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Article overview
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Characterization of the Gray-Wyner Rate Region for Multivariate Gaussian Sources: Optimality of Gaussian Auxiliary RV | | Evagoras Stylianou
; Charalambos D. Charalambous
; Jan H. van Schuppen
; | | Date: |
16 May 2022 | | Abstract: | Examined in this paper, is the Gray and Wyner achievable lossy rate region
for a tuple of correlated multivariate Gaussian random variables (RVs) $X_1 :
Omega
ightarrow {mathbb R}^{p_1}$ and $X_2 : Omega
ightarrow {mathbb
R}^{p_2}$ with respect to square-error distortions at the two decoders. It is
shown that among all joint distributions induced by a triple of RVs $(X_1,X_2,
W)$, such that $W : Omega
ightarrow {mathbb W} $ is the auxiliary RV taking
continuous, countable, or finite values, the Gray and Wyner achievable rate
region is characterized by jointly Gaussian RVs $(X_1,X_2, W)$ such that $W $
is an $n$-dimensional Gaussian RV. It then follows that the achievable rate
region is parametrized by the three conditional covariances $Q_{X_1,X_2|W},
Q_{X_1|W}, Q_{X_2|W}$ of the jointly Gaussian RVs. Furthermore, if the RV $W$
makes $X_1$ and $X_2$ conditionally independent, then the corresponding subset
of the achievable rate region, is simpler, and parametrized by only the two
conditional covariances $Q_{X_1|W}, Q_{X_2|W}$. The paper also includes the
characterization of the Pangloss plane of the Gray-Wyner rate region along with
the characterizations of the corresponding rate distortion functions, their
test-channel distributions, and structural properties of the realizations which
induce these distributions. | | Source: | arXiv, 2205.07588 | | Services: | Forum | Review | PDF | Favorites | |
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