  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.
