Belief propagation with Gaussian approximation for joint channel estimation and decoding

In order to increase the performance of joint channel estimation and decoding through belief propagation on factor graphs, we approximate the distribution of channel estimate in the factor graph as a mixture of Gaussian distributions. The result is a continuous downward and upward message propagation in the factor graph instead of discrete probability distributions. Using continuous downward messages, the computation complexity of belief propagation is reduced without performance degradation. With both continuous upward and downward messages, belief propagation almost achieves the same performance as expectation-maximization under good initialization and outperforms it under bad initialization.