Title: Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes Show Chinese title

Title: 分层归一化最小和解码与比特翻转用于FDPC码

Abstract: Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we introduce a layered normalized min-sum (LNMS) message-passing decoding algorithm for the FDPC codes. We also introduce a syndrome-guided bit flipping (SGBF) method to enhance the error-correction performance of our proposed decoder. The LNMS decoder leverages conflict graph coloring for efficient layered scheduling, enabling faster convergence by grouping non-conflicting check nodes and updating variable nodes immediately after each layer. In the event of decoding failure, the SGBF method is activated, utilizing a novel reliability metric that combines log-likelihood ratio (LLR) magnitudes and syndrome-derived error counts to identify the least reliable bits. A set of candidate sequences is then generated by performing single-bit flips at these positions, with each candidate re-decoded via LNMS. The optimal candidate is selected based on the minimum syndrome weight. Extensive simulation results demonstrate the superiority of the proposed decoder. Numerical simulations on FDPC$(256,192)$ code with a bit-flipping set size of $T = 128$ and a maximum of $5$ iterations demonstrate that the proposed decoder achieves approximately a $0.5\,\mathrm{dB}$ coding gain over standalone LNMS decoding at a frame error rate (FER) of $10^{-3}$, while providing coding gains of $0.75-1.5\,\mathrm{dB}$ over other state-of-the-art codes including polar codes and 5G-LDPC codes at the same length and rate and also under belief propagation decoding. Show Chinese abstract

Abstract: 公平密度奇偶校验（FDPC）码最近被引入，与5G系统中标准化的低密度奇偶校验（LDPC）码相比，特别是在高率范围内表现出更好的性能。 在本文中，我们为FDPC码引入了一种分层归一化最小和（LNMS）消息传递解码算法。 我们还引入了一种基于校验的位翻转（SGBF）方法，以提高所提出的解码器的纠错性能。 LNMS解码器利用冲突图着色进行高效的分层调度，通过将不冲突的校验节点分组，并在每个层之后立即更新变量节点，从而实现更快的收敛。 在解码失败的情况下，激活SGBF方法，利用一种新颖的可靠性度量，结合对数似然比（LLR）幅度和由校验得到的错误计数，以识别最不可靠的位。 然后通过在这些位置进行单比特翻转生成一组候选序列，每个候选序列通过LNMS重新解码。 根据最小校验重量选择最优候选序列。 广泛的仿真结果证明了所提出解码器的优势。 对FDPC$(256,192)$码的数值仿真，具有比特翻转集大小为$T = 128$和最多$5$次迭代，在帧错误率（FER）为$10^{-3}$时，所提出的解码器相比独立的LNMS解码器实现了大约$0.5\,\mathrm{dB}$的编码增益，同时在相同长度和速率下，与其他最先进的码（包括极化码和5G-LDPC码）以及在置信传播解码下也提供了$0.75-1.5\,\mathrm{dB}$的编码增益。