The joint shuffled scheduling decoding (JSSD) algorithm can reduce the decoding complexity of the joint source-channel coding system (JSCC) based on double protograph low-density parity-check (P-LDPC) codes. However, the JSSD algorithm will not work when the linking matrix between check nodes (CNs) of the source P-LDPC and variable nodes (VNs) of the channel P-LDPC is adopted in such a system, and this linking matrix has a significant influence on the system performance. In this paper, a generalized joint shuffled scheduling decoding (GJSSD) algorithm is designed to work for the system, and the JSSD algorithm can be regarded as a special case of this algorithm. Simulations show that the proposed GJSSD algorithm can reduce the decoding complexity with performance improvement when compared with the joint belief-propagation (JBP) algorithm.INDEX TERMS Joint source-channel coding, P-LDPC code, shuffled decoding.