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A modified joint source-channel decoding (JSCD) algorithm based on Low-density parity-check (LDPC) codes and hidden Markov estimation has been presented and extended to applying over Rayleigh fading channels. The proposed algorithm utilizes the source residual redundancy lack of any priori information of the source parameters, and the modifications employ the self-checking and convergence mechanisms of LDPC codes in adjusting the error probability of the hidden Markov Model (HMM). To show the validation of the proposed JSCD methods, we also give a framework for the density evolution analysis for JSCD. Simulation results show that the joint decoding scheme on Rayleigh fading channels greatly reduces the number of iterations and improves the system performance more than 0.7dB. Moreover, the modified JSCD algorithm leads to the joint decoder converge at least 10% faster than the unmodified method without any degradation in the decoding performance.