论文标题
使用解码器设计的非二进制LDPC代码的二进制代表
Binary Representaion for Non-binary LDPC Code with Decoder Design
论文作者
论文摘要
无周期非二元LDPC代码的二进制图像的等效二进制均衡检查矩阵具有许多比特级周期。在本文中，我们展示了如何将这些二元平价检查矩阵转换为无周期形式。结果表明，所提出的方法不仅可以用于非二进制LDPC代码的二进制图像，还可以用于大量的二进制LDPC代码。具体而言，我们提出了一个扩展的$ P $可还原（EPR）LDPC代码结构，以消除位级周期。对于具有短长度符号级周期的非二元LDPC代码，EPR-LDPC代码可以在很大程度上避免相应的短长度位循环。至于EPR-LDPC代码的解码，我们分别提出了一个混合硬化解码器和二进制对称通道和二进制输入高斯通道的混合硬性解码器。还提供了这些二进制解码器的简单代码优化算法。模拟显示了比较结果，并证明了所提出的二进制构造的优势，即更好的性能和较低的解码复杂性。
The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free forms. It is shown that the proposed methodology can be adopted not only for the binary images of non-binary LDPC codes but also for a large class of binary LDPC codes. Specifically, we present an extended $p$-reducible (EPR) LDPC code structure to eliminate the bit-level cycles. For the non-binary LDPC codes with short length symbol-level cycles, the EPR-LDPC codes can largely avoid the corresponding short length bit-level cycles. As to the decoding of the EPR-LDPC codes, we propose a hybrid hard-decision decoder and a hybrid parallel decoder for binary symmetric channel and binary input Gaussian channel, respectively. A simple code optimization algorithm for these binary decoders is also provided. Simulations show the comparative results and justify the advantages, i.e., better performance and lower decoding complexity, of the proposed binary constructions.
