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In this work, geometric shaping (GS) and probabilistic shaping (PS) for theAWGN channel is reviewed. Both approaches are investigated in terms ofsymbol-metric decoding (SMD) and bit-metric decoding (BMD). For GS, anoptimization algorithm based on differential evolution is formulated.Achievable rate analysis reveals that GS suffers from a 0.4 dB performancedegradation compared to PS when BMD is used. Forward-error correctionsimulations of the ATSC 3.0 modulation and coding formats (modcods) confirm thetheoretical findings. In particular, PS enables seamless rate adaptation withone single modcod and it outperforms ATSC 3.0 GS modcods by more than 0.5 dBfor spectral efficiencies larger than 3.2 bits per channel use.

Comparison of Geometric and Probabilistic Shaping with Application to ATSC 3.0