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In this paper, we consider the transmission of a Gaussian signal over a slow fading channel. The channel state information is assumed to be only known at the receiver. The source is layer-coded and transmitted using the broadcast strategy. We are interested in the optimization problem of minimizing the expected end-to-end distortion of the reconstructed signal at the receiver. An efficient iterative algorithm is proposed to jointly solve the rate allocation problem and the channel discretization problem. Numerical results show that the proposed algorithm outperforms the schemes using fixed channel discretization by a large margin. Meanwhile, the computational cost of our method is lower than those of the joint optimization approaches that involve partial exhaustive search.