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