Nonbinary LDPC Coded QAM Signals With Optimized Mapping: Bounds and Simulation Results

This paper studies 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 the Galois extension fields GF(2(m)) with m = 6 used with QAM signaling. Performance of NB LDPC coded transmission strongly depends on the 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 squared 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.

Automated summary

This study focuses on the properties of nonbinary low-density parity-check (NB LDPC) codes in coded modulation systems. Specifically, it examines the performance of NB LDPC codes over the Galois extension fields GF(2(m)) with m = 6 used with QAM signaling. The paper analyzes the impact of symbol-to-signal point mappings on the performance of NB LDPC coded transmission and presents simulation results for belief-propagation decoding in coded modulation schemes with NB quasi-cyclic (QC)-LDPC codes. Comparisons are made with optimized binary QC-LDPC codes in WiFi and 5G standards as well as a new bound.