Eight-dimensional trellis coded modulation scheme based on probabilistic-geometric joint shaping in high-speed optical communications

In order to solve the problems of fiber nonlinear effects due to constellation expansion and the reduction of information entropy due to constellation shaping, an 8-dimensional trellis coded 16-quadrature amplitude modulation format with probabilistic-geometric joint shaping (8D-TCM-PS-GS-16QAM) in high-speed optical communications is proposed. The BER performance of 8D-TCM-PS-GS-16QAM signals with unshaped, geometrical shaping only, and probabilistic-geometrical joint shaping (H=14/13/12 bits/symbol) is simulated. At a BER of 3.8e-3, the four shaped signals are able to obtain a gain of 0.36dB, 1.52dB, 2.02dB, and 2.46dB, respectively, compared with the unshaped signal. The BER performance of low-dimensional, i.e., 2D and 4D signals is also simulated. Comparing the gains obtained for 8D-TCM-PS-GS-16QAM (H=14 bits/symbol), 4D-TCM-PS-GS-16QAM (H=6 bits/symbol), and 2D-TCM-PS-GS-16QAM (H=2 bits/symbol) with the unshaped signals in the corresponding dimensions, the gains obtained at 3.8e -3 BER, are 1.52 dB, 2.29 dB, and 4.16 dB, respectively. Constellation shaping causes all three to sacrifice the same total information entropy of 1bits/symbol, but the information entropy sacrificed by the basic 2D constellations of the 8D signal is only 50%, 25% of that of the 4D and 2D signals. Meanwhile, the shaping gain obtained by the 8D signal reaches 66.4% and 36.5% of the 4D and 2D signals, respectively. This scheme enables the whole scheme to flexibly adjust the spectral efficiency (SE). Meanwhile, it increases the degree of freedom of the signal. This scheme can realize high BER performance transmission of high SE signals. It has great potential for future construction in high-capacity and high-speed optical communications.