A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency

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Span loss budget for 50-span transmission link with a target BER of 10^-3 (a) with 95% inline dispersion compensation per span, and (b) without inline dispersion compensation.

Although 4-dimensional (4D) modulation formats have been known to the optical communications community since the early days of coherent detection [1], the recent work of Agrell and Karlsson [2,3], has led to a great deal of interest in optimized constellations in 4D. These modulation formats can achieve substantial gains compared with conventional formats such as dual-polarization quaternary phase-shift keying (DP-QPSK) and 16-ary quadrature amplitude modulation (DP-16QAM). For example, polarization-switched QPSK (PS-QPSK) [4], and set-partitioned 128-ary QAM (SP-128QAM) [5], achieve 1.76 dB and 2.43 dB gains in asymptotic power efficiency, respectively. Experimental results have demonstrated gains of up to 1.5 dB in the forward-error correction (FEC) limit regimes [6, 7]. While higher-dimensional modulations have been investigated for many years [8,9], their application to optical communications has been limited to 4D case.

In this paper, we investigate the performance of a 24D format based on mapping the codewords of the extended Golay code [10], onto a 24D hypercube, achieving a spectral efficiency of 1 b/s/Hz/pol. We refer to this format as 12-bit 24D Golay coded hypercube (12b-24D-GCHC). Tolerance to additive white Gaussian noise (AWGN) is found to be better than dual-polarization binary PSK (DP-BPSK) by 3 dB at a BER of 10^ -3, and 1.9 dB at a BER of 10^ -2. Transmission performance is simulated over a link of 50 spans of standard single mode fiber (SSMF) with erbium doped fiber amplification (EDFA) both with and without inline optical dispersion compensation, and 12b-24D-GCHC is compared to DP-BPSK and DP-QPSK. We find an increase in maximum tolerable span loss of at least 4 dB compared to DP-BPSK and 8 dB compared to DP-QPSK.