The goal of the paper is to study specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over extensions of the Galois field GF$(2^m)$ with $m \le 6$ used with QAM signaling. Performance of NB QC LDPC coded transmission strongly depends on mapping of nonbinary symbols to signal constellation points. We obtain a random coding bound on the maximum-likelihood decoding error probability for an ensemble of random irregular NB LDPC codes used with QAM signaling for specific symbol-to-signal point mappings. This bound is based on the ensemble average Euclidean distance spectra derived for these mappings. The simulation results for the belief-propagation decoding in the coded modulation schemes with the NB quasi-cyclic (QC)-LDPC codes under different mappings are given. Comparisons with the optimized binary QC-LDPC codes in the WiFi and 5G standards, as well as with the new bound, are performed.
翻译:本文的目的是研究非二元低密度对等器编码(NB LDPC)在编码调制系统中使用时的具体特性。本文侧重于Galois Foel GF$(2 cmm)的实用的NB LDPC代码,该代码与QAM信号信号中所用的Golois Foel Foel $(2 cm) $= le 6美元,与QAM信号中所用的Glois field GF$(2 cm m美元)相对应。NB QC LDPC编码传输的性能很大程度上取决于对信号星座点的非二元符号的映射图。我们获得随机编码,该编码与混合使用的随机的随机不规则(最大相似的)解码差错概率相约束,该编码与QAM信号信号信号中特定符号到信号点映射的QDPC代码之间的虚拟数字数字一致。该代码以用于这些绘图的共通性电算平均 Euclideidean远光光谱为基础。在编码中与NB 准循环-LDPC-LDPC编码下,与WI-FA和WI-LDC-LD代码之间进行了对比。