To provide reliable transmissions with flexible rates for satellite communications, this paper presents a novel method of constructing multi-rate quasi-cyclic low-density parity-check (LDPC) codes. The basic idea is to generate low-rate codes from a high-rate mother code by combining shortening and extending, which ensures that the generated code family owns the same code length, in order to maintain the same frame structure. The code construction involves the design of base matrices and exponent matrices for the designed codes. A progressive row elimination and addition algorithm is proposed for designing the code base matrices from a high rate to low rates. This algorithm leads to the nested and systematic structure of the parity-check matrices, which are desirable for practical implementations of their encoders and decoders, while ensuring the optimal decoding thresholds. In addition, we construct a circulation coefficient matrix based on finite fields and select the optimal rows in this matrix to construct exponent matrices while considering of cycle structures. We demonstrate that the designed codes achieve better performance for all the code rates than the LDPC codes in DVB-S2X standards. In addition, the proposed codes do not exhibit error floors for their block error rates down to 10 −5 .

中文翻译：

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卫星通信多速率准循环LDPC码的构建


为了为卫星通信提供灵活速率的可靠传输，本文提出了一种构造多速率准循环低密度奇偶校验（LDPC）码的新方法。其基本思想是通过缩短和扩展相结合的方式，将高速率母码生成低速率码，从而保证生成的码族具有相同的码长，从而保持相同的帧结构。代码构造涉及设计代码的基矩阵和指数矩阵的设计。提出了一种渐进行消除和添加算法，用于设计从高速率到低速率的代码库矩阵。该算法产生了奇偶校验矩阵的嵌套和系统结构，这对于编码器和解码器的实际实现是理想的，同时确保最佳解码阈值。此外，我们基于有限域构造循环系数矩阵，并在考虑循环结构的同时选择该矩阵中的最优行来构造指数矩阵。我们证明所设计的代码在所有码率下都比 DVB-S2X 标准中的 LDPC 代码具有更好的性能。此外，所提出的代码在其块错误率低至10 -5 的情况下不会表现出错误平台。