Consider the problem of estimating a vector source with a bandwidth constrained sensor network in which sensors make distributed observations on the source and collaborate with a fusion center (FC) to generate a final estimate. Due to power and band-width limitations, each sensor must compress its data and transmit to the FC only the minimum amount of information necessary to ensure the final estimate meets a given distortion bound. The optimal power allocation for the class of linear decentralized analog compression schemes was considered in  and proved to be NP-hard in general. In this paper, we consider the optimal rate allocation problem in the so called Berger-Tung achievable rate distortion region. In contrast to the power allocation for the linear analog compression schemes, we show that the optimal rate allocation can be formulated as a convex optimization problem which can be efficiently solved by interior point methods. Our convex reformulation technique is also applicable to the vector Gaussian multiterminal source coding problem.