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arXiv · 2108.08716

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

Irina E. Bocharova·Boris D. Kudryashov·Evgenii P. Ovsyannikov·Vitaly Skachek
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Abstract

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.

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Irina E. Bocharova, Boris D. Kudryashov, Evgenii P. Ovsyannikov, Vitaly Skachek. 2022-05-23. NB QC-LDPC Coded QAM Signals with Optimized Mapping: Bounds and Simulation Results. https://arxiv.org/abs/2108.08716

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