On the Minimum Sum Rate of Gaussian Multiterminal Source Coding: New Proofs

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.