The paper proposes a Soft-input-softoutput(SISO) A posteriori probability (APP) decoding algorithmfor variable-length coded correlated sources. Thistechnique can obtain Maximum likelihood (ML) sequenceestimation and bit-based reliability. The notable featureof this technique is its low computational complexity. Anotherinnovation of the paper is that, based on the Extrinsicinformation transfer (EXIT) charts analysis, we obtainedconstant Scaling factors (SFs) to refine the extrinsicinformation in the Iterative joint source-channel decoding(ISCD) process. This technique improves the ISCD performancewith adding very limited computational complexity.Simulation results showed that the proposed ISCD schemeprovided a great improvement on error protection capabilityfor the variable-length coded correlated sources.