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Journal ArticleDOI

Capacity Limits of Optical Fiber Networks

25 Feb 2010-Journal of Lightwave Technology (IEEE)-Vol. 28, Iss: 4, pp 662-701
TL;DR: In this article, the capacity limit of fiber-optic communication systems (or fiber channels?) is estimated based on information theory and the relationship between the commonly used signal to noise ratio and the optical signal-to-noise ratio is discussed.
Abstract: We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors review recent progress in non-silicon CMOS-compatible platforms for nonlinear optics, with a focus on Si3N4 and Hydex®.
Abstract: Nonlinear photonic chips can generate and process signals all-optically with far superior performance to that possible electronically — particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunication wavelengths poses a fundamental limitation. We review recent progress in non-silicon CMOS-compatible platforms for nonlinear optics, with a focus on Si3N4 and Hydex®. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement. We highlight their potential future impact as well as the challenges to achieving practical solutions for many key applications. This article reviews recent progress in the use of silicon nitride and Hydex as non-silicon-based CMOS-compatible platforms for nonlinear optics. New capabilities such as on-chip optical frequency comb generation, ultrafast optical pulse generation and measurement using these materials, and their potential future impact and challenges are covered.

1,218 citations

Journal ArticleDOI
TL;DR: In this article, simultaneous transmission of six spatial and polarization modes, each carrying 40 Gb/s quadrature-phase-shift-keyed channels over 96 km of a low-differential group delay few-mode fiber, is reported.
Abstract: We report simultaneous transmission of six spatial and polarization modes, each carrying 40 Gb/s quadrature-phase-shift-keyed channels over 96 km of a low-differential group delay few-mode fiber. The channels are successfully recovered by offline DSP based on coherent detection and multiple-input multiple-output processing. A penalty of ;28 dB.

901 citations


Cites background from "Capacity Limits of Optical Fiber Ne..."

  • ...A FTER growing for over two decades by about three orders of magnitude, the capacity of single-mode fibers (SMFs) is rapidly approaching the capacity limits imposed by the combination of Shannon’s information theory and nonlinear fiber effects [1]....

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Journal ArticleDOI
TL;DR: This paper tries to gather the recent results regarding the Gaussian-noise model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.
Abstract: Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.

618 citations


Cites background or methods or result from "Capacity Limits of Optical Fiber Ne..."

  • ...However, all of the disturbance due to XCI and MCI retains its memory, making the results of [70] ‘lower bound estimates of the actual...

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  • ...[70] single-channel BP was applied to the channel under test....

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  • ...As pointed out in [70], a lower-bound to the capacity of an optical channel can be obtained by estimating the mutual information I(X,Y ) between the Tx-side input alphabet X and the Rx-side output alphabet Y , assuming a memoryless model for the channel....

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  • ...The reasons and proof why this is a lower bound can be found in [70], Section III-F....

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  • ...Only in one case we will assume single-channel BP (namely, for a Gaussian constellation at the Nyquist limit) to show that our results match those of [70]....

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Journal ArticleDOI
TL;DR: This work shows that systematic adjustment of pump conditions for low phase noise enables coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the comb and offers an attractive solution towards chip-scale terabit/s transceivers.
Abstract: Optical frequency combs have the potential to revolutionize terabit communications1. Generation of Kerr combs in nonlinear microresonators2 represents a particularly promising option3 enabling line spacings of tens of GHz. However, such combs may exhibit strong phase noise4-6, which has made high-speed data transmission impossible up to now. Here we demonstrate that systematic adjustment of pump conditions for low phase noise4,7-9 enables coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the comb. In a first experiment, we encode a data stream of 392 Gbit/s on a Kerr comb using quadrature phase shift keying (QPSK) and 16-state quadrature amplitude modulation (16QAM). A second experiment demonstrates feedback-stabilization of the comb and transmission of a 1.44 Tbit/s data stream over up to 300 km. The results show that Kerr combs meet the highly demanding requirements of coherent communications and thus offer an attractive solution towards chip-scale terabit/s transceivers.

606 citations


Cites background from "Capacity Limits of Optical Fiber Ne..."

  • ...Assuming that the demonstrated spectral efficiency of 6 bit/s/Hz can be maintained over the entire bandwidth of the Kerr comb, we envision chip-scale transmitters providing aggregate data rates beyond 100 Tbit/s, only limited by nonlinear effects in the single-mode silica fibres used for transmission [37]....

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Journal ArticleDOI
TL;DR: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit, and it is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16- QAM and regular 64-ZAM signals.
Abstract: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit. The proposed system is based on probabilistically shaped 64-QAM modulation formats. Adjustable shaping is combined with a fixed-QAM modulation and a fixed forward-error correction code to realize a system with adjustable net data rate that can operate over a large reach range. At the transmitter, an adjustable distribution matcher performs the shaping. At the receiver, an inverse distribution matcher is used. Probabilistic shaping is implemented into a coherent optical transmission system for 64-QAM at 32 Gbaud to realize adjustable operation modes for net data rates ranging from 200 to 300 Gb/s. It is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16-QAM and regular 64-QAM signals by more than 40% in the transmission reach.

564 citations


Cites background from "Capacity Limits of Optical Fiber Ne..."

  • ...In particular, [19] estimates lower bounds on the capacity, while [20] derives an upper...

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References
More filters
Journal ArticleDOI
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.

65,425 citations

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25,017 citations

Book
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.

16,062 citations

Book
Govind P. Agrawal1
01 Jan 1989
TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
Abstract: Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2]. Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4]. By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5]. This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics.

15,770 citations

Book
01 Jan 2002
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

12,407 citations