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This paper studies scalable global state synchronization of discrete-time double integrator multi-agent systems in presence of input saturation based on localized information exchange. A scale-free collaborative linear dynamic protocols design methodology is developed for discrete-time multi-agent systems with both full and partial-state couplings. And the protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Meanwhile, the protocols are parametric based on a parameter set in which the designed protocols can guarantee the global synchronization result. Furthermore, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents.