Low-Complexity Geometrical Shaping for 4D Modulation Formats via Amplitude Coding

Signal shaping is vital to approach Shannon's capacity, yet it is challenging to implement at very high speeds. For example, probabilistic shaping often requires arithmetic coding to realize the target distribution. Geometric shaping requires look-up tables to store the constellation points. In this letter, we propose a four-dimensional amplitude coding (4D-AC) geometrical shaper architecture. The proposed architecture can generate in real time geometrically shaped 4D formats via simple logic circuit operations and two conventional quadrature amplitude modulation (QAM) modulators. This letter describes the 4D-AC used in generating approximated versions of two recently proposed 4D orthant symmetric modulation formats with spectral efficiencies of 6 bit/4D-sym and 7 bit/4D-sym, respectively. Numerical results show losses below 0.05 dB when compared against the baseline formats.

Automated summary

Signal shaping is crucial in approaching Shannon's capacity but challenging at very high speeds. This letter proposes a 4D amplitude coding (4D-AC) geometric shaper architecture that can generate geometrically shaped 4D formats in real time through simple logic circuit operations. Numerical results show low losses compared to baseline formats.