On the sum rate of Gaussian multiterminal source coding: new proofs and results

Authors:
Jia Wang;Jun Chen;Xiaolin Wu
Affiliations:
Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China;Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada;Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 12
Cited 0

Probability, random processes, and estimation theory for engineers

Probability, random processes, and estimation theory for engineers
Convex Optimization

Convex Optimization
The Gaussian many-help-one distributed source coding problem

IEEE Transactions on Information Theory
The CEO problem [multiterminal source coding]

IEEE Transactions on Information Theory
The quadratic Gaussian CEO problem

IEEE Transactions on Information Theory
Gaussian multiterminal source coding

IEEE Transactions on Information Theory
The rate-distortion function for the quadratic Gaussian CEO problem

IEEE Transactions on Information Theory
Multiterminal source coding with high resolution

IEEE Transactions on Information Theory
The worst additive noise under a covariance constraint

IEEE Transactions on Information Theory
Rate-distortion theory for Gaussian multiterminal source coding systems with several side informations at the decoder

IEEE Transactions on Information Theory
The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel

IEEE Transactions on Information Theory
Rate Region of the Quadratic Gaussian Two-Encoder Source-Coding Problem

IEEE Transactions on Information Theory

Quantified Score

Hi-index	754.84

Visualization

Abstract

We show that the lower bound on the sum rate of the direct and indirect Gaussian multiterminal source coding problems can be derived in a unified manner by exploiting the semidefinite partial order of the distortion covariance matrices associated with the minimum mean squared error (MMSE) estimation and the so-called reduced optimal linear estimation, through which an intimate connection between the lower bound and the Berger-Tung upper bound is revealed. We give a new proof of the minimum sum rate of the indirect Gaussian multiterminal source coding problem (i.e., the Gaussian CEO problem). For the direct Gaussian multiterminal source coding problem, we derive a general lower bound on the sum rate and establish a set of sufficient conditions under which the lower bound coincides with the Berger-Tung upper bound. We show that the sufficient conditions are satisfied for a class of sources and distortion constraints; in particular, they hold for arbitrary positive definite source covariance matrices in the high-resolution regime. In contrast with the existing proofs, the new method does not rely on Shannon's entropy power inequality.