Geometrically Shaped Four-Dimensional Modulation Formats for 5–7 Bits/Symbol Designed by Autoencoder

Abstract

We design geometrically shaped four-dimensional (4D) modulation formats for 5–7 bits/4D symbol with an autoencoder, which is one of the deep learning applications, using pre-training with 4D formats based on 2-ary amplitude 8-ary phase-shift keying. The numerical evaluation shows that the obtained 4D modulation formats have 0.5-0.7dB signal-to-noise sensitivity gains in terms of normalized generalized mutual information (NGMI) as well as bit error ratio (BER) performances. Furthermore, we show the NGMI and BER performances of these 4D modulation formats are almost equivalent to those of probabilistic amplitude shaping with enumerative sphere shaping with a block length of 20.