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In this paper, the authors study a communication scheme in which nodes transmit sufficient statistics of their observations over non-orthogonal medium access channels for distributed estimation. This scheme unifies and generalizes several multiple access schemes such as uncoded transmissions of Gaussian observations and Type-Based Multiple Access. For the exponential family of distributions, they show that the Sufficient-Statistic Based Multiple Access (SSBMA) achieves the Cramer-Rao bound on the estimation error asymptotically. Further, they argue that such an optimality result only applies to the exponential family of distributions. In addition, they present a simplified and unified analysis of asymptotic distribution of estimation error for a very general class of communication schemes and estimators.
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