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We propose a superposition scheme, based on the use of serially-concatenated LDGM codes, for the transmission of spatially correlated sources over Gaussian broadcast channels. The messages intended for each receiver are independently encoded using the same code. In this manner, a strong degree of correlation is kept between the encoded sequences, which are then modulated with different energies and symbol-wise added. By properly designing the encoding process, simulation results show that our proposed scheme easily outperforms the suboptimal theoretical limit assuming separation between source and channel coding.