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Product codes (PCs) are typically decoded using iterative bounded distance decoding (iBDD) to ensure a low decoding complexity. To obtain further performance gain, a soft-aided decoding algorithm, termed the iBDD with scaled reliability (iBDD-SR), was proposed for PCs. In this paper, we propose an enhanced iBDD-SR by introducing threshold and memory when passing messages between the component decoders. The resulting algorithm is referred to as the threshold-based binary message passing (TB-BMP) with memory. In the proposed decoding algorithm, the soft reliability of the BDD output at the current half-iteration is a weighted sum of the BDD output, the channel reliability, and the content of the memory unit, where the content of the memory unit at the current half-iteration is related to the selected threshold and the BDD output at last half-iteration. Due to the existence of memory, the Bayesian network …