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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 bandwidth 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 Z-Q Luo et al. (2005) 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.