Condensation methodologies for two-dimensional non-uniform constellations

Two-dimensional non-uniform constellations (2D-NUC) have been adopted for the most recent terrestrial broadcasting system called ATSC 3.0. They are known for being more efficient than one-dimensional non uniform constellations (1D-NUC) and uniform constellations (UC). They can be used in any communication system with the bit-interleaved coded modulation (BICM) structure. However, one of the main challenges of such constellations is their design for optimal behaviour in a wide range of cases and the design of a demapper that exploits their advantages. This paper presents two different condensation methodologies to design efficient 2D-NUCs simple in design and with limited demapping complexity. The proposal provides a complexity reduction of the design and demapping processes in the range from 13% to 94%. The demapping stage provides performance losses less than 0.1 dB if compared with standard 2D-NUC demapping.