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This paper focuses on the analysis of the decoding algorithm for low-density parity-check (LDPC) coded bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme. An equivalent channel model for hard-decision feedback and soft-decision feedback iterative decoding is proposed. With the theory of independent and identically distributed (i.i.d.) binary transmitted system, the equivalent model is structured by random move between different points in the constellation and elimination of the effects of it afterwards. It is proved in the literature that by using the simplified method, the transmitter only considering all-zeros codeword suffices to elaborate the error performance compared with the entire encode-decode system. Simulation results show that conventional LDPC coded BICM-ID system and the simplified all-zeros model have the same expected decoder behavior. The proposed technique is flexible in LDPC coded BICM-ID system using the binary sum-product algorithm (SPA) and can be extended to any communication systems based on linear code and binary iterative decoder, which can bring about low complexity implementation during the simulation.