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For linear block codes without a sparse graph representation, there exists an iterative decoding algorithm which combines the traditional reliability-based decoding (RBD) with adaptive belief propagation (ABP) to achieve a good tradeoff between the error performance and decoding complexity. However, in the original design of the iterative scheme, only a one-way flow of soft-information from the ABP-part to the RBD-part is available, hence limiting the performance of iterative processing. In this study, several low-complexity schemes are presented for the RBD-part to produce desirable soft-outputs such that decoded results can be bilaterally exchanged between both of the RBD and ABP parts. Simulation results also verify the superiority of the proposed idea over the conventional design.