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Restructuring in power systems has introduced new complexities and difficulties in controlling of these systems. Therefore, new control strategies should be investigated in operation of power systems. On the other hand, communication infrastructure (CI) is responsible for establishing any control strategy. The purposes of this study are twofold: firstly, to design a communication infrastructure for any given power network with determined measurements; secondly, to compare communication infrastructures for centralized and decentralized control strategies in power grids. The comparison criteria are communication network cost, delay (latency), and reliability. In this study, hybrid state estimation (HSE), as one of the most important wide area measurement systems (WAMS), is opted. Communication infrastructures are designed for two different control strategies; centralized and decentralized (multi-area) HSE. These strategies have been investigated in IEEE 118-bus test network. Some new concepts, that help us to compare any two given communication infrastructures with each other, are introduced. Finally, two designed communication infrastructures for these two strategies are compared with each other. The results show that, although communication infrastructure investments are almost the same in both cases, decentralizing, as a cause of decentralized control strategy, results in improvement of latency and reliability of CI.