空间耦合MacKay-Neal码和Hsu-Anastasopoulos码
Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes
摘要：
Kudekar等人最近证明，对于在二进制擦除信道（BEC）上的传输，LDPC码的空间耦合将耦合系综的BP阈值增加到底层LDPC码的MAP阈值。实现容量的空间耦合LDPC码的一个主要缺点是需要增加底层LDPC码的奇偶校验矩阵的列和行权重。本文证明了Hsu-Anastasopoulos（HA）码和MacKay-Neal（MN）码在校验矩阵的行和列权有界的MAP译码下都能达到无记忆二进制输入双输出信道的容量。HA码和MN码彼此是对偶码。本文的目的是提出一个经验证据，空间耦合MN（分别）。HA）码具有有界的列和行重量达到BEC的容量。为此，我们介绍了MN（分别）的空间耦合方案。HA）代码。通过密度演化分析，我们将表明，由此产生的空间耦合MN（分别为。HA）码具有接近香农极限的BP阈值。
英文摘要：
Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.
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