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首页> 外文会议>2012 International Symposium on Information Theory and its Applications. >Asymptotic analysis of spatially coupled MacKay-Neal and Hsu-Anastasopoulos LDPC codes
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Asymptotic analysis of spatially coupled MacKay-Neal and Hsu-Anastasopoulos LDPC codes

机译：MacKay-Neal和Hsu-Anastasopoulos LDPC码在空间上的渐近分析

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摘要

MacKay-Neal (MN) and Hsu-Anastasopoulos (HA) low-density parity-check (LDPC) codes are known to achieve the capacity of memoryless binary-input symmetric-output channels under maximum likelihood (ML) decoding with bounded column and row weight in their associated parity-check matrices. Recently, Kasai and Sakaniwa showed that spatially coupled (SC) versions of the MN and HA LDPC codes have belief propagation (BP) iterative decoding thresholds that approach capacity on the binary erasure channel (BEC) as the coupling length increases. In this paper, we extend the results of Kasai and Sakaniwa to the additive white Gaussian noise (AWGN) channel and show that the thresholds of the SC-MN and SC-HA ensembles approach capacity with bounded density as the coupling length increases, i.e., the number of edges per information bit approaches a finite value as the estimated BP threshold approaches the Shannon limit. We also perform an asymptotic weight enumerator analysis and show that, provided the density parameters are chosen to be sufficiently large, the SC-MN and SC-HA ensembles are asymptotically good. Further, for certain selections of parameters, some of these ensembles are shown to have both excellent thresholds and good distance properties.
机译：已知MacKay-Neal（MN）和Hsu-Anastasopoulos（HA）低密度奇偶校验（LDPC）码可在有界列和行有界的最大似然（ML）解码下实现无存储二进制输入对称输出通道的容量它们相关的奇偶校验矩阵的权重。最近，Kasai和Sakaniwa显示，MN和HA LDPC码的空间耦合（SC）版本具有置信传播（BP）迭代解码阈值，随着耦合长度的增加，该阈值接近二进制擦除信道（BEC）的容量。在本文中，我们将Kasai和Sakaniwa的结果扩展到加性高斯白噪声（AWGN）通道，结果表明，随着耦合长度的增加，SC-MN和SC-HA的阈值趋近于具有有限密度的容量，即当估计的BP阈值接近Shannon极限时，每个信息比特的边沿数量接近一个有限值。我们还进行了渐近权重枚举器分析，结果表明，如果将密度参数选择为足够大，则SC-MN和SC-HA集成是渐近良好的。此外，对于某些参数的选择，这些合奏中的某些已显示具有出色的阈值和良好的距离特性。

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