Subset-Optimized Polarization-Multiplexed PSK for Fiber-Optic Communications

A more power-efficient modulation format than polarization-multiplexed quadrature phase-shift keying (PM-QPSK) can be obtained by optimizing the amplitude ratio between symbols with odd and even parity in the PM-QPSK constellation. The optimal amplitude ratio approaches the golden ratio at high signal-to-noise ratio (SNR), yielding a 0.44 dB increase in asymptotic power efficiency compared to PM-QPSK. Union bound expressions are derived for the bit and symbol error rate of the new format, which together with Monte Carlo simulations give the power efficiency at both low and high SNR. A similar optimization performed on PM-8PSK gains 1.25 dB

Achievable Rates for Four-Dimensional Coded Modulation with a Bit-Wise Receiver

We study achievable rates for four-dimensional (4D) constellations for spectrally efficient optical systems based on a (suboptimal) bit-wise receiver. We show that PM-QPSK outperforms the best 4D constellation designed for uncoded transmission by approximately 1 dB. Numerical results using LDPC codes validate the analysis

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

Rate-adaptive optical transceivers can play an important role in exploiting the available resources in dynamic optical networks, in which different links yield different signal qualities. We study rate-adaptive joint coding and modulation, often called coded modulation (CM), addressing non-dispersion-managed (non-DM) links, exploiting recent advances in channel modeling of these links. We introduce a four-dimensional CM scheme, which shows a better tradeoff between digital signal processing complexity and transparent reach than existing methods. We construct a rate-adaptive CM scheme combining a single low-density parity-check code with a family of three signal constellations and using probabilistic signal shaping. We evaluate the performance of the proposed CM scheme for single-channel transmission through long-haul non-DM fiber-optic systems with electronic chromatic-dispersion compensation. The numerical results demonstrate improvement of spectral efficiency over a wide range of transparent reaches, an improvement over 1 dB compared to existing methods

Multidimensional Optimized Optical Modulation Formats

This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. 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

Power-efficient modulation formats in coherent transmission systems

Coherent optical transmission systems have a four-dimensional (4-D) signal space (two quadratures in two polarizations). These four dimensions can be used to create modulation formats that have a better power efficiency (higher sensitivity) than the conventional binary phase shift keying/quadrature phase shift keying (BPSK/QPSK) signals. Several examples are given, with some emphasis on a 24-level format and an 8-level format, including descriptions of how they can be realized and expressions for their symbol and bit error probabilities. These formats are, respectively, an extension and a subset of the commonly used 16-level dual-polarization QPSK format. Sphere packing simulations in 2, 3, and 4 dimensions, up to 32 levels, are used to verify their optimality. The numerical results, as the number of levels increases, are shown to agree with lattice-theoretical results. Finally, we point out that the use of these constellations will lead to improved fundamental sensitivity limits for optical communication systems, and they may also be relevant as a way of reducing power demands and/or nonlinear influence. \ua9 2009, IEEE. All rights reserved

Four-Dimensional Coded Modulation with Bit-wise Decoders for Future Optical Communications

Coded modulation (CM) is the combination of forward error correction (FEC) and multilevel constellations. Coherent optical communication systems result in a four-dimensional (4D) signal space, which naturally leads to 4D-CM transceivers. A practically attractive design paradigm is to use a bit-wise decoder, where the detection process is (suboptimally) separated into two steps: soft-decision demapping followed by binary decoding. In this paper, bit-wise decoders are studied from an information-theoretic viewpoint. 4D constellations with up to 4096 constellation points are considered. Metrics to predict the post-FEC bit-error rate (BER) of bit-wise decoders are analyzed. The mutual information is shown to fail at predicting the post- FEC BER of bit-wise decoders and the so-called generalized mutual information is shown to be a much more robust metric. For the suboptimal scheme under consideration, it is also shown that constellations that transmit and receive information in each polarization and quadrature independently (e.g., PM-QPSK, PM- 16QAM, and PM-64QAM) outperform the best 4D constellations designed for uncoded transmission. Theoretical gains are as high as 4 dB, which are then validated via numerical simulations of low-density parity check codes

End-to-end optimization of coherent optical communications over the split-step Fourier method guided by the nonlinear Fourier transform theory

Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical models. However, this task becomes extremely challenging for nonlinear dispersive channels such as the optical fiber. End-to-end optimization through autoencoders (AEs) can be applied to define symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings, but so far it has been mainly shown for systems relying on approximate channel models. Here, for the first time, we propose an AE scheme applied to the full optical channel described by the nonlinear Schr\{"o}dinger equation (NLSE). Transmitter and receiver are jointly optimized through the split-step Fourier method (SSFM) which accurately models an optical fiber. In this first numerical analysis, the detection is performed by a neural network (NN), whereas the symbol-to-waveform mapping is aided by the nonlinear Fourier transform (NFT) theory in order to simplify and guide the optimization on the modulation side. This proof-of-concept AE scheme is thus benchmarked against a standard NFT-based system and a threefold increase in achievable distance (from 2000 to 6640 km) is demonstrated

Clustering algorithms for Stokes space modulation format recognition

\u3cp\u3eStokes space modulation format recognition (Stokes MFR) is a blind method enabling digital coherent receivers to infer modulation format information directly from a received polarization-division-multiplexed signal. A crucial part of the Stokes MFR is a clustering algorithm, which largely influences the performance of the detection process, particularly at low signal-to-noise ratios. This paper reports on an extensive study of six different clustering algorithms: k-means, expectation maximization, density-based DBSCAN and OPTICS, spectral clustering and maximum likelihood clustering, used for discriminating between dual polarization: BPSK, QPSK, 8-PSK, 8-QAM, and 16-QAM. We determine essential performance metrics for each clustering algorithm and modulation format under test: minimum required signal-to-noise ratio, detection accuracy and algorithm complexity.\u3c/p\u3

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

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 approximately 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.Comment: 12 pages, 12 figure

Digital Signal Processing of POL-QAM and SP-QAM in Long-Haul Optical Transmission Systems

Coherent detection employing high modulation formats has become one of the most attractive technologies for long-haul transmission systems due to the high power and spectral efficiencies. Appropriate digital signal processing (DSP) is used to equalize and compensate for distortion caused by laser and fiber characteristics and impairments, such as polarization mode dispersion (PMD), polarization rotation, laser phase noise and nonlinear effects. Research on the various DSP algorithms in the coherent optical communication systems is the most promising investigation. In this research, two new modulation formats; polarization QAM modulation (POL-QAM) and set-partitioning QAM (SP-QAM) are investigated due to their high spectral efficiency and novelty. For PMD and polarization rotation equalization, a new modified constant modulus algorithm (CMA) is proposed for POL-QAM. We investigate the bit error rate (BER) performance of the two modulation formats over fiber channel considering PMD and polarization rotation effects. Furthermore, we investigate the BER performance of the two modulation formats over long-haul fiber optic transmission systems. Carrier phase estimation (CPE) algorithms are also investigated, which are used to mitigate phase noise caused by the transmitter