To deal with the channel uncertainty of the correlated block fading channels,a joint estimation-decoding approach based on Factor Graph Expectation Maximization(FGEM) algorithms was proposed.In the receiver,a message passing method on factor graph was adopted to jointly estimate the channel and decode the message.EM algorithm was used to remove the effect of loops on the convergence of message passing.It also solved the calculation problem of Gaussian mixture message.The calculation of message passing was simplified by the Kalman forward-backward algorithm,which resulted in reduced complexity in joint estimation-decoding.The simulation results show that the proposed algorithm can improve the accuracy of the channel estimation and improve the decoding performance.