A perturbation proof of the vector Gaussian one-help-one problem

In this paper, we give a perturbation proof to vector Gaussian one-help-one problem for characterizing the rate distortion region, in which the challenge is that the conventional entropy power inequality used in scalar Gaussian case is not necessarily tight in vector case. Different from enhancement technique, we take the Fisher information matrix to present the entropy, and then derive a new extremal inequality based on the method of integration along a path of a continuous Gaussian perturbation. This new extremal inequality enables us to give a perturbation proof of Rahman and Wagner's theorem.