Irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes with the block dual-diagonal (BDD) parity structure are widely adopted in many communication standards because the BDD structure supports an efficient encoding and many degree-2 variable nodes inside are adequate for the construction of mid- to high-rate codes. However, we observe that low-rate irregular QC LDPC codes with the BDD parity structure inherently contain too many degree-2 variable nodes and suffer from error floors in high signal-to-noise ratio (SNR) region. In this paper, a generalized BDD structure including double-weight circulants as well as circulant permutation matrices is proposed for low-rate irregular QC LDPC codes with low error floors which is achieved with a little bit giving up error performance in the waterfall region. When constructing the parity part of a code with the generalized BDD structure, the portion of double-weight circulants is variable so that the resulting LDPC code can achieve a desired degree distribution including degrees 2 and 3 while supporting the efficient encoding. We show that low-rate QC LDPC codes constructed with the proposed BDD structure have better theoretical properties and lower error floor than those with the conventional BDD structure.

中文翻译：

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用于具有低误码层的低速率 QC LDPC 码的可变权重块双对角结构

具有块双对角 (BDD) 奇偶校验结构的不规则准循环 (QC) 低密度奇偶校验 (LDPC) 码在许多通信标准中被广泛采用，因为 BDD 结构支持高效编码和许多度 2 变量节点内部足以构建中高速率代码。然而，我们观察到具有 BDD 奇偶校验结构的低速率不规则 QC LDPC 码固有地包含过多的 2 度变量节点，并且在高信噪比 (SNR) 区域存在错误底线。在本文中，提出了一种包括双权重循环和循环置换矩阵的广义 BDD 结构，用于具有低误码率的低速率不规则 QC LDPC 码，这是通过在瀑布区域中稍微放弃误码性能来实现的。当用广义BDD结构构造代码的奇偶校验部分时，双权重循环部分是可变的，因此得到的LDPC码可以实现包括2度和3度在内的所需度数分布，同时支持高效编码。我们表明，与传统 BDD 结构相比，用所提出的 BDD 结构构造的低速率 QC LDPC 码具有更好的理论特性和更低的误码率。