Comparison of Geometric and Probabilistic Shaping with Application to   ATSC 3.0
  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. 
Fabian Steiner, Georg B\"ocherer
cs.IT math.IT