Constellation Shaping in Optical Communication Systems

Exploiting the full-dimensional capacity of coherent optical communication systems is needed to overcome the increasing bandwidth demands of the future Internet. To achieve capacity, both coding and shaping gains are required, and they are, in principle, independent. Therefore it makes sense to study shaping and how it can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping (GS) and probabilistic shaping (PS) in coherent fiber-optic systems. To study GS, instead of considering machine learning approaches or optimization of irregular constellations in two dimensions, we have explored multidimensional lattice-based constellations. These constellations provide a regular structure with a fast and low-complexity encoding and decoding. In simulations, we show the possibility of transmitting and detecting constellation with a size of more than 10^{28} points which can be done without a look-up table to store the constellation points. Moreover, improved performance in terms of bit error rate, symbol error rate, and transmission reach are demonstrated over the linear additive white Gaussian noise as well as the nonlinear fiber channel compared to QAM formats.Furthermore, we investigate the performance of PS in two separate scenarios, i.e., transmitter impairments and transmission over hybrid systems with on-off keying channels. In both cases, we find that while PS-QAM outperforms the uniform QAM in the linear regime, uniform QAM can achieve better performance at the optimum power in the presence of transmitter or channel nonlinearities

Multidimensional Constellation Shaping for Coherent Optical Communication Systems

To overcome the increasing demands for Internet traffic, exploiting the available degrees of freedom in optical communication systems is necessary. In this thesis, we study how constellation shaping can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping and probabilistic shaping in coherent fiber-optic systems.To study geometric shaping, we explore multidimensional lattice-based constellations. These constellations provide a regular structure with fast and low-complexity encoding and decoding. We show the possibility of transmitting and detecting constellations with a size of more than 10^{28} points, which can be done without a look-up table to store the constellation points. Moreover, we experimentally realize our proposed multidimensional modulation formats in long-haul optical communication systems.Finally, we investigate the performance of probabilistically shaped quadrature amplitude modulation and compare it with uniform cross quadrature amplitude modulation in the presence of transmitter impairments, and with uniform quadrature amplitude modulation in links where higher-order modulation formats co-propagate with on-off keying wavelength channels

Low-Complexity Geometric Shaping

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To overcome these challenges, in this paper, we study lattice-based geometrically shaped modulation formats in multidimensional Euclidean space. We describe and evaluate fast and low complexity modulation and demodulation algorithms that make these modulation formats practical, even with extremely high constellation sizes with more than $10^{28}$ points. The uncoded bit error rate performance of these constellations is compared with the conventional QAM formats in the additive white Gaussian noise and nonlinear fiber channels. At a spectral efficiency of 2 bits/sym/polarization, compared with 4-QAM format, transmission reach improvement of more than 38% is shown at the hard-decision forward error correction threshold of $2.26\times 10^{-4}$

Lattice-based geometric shaping

Geometrically shaped multidimensional constellations with more than 1028 points are simulated using fast and low-complexity algorithms without any look-up tables to store the constellation points. At the same symbol error rate, more than 78% and 114% reach improvement are demonstrated compared with 4- and 16-QAM, respectively

THE RELATION BETWEEN SATISFACTION AMONG SPORTS CLUBS’ CUSTOMERS AND COACHES’ PERSONALITY AND WORK ETHICS

In terms of manner of data collection, the present research is considered as a descriptive-correlative study and also in terms of purpose, it is considered as an applied research which is carried out under field methods. The population of this research includes the staff and customers of governmental and private pools of the province of Kurdistan. The number of the staff is equal to 135 individuals and according to the Morgan’s chart, the sample number was determined as 100 individuals. Since this research includes two separate populations, and only the number of the staff of pools is known; the method of synchronization is employed and the same amount of samples is considered for customers as well. For the purpose of data collection, Gregory C. Petty’s (1990) questionnaire of ethics including 23 questions and the factors of interest in work, perseverance, human relations at work environment and collaboration in work was used. The validity of this questionnaire is approved by 15 sports management professors and also its reliability was calculated as 0.81 by the Cronbach’s Alpha method. For evaluation of customer satisfaction, the Huang’s questionnaire including 19 questions and the components of visuals and looks of the club, personnel, facilities and current equipment. Its validity and reliability are respectively calculated as 0.78 and 0.86. In addition, the short form of questionnaire of personality characteristics was used: aimed at evaluation of players’ personality characteristics, the short for of the NEO questionnaire including 60 questions was used. This questionnaire was developed by Caste and McCree in 1982. The first translation of this questionnaire into Persian language was prepared by Kiamehr (2005). This test evaluates 5 major personality characteristics which include Neuroticism (N), extraversion (E), openness of mind towards experiences (O), Agreeableness (A), and conscientiousness (C). The Cronbach’s alpha method has calculated reliability of different aspects of this questionnaire in the range of 0.63 to 0.84.  Article visualizations

