Advanced GF(3²) nonbinary LDPC coded modulation with non-uniform 9-QAM outperforming star 8-QAM.

Area of Science:

• Electrical Engineering
• Information Theory
• Digital Communications

Background:

• Non-uniform signaling schemes offer potential advantages in communication systems by assigning different probabilities to symbols.
• Quadrature Amplitude Modulation (QAM) is a widely used digital modulation technique.
• Low-Density Parity-Check (LDPC) codes are advanced error-correcting codes known for their near-capacity performance.

Purpose of the Study:

• To develop and analyze a 9-symbol non-uniform signaling scheme based on Huffman coding.
• To design an optimal signal constellation for this non-uniform scheme, maximizing the Constellation Figure of Merit (CFM).
• To propose and evaluate a coded modulation system combining the non-uniform 9-QAM with a nonbinary quasi-cyclic LDPC code.

Main Methods:

• Huffman coding procedure for designing prefix codes with optimal performance.
• Algorithm development to determine optimal signal constellation sets for non-uniform signaling.
• Design of a GF(3^2) nonbinary quasi-cyclic LDPC code tailored for the 9-QAM scheme.
• Monte Carlo simulations to assess the performance of the coded modulation system.

Main Results:

• A 9-symbol non-uniform signaling scheme and a 9-QAM constellation were successfully designed.
• The proposed non-uniform 9-QAM scheme achieves the same spectral efficiency as conventional 8-QAM.
• The combined nonbinary LDPC coded 9-QAM scheme demonstrated a performance gain of at least 0.8dB over nonbinary LDPC coded uniform 8-QAM.

Conclusions:

• The proposed non-uniform 9-QAM signaling scheme, optimized using CFM, offers an effective approach for digital communications.
• The integration with specially designed nonbinary LDPC codes significantly enhances the system's error correction capabilities.
• This advanced coded modulation system provides a superior alternative to conventional uniform schemes, particularly in terms of achievable data rates and reliability.