高围长低密度奇偶校验码的置换多项式构造
Low-Density Parity-Check Codes of High Girth from Permutation Polynomials
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中文总结 AI 辅助
本文利用非交换二项式置换多项式构造基于原模图的LDPC码，突破围长和最小距离上界，仿真显示译码性能优于基于仿射置换多项式的QC-LDPC码。
中文摘要 AI 辅助
准循环低密度奇偶校验（QC-LDPC）码因其结构简单、编码器和译码器实现高效而被广泛应用于现代通信标准中。然而，其构造中使用的循环置换矩阵的交换性显著限制了码的围长和最小距离，影响了迭代译码性能。本文研究了使用高次置换多项式构造的基于原模图的码，重点关注一类封闭的非交换二项式置换多项式，该多项式使得这些构造能够突破围长和最小距离的上界，同时保持简单的表示形式。仿真结果表明，与基于仿射置换多项式（包括QC-LDPC码）的构造相比，所提出的构造具有更好的译码性能。
英文摘要
Quasi-cyclic low-density parity-check (QC-LDPC) codes are widely used in modern communication standards due to their simple structure and efficient encoder and decoder implementations. However, the commutativity of the circulant permutation matrices used in their construction significantly limits their girth and minimum distance, affecting iterative decoding performance. In this paper, we investigate protograph-based codes constructed using permutation polynomials of higher degree, focusing on a closed family of non-commuting binomial permutation polynomials that enables these constructions to exceed both of these girth and minimum distance upper bounds while maintaining a simple representation. Simulation results demonstrate improved decoding performance compared to constructions based on affine permutation polynomials, which include QC-LDPC codes.
发表机构
- University of South Florida（南佛罗里达大学）
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