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In this paper, we consider the design of a network-coded cooperation (NetCC) transmission scheme for free-space optical (FSO) two-way relay networks (TWRN). The achieved network-coded spatial diversity gain can effectively enhance the FSO communication quality over strong turbulence channels. Different from traditional assumption of perfect channel state information (CSI) prior known at destination, we develop an optimal bit detection method based on Bayesian estimate for receiving nodes in the absence of CSI. We then derive the closed-form algorithm for it by taking advantage of Meijer's G-function characterized by gamma-gamma strong turbulence model. Numerical simulations confirm that the proposed NetCC relay scheme has significant BER performance improvement compared with that of direct transmission scheme. In addition, we also investigate the impact of turbulence level with various scintillation indices on the NetCC scheme.