Bit-Flipping (BF) decoders are a family of decoders widely employed in post-quantum cryptographic schemes based on Quasi-Cyclic Moderate-Density Parity-Check (QC-MDPC) codes, such as BIKE. BF decoders suffer from trapping sets, corresponding to low-weight error patterns that likely lead to decoding failures. For QC-MDPC codes, the most relevant family of trapping sets is that of near-codewords, which are error patterns associated to low-weight syndromes. Indeed, recent works show that error patterns having a large overlap with near-codewords are the main culprits for decoding failures at very low Decoding Failure Rate (DFR) values. In this paper, we show that any BF decoder can be tweaked and made somehow aware of near-codewords, which means being able to recognize, and recover from, bad configurations due to near-codewords. We show that this modification results in minimal computational overhead. Through intensive numerical simulations, we evaluate the effectiveness of this approach on several BF decoders, considering both toy code parameters and BIKE parameters for NIST security category 1. Our results show drastic reductions in the DFR. We also find that, with this modification, a recently proposed BF variant called BF-Max outperforms the two decoders used by BIKE within the NIST competition.

翻译：比特翻转（BF）译码器是一类广泛应用于基于准循环中密度奇偶校验（QC-MDPC）码的后量子密码方案（如BIKE）的译码器。BF译码器受困于捕获集，这些捕获集对应可能导致译码失败的低重量错误模式。对于QC-MDPC码，最相关的捕获集族是近码词，即与低重量伴随式相关的错误模式。事实上，最新研究表明，与近码词存在大量重叠的错误模式是极低译码失败率（DFR）值下译码失败的主要原因。本文证明，任何BF译码器均可调整并使其在一定程度上感知近码词，即能够识别并恢复由近码词导致的错误配置。我们表明，这一修改仅带来极小的计算开销。通过大量数值模拟，我们在多个BF译码器上评估了该方法的有效性，同时考虑了玩具码参数和NIST安全等级1的BIKE参数。结果表明，DFR显著降低。我们还发现，采用此修改后，近期提出的BF变体BF-Max在性能上优于BIKE在NIST竞赛中使用的两种译码器。