%0 Journal Article
%T Optimal Identical Binary Quantizer Design for Distributed Estimation
%A Swarnendu Kar
%A Hao Chen
%A Pramod K. Varshney
%J Mathematics
%D 2012
%I arXiv
%R 10.1109/TSP.2012.2191777
%X We consider the design of identical one-bit probabilistic quantizers for distributed estimation in sensor networks. We assume the parameter-range to be finite and known and use the maximum Cram\'er-Rao Lower Bound (CRB) over the parameter-range as our performance metric. We restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified. We identify a broad class of noise distributions, which includes Gaussian noise in the low-SNR regime, for which the often used threshold-quantizer is found to be minimax-optimal. Aided with theoretical results, we formulate an optimization problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise distributions, we demonstrate the superior performance of the new quantizer - particularly in the moderate to high-SNR regime.
%U http://arxiv.org/abs/1205.6907v1