Recently, new signal constellations specifically designed and optimized in 4D space have been proposed, among which polarization-switched QPSK (PS-QPSK), consisting of a 8-point constellation at the vertices of a 4D polychoron called hexadecachoron. A well-known and successful format exploiting such 4D space is Polarization-multiplexed QPSK (PM-QPSK). It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation.Ĭoherent-detection (CoD) permits to fully exploit the four-dimensional (4D) signal space consisting of the in-phase and quadrature components of the two fiber polarizations. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. Then, the chapter discusses optimization of modulation formats in coded systems. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. All these results indicate that the 4D-2A8PSK family show great promise of excellent linear and nonlinear performances in the spectral efficiency between 3.5 and 8 bits/4D symbol. Furthermore, an overview of an eight-dimensional 2A8PSK-based modulation format based on a Grassmann code is also given. Their application to time-domain hybrid modulation for 4–8 bits/4D symbol is also reviewed. We also review DSP algorithms and experimental results. Nonlinear transmission simulations indicate that these modulation formats outperform the conventional formats at each spectral efficiency. Since these modula- tion formats share the same constellation and use different parity bit expressions only, digital signal processing can accommodate those multiple modulation formats with minimum additional complexity. These coded modulation formats fill the gap of spectral efficiency between DP-QPSK and DP-16QAM, showing superb performance both in linear and nonlinear regimes. We recently proposed family of 4D modulation formats based on 2-ary amplitude 8-ary phase-shift keying (2A8PSK), covering the spectral efficiency of 5, 6, and 7 bits/4D symbol, which will be explained in detail in this chapter. We overview several modulation formats intrinsically tolerant to fiber nonlinearity. Simulation results show that the proposed NLI model-based 4D modulation format could increase the effective SNRs by 0.25 dB with respect to the AWGN channel-optimal 4D modulation format.įiber nonlinearity is the main factor limiting the transmission distance of coherent optical communications. Lastly,with the help of a recently introduced nonlinear interference (NLI) model, an optimization for designing nonlinear-tolerant 4D modulation formats is introduced for a single-span optical fiber system. Reach increases of up to 25% for a multi-span optical fiber transmission system are reported. In the second part, we extend the recently proposed four-dimensional (4D) modulation format family based on the constraint of orthant-symmetry to high spectrum efficiencies up to 10 bit/4D-sym by maximizing generalized mutual information for AWGN channel. Practical limitations and challenges are also discussed together with efficient solutions. It is shown that large gains can be obtained by exploiting correlation in the dimensions or/and by increasing the cardinality of the modulation format. In the first part of this paper, existing MD geometrically-shaped modulations for fiber optical communications are reviewed. Shaping modulation formats in multi-dimensional (MD) space is an effective approach to harvest spectral efficiency gains in both the additive white Gaussian noise (AWGN) channel and the optical fiber channel.
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