Vector Gaussian Two-Terminal Source Coding

We derive a lower bound on each supporting line of the rate region of the vector Gaussian two-terminal CEO problem, which is a special case of the indirect vector Gaussian two-terminal source coding problem. The key technical ingredient is a new extremal inequality. It is shown that the lower bound coincides with the Berger-Tung upper bound in the high-resolution regime. Similar results are derived for the direct vector Gaussian two-terminal source coding problem.