Tightness of the Wagner-Anantharam (W-A) outer bound, for the quadratic Gaussian two-terminal source coding problem, is examined. The proof of the sum rate constraint for the rate region of this problem provides some hints on possible looseness of the bound. We prove tightness to the rate region for this setup, by first proving tightness for the many-help-one problem with conditional independence. We also look at the performance of the W-A bound and find the worst choice of the auxiliary random variable X, appearing in the expression of the bound, for the sum rate constraint.

In the second part of this work, the Gaussian point-to-point source coding problem is considered. The error exponent for this problem was presented by Ihara and Kubo. We generalize the Gaussian method of types, introduced by Arikan and Merhav, and use Marton's approach to retrieve the best achievable error exponent for this setup. Our method is readily extendable to more complex Gaussian source coding problems.