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In this paper, we investigate the performance and the design of Joint Source-Channel Decoding (JSCD) schemes involving structured Low-Density Parity-Check (LDPC) codes such as protograph based codes. We first present the asymptotic analysis of such iterative receivers based on multi-dimensional EXIT charts. Since a protograph can be interpreted as different encoding schemes, the information mapping becomes an issue. We will thus show that, using the EXIT chart analysis, it is possible to select the best suited scheme for JSCD. Finally, the design of protographs for JSCD systems is addressed and finite length simulation results are provided.