This correspondence proposes a jointly-designed quasi-cyclic (QC) low-density parity-check (LDPC)-coded multi-relay cooperation with a destination node realized by multiple receive antennas. First, a deterministic approach is utilized to construct different classes of binary QC-LDPC codes with no length-4 cycles. Existing methods put some limitations in terms of code length and rate in order to provide high error-correction performance. Therefore, this article gives three classes of QC-LDPC codes based on a combinatoric design approach, known as cyclic difference packing (CDP), with flexibility in terms of code-length and rate selection. Second, the proposed CDP-based construction is utilized to jointly-design QC-LDPC codes for coded-relay cooperation. At the receiver, the destination node is realized by multiple receive antennas, where maximal-ratio combining (MRC) and sum-product algorithm (SPA)-based joint iterative decoding are utilized to decode the corrupted sequences coming from the source and relay nodes. Simulation results show that the proposed QC-LDPC coded-relay cooperations outperform their counterparts with a coding gain of about 0.25 dB at bit-error rate (BER) 10 − 6 over a Rayleigh fading channel in the presence of additive white Gaussian noise. Furthermore, the extrinsic-information transfer (EXIT) chart analysis has been used to detect the convergence threshold of proposed jointly-designed QC-LDPC codes. Numerical analysis shows that the proposed jointly-designed QC-LDPC codes provide a better convergence as compared to their counterparts under the same conditions.

中文翻译：

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联合设计的准循环 LDPC 编码协作与接收端分集合并

这种对应提出了一种联合设计的准循环 (QC) 低密度奇偶校验 (LDPC) 编码的多中继协作，与由多个接收天线实现的目标节点合作。首先，利用确定性方法来构造不同类别的二进制 QC-LDPC 码，没有长度为 4 的周期。现有方法在码长和码率方面存在一些限制，以提供高纠错性能。因此，本文基于称为循环差分打包 (CDP) 的组合设计方法给出了三类 QC-LDPC 码，在码长和速率选择方面具有灵活性。其次，所提出的基于 CDP 的构造用于联合设计用于编码中继合作的 QC-LDPC 码。在接收端，目的节点由多个接收天线实现，其中最大比合并 (MRC) 和基于和积算法 (SPA) 的联合迭代解码用于解码来自源节点和中继节点的损坏序列。仿真结果表明，在存在加性高斯白噪声的情况下，所提出的 QC-LDPC 编码中继合作在误码率 (BER) 为 10 - 6 时在瑞利衰落信道上的编码增益约为 0.25 dB。此外，外部信息传输 (EXIT) 图分析已被用于检测提出的联合设计的 QC-LDPC 码的收敛阈值。数值分析表明，在相同条件下，所提出的联合设计的 QC-LDPC 码与其对应物相比具有更好的收敛性。