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

  • Authors:
  • Jia Wang;Jun Chen;Xiaolin Wu

  • Affiliations:
  • Dept. of EE, Shanghai Jiao Tong Univ., Shanghai, China;Dept. of ECE, McMaster Univ., Hamilton, ON, Canada;Dept. of ECE, McMaster Univ., Hamilton, ON, Canada

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
  • Year:
  • 2009

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Abstract

We show that the minimum sum rate of the 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 MMSE estimation and the so-called reduced optimal linear estimation. In contrast to the existing proofs, the new method does not rely on Shannon's entropy power inequality. Furthermore, this new method leads to a direct proof of the minimum sum rate of the Gaussian two-terminal source coding problem without coupling it to a Gaussian CEO problem.