Designing Voronoi Constellations to Minimize Bit Error Rate

In a classical 1983 paper, Conway and Sloane presented fast encoding and decoding algorithms for a special case of Voronoi constellations (VCs), for which the shaping lattice is a scaled copy of the coding lattice. Feng generalized their encoding and decoding methods to arbitrary VCs. Less general algorithms were also proposed by Kurkoski and Ferdinand, respectively, for VCs with some constraints on their coding and shaping lattices. In this work, we design VCs with a cubic coding lattice based on Kurkoski\u27s encoding and decoding algorithms. The designed VCs achieve up to 1.03 dB shaping gains with a lower complexity than Conway and Sloane\u27s scaled VCs. To minimize the bit error rate (BER), pseudo-Gray labeling of constellation points is applied. In uncoded systems, the designed VCs reduce the required SNR by up to 1.1 dB at the same BER, compared with the same VCs using Feng\u27s and Ferdinand\u27s algorithms. In coded systems, the designed VCs are able to achieve lower BER than the scaled VCs at the same SNR. In addition, a Gray penalty estimation method for such VCs of very large size is introduced

Low-Complexity Voronoi Shaping for the Gaussian Channel

Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up version of the coding lattice. In this paper, we design low-complexity VCs with a cubic coding lattice of up to 32 dimensions, in which pseudo-Gray labeling is applied to minimize the bit error rate. The designed VCs have considerable shaping gains of up to 1.03 dB and finer choices of spectral efficiencies in practice compared with conventional VCs. A mutual information estimation method and a log-likelihood approximation method based on importance sampling for very large constellations are proposed and applied to the designed VCs. With error-control coding, the proposed VCs can have higher information rates than the conventional scaled VCs because of their inherently good pseudo-Gray labeling feature, with a lower decoding complexity

Power-Efficient Voronoi Constellations for Fiber-Optic Communication Systems

Voronoi constellations (VCs) are considered as an effective geometric shaping method due to their high power efficiencies and low complexity. In this paper, the performance of 16- and 32-dimensional VCs with a variety of spectral efficiencies transmitted in the nonlinear fiber channel are investigated. Both single-channel and wavelength-division multiplexing systems are considered for the transmission of the VCs, as well as different signal processing schemes, including chromatic dispersion compensation and digital backpropagation. Multiple performance metrics including the uncoded bit error rate, mutual information (MI), and generalized mutual information (GMI) of VCs are evaluated. Compared with quadrature amplitude modulation (QAM) formats, the VCs provide 1.0--2.4 dB launch power gains, up to 0.50 bits/symbol/dimension-pair MI gains, up to around 30% potential reach increase at the same MI, and up to 0.30 bits/symbol/dimension-pair GMI gains in a limited launch power range. The observed performance gains over QAM are found higher than in the back-to-back case. Moreover, a general GMI estimation method for very large constellations using importance sampling is proposed for the first time

Phase-coherent lightwave communications with frequency combs

Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. In the future, optical frequency combs may replace multiple lasers used for the different wavelength channels. We demonstrate two novel signal processing schemes that take advantage of the broadband phase coherence of optical frequency combs. This approach allows for a more efficient estimation and compensation of optical phase noise in coherent communication systems, which can significantly simplify the signal processing or increase the transmission performance. With further advances in space division multiplexing and chip-scale frequency comb sources, these findings pave the way for compact energy-efficient optical transceivers.Comment: 17 pages, 9 figure