A Threshold-Based Binary Message Passing Decoder With Memory for Product Codes

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 is used to model the decoding process of the TB-BMP. Based on the Bayesian network, we derive the density evolution (DE) equations for the TB-BMP under the constraint of extrinsic message passing (EMP). The analytical results of the DE analysis can be used to guide the selection of the parameters of the TB-BMP decoder. Extensive simulation results show that the TB-BMP decoder outperforms the iBDD-SR over the binary-input additive white Gaussian noise (Bi-AWGN) channels. In particular, for a PC based on a two-error-correcting extended Bose-Chaudhuri-Hocquenghem (BCH) code of length 256, the TB-BMP decoder performs about 0.28 dB better than the iBDD-SR at a bit error rate (BER) of 10
⁻⁷
.