For decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs), i.e., in the “waterfall region” of the bit error rate curve. This paper demonstrates that, for quantized decoders, MSA actually outperforms AMSA and OMSA in the “error floor” region, and that all three algorithms suffer from a relatively high error floor. This motivates the introduction of a modified MSA that is designed to outperform MSA, AMSA, and OMSA across all SNRs. The new algorithm is based on the assumption that trapping sets are the major cause of the error floor for quantized LDPC decoders. A performance estimation tool based on trapping sets is used to verify the effectiveness of the new algorithm and also to guide parameter selection. We also show that the implementation complexity of the new algorithm is only slightly higher than that of AMSA or OMSA. Finally, the simulated performance of the new algorithm, using several classes of LDPC codes (including spatially coupled LDPC codes), is shown to outperform MSA, AMSA, and OMSA across all SNRs.

中文翻译：

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一种降低量化 LDPC 解码器误差层的基于阈值的最小和算法

对于解码低密度奇偶校验 (LDPC) 码，衰减最小和算法 (AMSA) 和偏移最小和算法 (OMSA) 可以在低信噪比下优于传统的最小和算法 (MSA) -ratios (SNR)，即在误码率曲线的“瀑布区”中。本文证明，对于量化解码器，MSA 在“错误底限”区域实际上优于 AMSA 和 OMSA，并且所有三种算法都遭受相对较高的错误底限。这促使引入改进的 MSA，旨在在所有 SNR 中优于 MSA、AMSA 和 OMSA。新算法基于以下假设：陷阱集是量化 LDPC 解码器的错误底限的主要原因。基于陷阱集的性能估计工具用于验证新算法的有效性并指导参数选择。我们还表明，新算法的实现复杂度仅略高于 AMSA 或 OMSA。最后，使用几类 LDPC 码（包括空间耦合 LDPC 码）的新算法的模拟性能在所有 SNR 上均优于 MSA、AMSA 和 OMSA。