论文标题
具有卷积代码约束的广义LDPC代码
Generalized LDPC Codes with Convolutional Code Constraints
论文作者
论文摘要
编织的卷积代码（BCC）是一类具有空间耦合的类涡轮状的代码，可以通过$（2,3）$ - 常规紧凑型图来描述。在本文中，我们介绍了一个$（D_V，D_C）$的家庭 - 带有卷积代码约束（CC-GLDPC代码）的常规GLDPC代码，该代码形成了经典BCC的扩展到任意常规图。为了表征瀑布和误差地板区域的性能，我们对密度演化阈值以及有限长度的集合权重枚举和合奏的最小距离进行分析。特别是，我们考虑了总体速率$ r = 1/3 $和$ r = 1/2 $的各种集合，并研究了可变节点学位和组件代码强度之间的权衡。我们还将结果与相同程度和速率的相应经典LDPC代码进行了比较。可以观察到，对于具有可变节点学位的考虑的LDPC代码$ d_v> 2 $，我们可以找到具有较小$ d_v $的CC-GLDPC代码，该代码在BP和MAP阈值方面提供相似或更好的性能，而以最小距离的损失可忽略不计。
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code constraints (CC-GLDPC codes), which form an extension of classical BCCs to arbitrary regular graphs. In order to characterize the performance in the waterfall and error floor regions, we perform an analysis of the density evolution thresholds as well as the finite-length ensemble weight enumerators and minimum distances of the ensembles. In particular, we consider various ensembles of overall rate $R=1/3$ and $R=1/2$ and study the trade-off between variable node degree and strength of the component codes. We also compare the results to corresponding classical LDPC codes with equal degrees and rates. It is observed that for the considered LDPC codes with variable node degree $d_v>2$, we can find a CC-GLDPC code with smaller $d_v$ that offers similar or better performance in terms of BP and MAP thresholds at the expense of a negligible loss in the minimum distance.
