High-dimensional modulation for coherent optical communications systems.

In this paper, we examine the performance of several modulation formats in more than four dimensions for coherent optical communications systems. We compare two high-dimensional modulation design methodologies based on spherical cutting of lattices and block coding of a 'base constellation' of binary phase shift keying (BPSK) on each dimension. The performances of modulation formats generated with these methodologies is analyzed in the asymptotic signal-to-noise ratio regime and for an additive white Gaussian noise (AWGN) channel. We then study the application of both types of high-dimensional modulation formats to standard single-mode fiber (SSMF) transmission systems. For modulation with spectral efficiencies comparable to dual-polarization (DP-) BPSK, polarization-switched quaternary phase shift keying (PS-QPSK) and DP-QPSK, we demonstrate SNR gains of up to 3 dB, 0.9 dB and 1 dB respectively, at a BER of 10(-3).