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The goal of the paper is to study specific properties of nonbinarylow-density parity-check (NB LDPC) codes when used in coded modulation systems.The paper is focused on the practically important NB LDPC codes over extensionsof 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 ofnonbinary symbols to signal constellation points. We obtain a random codingbound on the maximum-likelihood decoding error probability for an ensemble ofrandom irregular NB LDPC codes used with QAM signaling for specificsymbol-to-signal point mappings. This bound is based on the ensemble averageEuclidean distance spectra derived for these mappings. The simulation resultsfor the belief-propagation decoding in the coded modulation schemes with the NBquasi-cyclic (QC)-LDPC codes under different mappings are given. Comparisonswith the optimized binary QC-LDPC codes in the WiFi and 5G standards, as wellas with the new bound, are performed.

NB QC-LDPC Coded QAM Signals with Optimized Mapping: Bounds and Simulation Results