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We propose a trellis-based soft-input-soft-output (SISO) a posteriori probability (APP) decoding technique for variable-length coded correlated sources. This technique allows not only the (ML) sequence estimation but also the computation of bit-based reliability values. The notable feature of the proposed technique is that its calculation complexity and memory space requirement are both low. Moreover, we bring the technique of scaling extrinsic information to the field of iterative joint source-channel decoding (ISCD), and obtain fixed scaling factors (SFs) based on the extrinsic information transfer (EXIT) charts analysis. This technique obviously improves the ISCD performance with increasing neglectable complexity. Simulation results show that the proposed ISCD scheme provides a significant improvement on error protection capability for the variable-length coded correlated sources.