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Two-dimensional (2-D) intersymbol-interference (ISI) channels represent an important class of next-generation data-storage systems. In order to mitigate the 2-D ISI and improve system performance, a joint message-passing decoding algorithm is proposed in this paper. The proposed algorithm conducts an iterative decoding of low-density parity-check code and a 2-D ISI channel, which can be implemented in a fully parallel manner. An extrinsic information transfer chart is also introduced to analyze the performance and convergence behavior of the proposed message-passing decoding system. Simulation results show that the proposed joint message-passing decoding algorithm outperforms some existing joint decoding algorithms.