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

TL;DR

This paper analyzes the performance of nonbinary LDPC codes with QAM modulation, deriving bounds and providing simulation results to optimize symbol-to-signal mappings for improved error performance.

Contribution

It introduces a random coding bound for NB LDPC codes with QAM and evaluates the impact of different mappings through simulations, comparing with existing standards.

Findings

Optimized mappings improve error performance.

Derived bounds closely match simulation results.

Nonbinary codes outperform binary codes in certain scenarios.

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.