This paper considers low-density parity-check (LDPC) decoders affected by deviations introduced by the electronic device on which the decoder is implemented. Noisy density evolution (DE) that allows to theoretically study the performance of these LDPC decoders can only consider symmetric deviation models due to the all-zero codeword assumption. A novel DE method is proposed that admits the use of asymmetric deviation models, thus widening the range of faulty implementations that can be analyzed. DE equations are provided for three noisy decoders: belief propagation, Gallager B, and quantized min-sum (MS). Simulation results confirm that the proposed DE accurately predicts the performance of LDPC decoders with asymmetric deviations. Furthermore, asymmetric versions of the Gallager B and MS decoders are proposed to compensate the effect of asymmetric deviations. The parameters of these decoders are then optimized using the proposed DE, leading to better ensemble thresholds and improved finite-length performance in the presence of asymmetric deviations.

中文翻译：

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非对称偏差模型的噪声密度演化

本文考虑了低密度奇偶校验 (LDPC) 解码器受实施解码器的电子设备引入的偏差的影响。由于全零码字假设，允许从理论上研究这些 LDPC 解码器的性能的噪声密度演化 (DE) 只能考虑对称偏差模型。提出了一种新的 DE 方法，该方法允许使用非对称偏差模型，从而扩大了可以分析的错误实现的范围。为三个噪声解码器提供了 DE 方程：置信传播、Gallager B 和量化最小和 (MS)。仿真结果证实，所提出的 DE 准确地预测了具有非对称偏差的 LDPC 解码器的性能。此外，提出了 Gallager B 和 MS 解码器的非对称版本来补偿非对称偏差的影响。然后使用所提出的 DE 优化这些解码器的参数，从而在存在不对称偏差的情况下获得更好的集成阈值和改进的有限长度性能。