基于QR码构造的广义LDPC码

在低密度奇偶校验(low density parity check， LDPC)码的图形表示中，存在着一种陷阱集结构，其对性能的影响表现在，陷阱集中变量节点所对应的比特在迭代过程中如果发生错误，就不容易被纠正回来。因此，结合平方剩余(quadratic residue， QR)码来设计一种新颖的广义LDPC码的编译码方案。该方案利用QR码这一性能优良的码型，为LDPC码的某些变量节点提供额外的保护，在损失少许码率的情况下，以期消除某些陷阱集的影响，并获得比原始LDPC码更好的性能。在仿真模拟中，通过统计原始LDPC码的错误比特位置，发现某些比特位置的出错频率较高，为此，从陷阱集的角度分析了其中的原因，并根据这些变量节点，构造广义LDPC码。仿真结果表明，该方案能够有效地降低某些LDPC码的错误平层。

Construction of generalized LDPC codes based on QR codes

In the Tanner graph of low density parity check (LDPC) code, there is a kind of structure called trapping set whose uncorrected variable nodes may not be corrected through iteration. In this paper, we will introduce a novel coding and decoding scheme of generalized LDPC codes with the assistance of quadratic residue code. In this scheme, by using quadratic residue code and sacrificing a bit of rate, some variable nodes will be selected to be given the additional protection, hoping that this scheme would help weaken the effects of trapping sets and improve the performance of the original LDPC codes. In the simulation, after counting uncorrected bits and analyzing the related error location histogram, we find that some bits or variable nodes may incline to be wrong. For this result, we figure out its reason from the perspective of trapping set, and select these variable nodes to construct the generalized LDPC codes. From our simulation, this scheme mitigates the error floor of some LDPC codes effectively.