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Distributed estimation of a common unknown parameter vector can be realized efficiently and robustly over an adaptive network employing diffusion strategies. In the adapt-then-combine implementation of these strategies, each node combines the intermediate estimates of the nodes within its closed neighborhood. This requires the nodes to transmit their intermediate estimates to all their neighbors after each update. In this paper, we consider transmitting a subset of the entries of the intermediate estimate vectors and examine two different schemes for selecting the transmitted entries at each iteration. Accordingly, we propose a partial-diffusion least mean-square (PDLMS) algorithm that reduces the internode communications while retaining the benefits of cooperation and provides a convenient trade-off between communication cost and estimation performance. Through analysis, we show that the PDLMS algorithm …