In this paper, we study a class of nonbinary LDPC (NBLDPC) codes whose parity-check matrices have column weight 2, called NBLDPC cycle codes. We propose a design framework of -regular binary quasi-cyclic (QC) LDPC codes and then construct NBLDPC cycle codes of large girth based on circulants and finite fields by randomly choosing the nonzero field elements in their parity-check matrices. For enlarging the girth values, our approach is twofold. First, we give an exhaustive search of circulants with column/row weight and design a masking matrix with good cycle distribution based on the edge-node relation in undirected graphs. Second, according to the designed masking matrix, we construct the exponent matrix based on finite fields. The iterative decoding performances of the constructed codes on the additive white Gaussian noise (AWGN) channel are finally provided.

中文翻译：

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从循环和有限域设计大周长非二元LDPC循环码

在本文中，我们研究了一类非二进制 LDPC (NBLDPC) 码，其奇偶校验矩阵的列权重为 2，称为 NBLDPC 循环码。我们提出了一个设计框架-常规二进制准循环 (QC) LDPC 码，然后通过随机选择奇偶校验矩阵中的非零字段元素，基于循环和有限域构造大周长的 NBLDPC 循环码。为了扩大周长值，我们的方法是双重的。首先，我们对具有列/行权重的循环进行了详尽的搜索，并基于无向图中的边节点关系设计了一个具有良好循环分布的掩码矩阵。其次，根据设计的掩蔽矩阵，构造基于有限域的指数矩阵。最后给出了所构造的代码在加性高斯白噪声（AWGN）信道上的迭代解码性能。