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In this paper, we study the complexity reduction problem of the iterative row-column soft decision feedback algorithm (IRCSDFA) for two-dimensional (2D) inter-symbol interference (ISI) detection. Specifically, Gaussian approximation (GA) is employed in both the component row and column detectors of the IRCSDFA in order to reduce its computational complexity. With the employment of GA, the state space dimension of the ISI trellis of either component detector can be reduced enormously (i.e., the number of branches in one ISI trellis section decreases). Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is then employed to perform detection over the GA-simplified ISI trellis. For brevity, we refer to the IRCSDFA with BCJR detection over the GA-simplified ISI trellis as IRCSDFA-GA-BCJR. Next, the iteration scheduling of component detectors and decoder in coded 2D ISI channels with low density parity check (LDPC) coding and IRCSDFA-GA-BCJR detection is studied. Specifically, three iteration schemes: single detector (row or column) scheme, alternate detector scheme, and combined detector scheme, are considered, with the last scheme showing the best coded performance. Finally, the computational complexity of the proposed IRCSDFA-GA-BCJR is analyzed, and shown to have significant reduction with a cost of only about 0.3 and 0.35 dB in coded BER/FER performance loss compared to the conventional IRCSDFA without GA and the optimal symbol-based BCJR algorithm, respectively.