, W}$ by Gaussian RVs $W : \Omega \rightarrow {\mathbb R}^n $ which make $(X_1,X_2)$ conditionally independent, and the weak stochastic realization of $(X_1, X_2)$. Item (2) is used to parametrize the lossy rate region of the Gray and Wyner source coding problem for joint decoding with mean-square error distortions ${\bf E}\big\{||X_i-\hat{X}_i||_{{\mathbb R}^{p_i}}^2 \big\}\leq \Delta_i \in [0,\infty], i=1,2$, by the covariance matrix of RV $W$. From this then follows Wyner's common information $C_W(X_1,X_2)$ (information definition) is achieved by $W$ with identity covariance matrix, while a formula for Wyner's lossy common information (operational definition) is derived. |

Plan Ahead

2021 IEEE International Symposium on Information Theory

**11-16 July 2021 ** | **Melbourne, Victoria, Australia**