<p>In this paper, the authors propose a distributed gradient tracking algorithm with compressed communication to address an aggregative optimization problem under communication constraints. The problem involves minimizing the sum of local cost functions, where each cost function depends on both local and global state variables. The authors aim to solve this optimization problem through local computation and efficient communication among agents in a network, without the need for a central coordinator. The proposed algorithm combines the variable tracking method to estimate global state variables and a compressed communication scheme to reduce communication costs during the optimization process. Among which, the compressed scheme can encompass both biased and unbiased compressors. Despite the loss of some transmitting information due to quantization, the proposed algorithm can still achieve the exact optimal solution with a linear convergence rate. The authors validate the theoretical results through simulation experiments on an optimal placement problem.</p>