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This paper presents a distributed estimation scheme (DES) along with the bit allocation algorithm, which minimizes the total required bandwidth while ensuing a given average estimation mean-squared error (MSE). The DES comprises of a probabilistic Lloyd-Max quantization rule, and a best linear unbiased estimation (BLUE). Since the optimum bit allocation problem does not have a closed form, we present a suboptimal solution utilizing the alternating minimization (AM) algorithm. Finally, simulation results are provided to show the effectiveness of the proposed DES along with the bit allocation algorithm.