Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths
Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths
复制标题
用于短块长度的基于准循环原图的类 Raptor LDPC 码
DOI：
10.1109/tit.2019.2895322
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发表时间：
2019
影响因子：
2.5
通讯作者：
R. Wesel
中科院分区：
文献类型：
--
作者：
S. V. S. Ranganathan;D. Divsalar;R. Wesel
基于原型图的类Raptor低密度奇偶校验码（PBRL码）是一类易于编码的速率兼容低密度奇偶校验码（LDPC码）。PBRL码在所有设计速率下都具有优异的性能。准循环（QC）PBRL码族允许高速解码器实现。PBRL码设计到目前为止，长和短的块长度，已基于优化的迭代解码阈值的原型的PBRL家庭在各种设计速率。本文介绍了一种在短块长度（几百比特）下获得更好的QC PBRL码族以满足低误帧率（FER）要求的设计方法。我们首先选择一个原矩阵的最高设计率。为了添加新行以降低速率，我们保持PBRL原矩阵的所有先前获得的行固定，并选择使可以从原矩阵获得的任何QC-LDPC码的最小距离的上限最大化的新行。新的QC PBRL码族通过提供显著更好的低FER性能而在短块长度下优于原始PBRL码。计算上述上界的标准方法需要复杂性，复杂性随着原矩阵的大小呈指数增长。然而，我们表明，PBRL原矩阵的结构，让我们得到的上界与复杂性的增长只有线性的PBRL原矩阵的大小。利用复杂性降低的结果，我们还建立了一个等价的穷举搜索设计一个新的行的PBRL原矩阵根据新的设计方法和整数线性规划。
Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a family of easily encodable rate-compatible low-density parity-check (LDPC) codes. PBRL codes have an excellent performance across all design rates. Quasi-cyclic (QC) PBRL code families permit high-speed decoder implementations. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the PBRL family at various design rates. This paper introduces a design method to obtain better QC PBRL code families at short block-lengths (of a few hundred bits) for low frame error rate (FER) requirements. We first select a protomatrix for the highest design rate. To add a new row to lower the rate, we keep all the previously obtained rows of the PBRL protomatrix fixed and select the new row that maximizes an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protomatrix. The new QC PBRL code families outperform the original PBRL codes at short block-lengths by providing a significantly better low-FER performance. The standard approach to computing the aforementioned upper bounds requires complexity that grows exponentially with the size of the protomatrix. However, we show that the structure of the PBRL protomatrix lets us obtain the upper bounds with complexity that grows only linearly with the size of the PBRL protomatrix. Using the complexity reduction results, we also establish an equivalence between the exhaustive search to design a new row for the PBRL protomatrix according to the new design method and an integer linear program.