In this paper, two joint phase estimation and decoding algorithms based on divergence minimization are presented for satellite coded transmissions in the presence of strong phase noise. The algorithms perform approximate Bayesian inference in a hybrid graphical model for time-varying phase and discrete symbols, where each pair of the random phase and data symbol are decoupled by minimizing the inclusive Kullback-Leibler (KL) divergence and minimizing the exclusive KL divergence, respectively. Simulations show that the algorithm using the inclusive KL divergence outperforms the expectation maximization (EM) algorithm, while the algorithm using the exclusive KL divergence achieves the same performance as that of the EM algorithm.