Ultra-high-cardinality geometric shaping in the finite SNR regime

Area of Science:

• Information Theory
• Digital Communications
• Coding Theory

Background:

• Optimizing data transmission in noisy channels is crucial for efficient communication systems.
• Four-dimensional (4D) constellations offer potential for higher data rates compared to lower dimensions.
• Existing constellation designs often face limitations in performance and scalability.

Purpose of the Study:

• To design and evaluate novel 4D constellations for improved performance in additive white Gaussian noise (AWGN) channels.
• To optimize constellations for high spectral efficiency, targeting a forward error correction (FEC) rate of 0.8.
• To investigate the impact of symmetry constraints on constellation performance.

Main Methods:

• Geometric shaping was employed to design 4D constellations with up to 131,072 points (17 bit/4D-sym).
• Mutual Information (MI) and Generalized MI (GMI) were used as optimization metrics for AWGN channels.
• A Monte Carlo-based approach, utilizing stochastic gradient descent and automatic differentiation, was used for performance evaluation and optimization.

Main Results:

• The designed 15-17 bit 4D constellations demonstrate state-of-the-art performance, achieving gaps to AWGN capacity as low as 0.17 dB (MI) and 0.45 dB (GMI) at 17 bit/4D-sym.
• For lower cardinalities, the proposed constellations match or surpass existing optimized designs.
• Symmetry constraints had minimal impact on GMI-optimized constellations above 8 bit/4D-sym but negatively affected MI-optimized constellations.

Conclusions:

• The developed geometric shaping technique yields highly efficient 4D constellations for AWGN channels.
• The optimization procedure is robust and extendable to other channel types.
• These findings advance the design of high-performance constellations for future communication systems.