Polarization-Ring-Switching for Nonlinearity-Tolerant Geometrically Shaped Four-Dimensional Formats Maximizing Generalized Mutual Information

Abstract

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8, 000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of ap- proximately 16% (1, 100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.Index Terms-Achievable information rates, binary labeling, generalized mutual information, mutual information, forward error correction, multidimensional constellations, signal shaping.

First Transmission of a 12D Format Across Three Coupled Spatial Modes of a 3-Core Coupled-Core Fiber at 4 bits/s/Hz

“…Some formats show natural resistance to nonlinear distortions like polarisation-division multiplexed quaternary phase shift keying (PDM-QPSK) being both constant power and on a cartesian grid (suitable for Gray mapping). Among advanced formats geared towards mitigating nonlinear effects, one notes formats resistant to phase distortions [8], shaped using shell mapping [9], 4D using points symmetrically located on two rings [12][13][14], 8D constellations based on selecting points within PDM-QPSK [10] or optimized for GMI [11], 12D [15] and 16D [16], the last two having large minimum distances but limited to low SE. So far, these formats have been implemented as time sequences of 4D symbols or across uncoupled fiber core on a single time slot.…”

11,700 km Transmission at 4.8 bit/4D-sym via Four-dimensional Geometrically-shaped Polarization-Ring-Switching Modulation

“…Multidimensional constant modulus modulation formats have been shown to minimize the non-linear interference noise by minimizing the signal power variations [1,2]. Recently, the four-dimensional 64-ary polarizationring-switching (4D-64PRS) format was introduced in [3], where the 4D coordinates and labeling were jointly optimized. Numerical results in [3] show that 4D-64PRS outperforms other modulation formats with spectral efficiency (SE) of 6 bit/4D-sym, including polarization-multiplexed (PM)-8QAM, 4D-64SP-12QAM [4] and 4D-2A8PSK [2].…”

“…Numerical results in [3] show that 4D-64PRS outperforms other modulation formats with spectral efficiency (SE) of 6 bit/4D-sym, including polarization-multiplexed (PM)-8QAM, 4D-64SP-12QAM [4] and 4D-2A8PSK [2]. Results were presented in both linear and non-linear channel for a bit-interleaved coded modulation (BICM) system [3]. 4D-64PRS was reported to yield over 0.8 dB better sensitivity than PM-8QAM by maximizing generalized mutual information (GMI) [3].…”

“…Results were presented in both linear and non-linear channel for a bit-interleaved coded modulation (BICM) system [3]. 4D-64PRS was reported to yield over 0.8 dB better sensitivity than PM-8QAM by maximizing generalized mutual information (GMI) [3].…”

Eight-Dimensional Polarization-Ring-Switching Modulation Formats

“…MD constant-modulus modulation formats have been proposed [6], [14], [15] to mitigate the nonlinear interference. One example of this is the 4D 64-ary polarization-ring-switching (4D-64PRS) format we recently proposed in [9]. 4D-64PRS was shown to outperform other modulation formats at SE of 6 bit/4D-sym by jointly optimizing the coordinates and labeling.…”