A Shaping Algorithm for Mitigating Inter-Channel Nonlinear Phase-Noise in Nonlinear Fiber Systems

We propose a practical shaping algorithm for mitigating the effect of nonlinear phase-noise in fiber-optic transmission. The proposed scheme is most beneficial in single-span fiber communications systems of the kind considered for inter-data-center communications. In such systems the correlation time of the nonlinear phase-noise is too short to allow the mitigation of nonlinear phase-noise by means of adaptive phase-recovery or equalization, but long enough for a shaping approach to be effective. We rely on the implementation of the shell mapping method, optimized so as to provide the largest sum of linear and nonlinear shaping gains.

[1]  I. Djordjevic Spatial-Domain-Based Hybrid Multidimensional Coded-Modulation Schemes Enabling Multi-Tb/s Optical Transport* , 2012, Journal of Lightwave Technology.

[2]  Frank R. Kschischang,et al.  Optical Nonlinear Phase Noise Compensation for $9\times 32$ -Gbaud PolDM-16 QAM Transmission Using a Code-Aided Expectation-Maximization Algorithm , 2015, Journal of Lightwave Technology.

[3]  P. Kabal,et al.  Shaping Multidimensional Signal Spaces-Part I : Optimum Shaping , Shell Mapping , 1998 .

[4]  M. Feder,et al.  Accumulation of nonlinear interference noise in fiber-optic systems. , 2013, Optics express.

[5]  M. Feder,et al.  Pulse Collision Picture of Inter-Channel Nonlinear Interference in Fiber-Optic Communications , 2014, Journal of Lightwave Technology.

[6]  I. Djordjevic Spatial-Domain-Based Hybrid Multidimensional Coded-Modulation Schemes Enabling Multi-Tb/s Optical Transport , 2012, Journal of Lightwave Technology.

[7]  B. Zhu,et al.  Coded PDM-OFDM Transmission With Shaped 256-Iterative-Polar-Modulation Achieving 11.15-b/s/Hz Intrachannel Spectral Efficiency and 800-km Reach , 2013, Journal of Lightwave Technology.

[8]  Xiaojun Liang,et al.  Analytical modeling of XPM in dispersion-managed coherent fiber-optic systems. , 2014, Optics express.

[9]  Frank R. Kschischang,et al.  A Pragmatic Coded Modulation Scheme for High-Spectral-Efficiency Fiber-Optic Communications , 2012, Journal of Lightwave Technology.

[10]  Lars P. B. Christensen,et al.  Constellation Shaping for Fiber-Optic Channels With QAM and High Spectral Efficiency , 2014, IEEE Photonics Technology Letters.

[11]  M. Feder,et al.  New bounds on the capacity of the nonlinear fiber-optic channel. , 2014, Optics letters.

[12]  Amir K. Khandani,et al.  Shaping multidimensional signal spaces - I: Optimum shaping, shell mapping , 1993, IEEE Trans. Inf. Theory.

[13]  Ronen Dar,et al.  Properties of nonlinear noise in long, dispersion-uncompensated fiber links , 2013, Optics express.

[14]  P. Winzer,et al.  Capacity Limits of Optical Fiber Networks , 2010, Journal of Lightwave Technology.

[15]  Ronen Dar,et al.  Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and Mitigation , 2015, Journal of Lightwave Technology.

[16]  Steven A. Tretter,et al.  On optimal shaping of multidimensional constellations , 1994, IEEE Trans. Inf. Theory.

[17]  Luca Barletta,et al.  Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems , 2015, Journal of Lightwave Technology.

[18]  Robert F. H. Fischer,et al.  Multilevel codes: Theoretical concepts and practical design rules , 1999, IEEE Trans. Inf. Theory.

[19]  Georg Böcherer,et al.  LDPC coded modulation with probabilistic shaping for optical fiber systems , 2015, 2015 Optical Fiber Communications Conference and Exhibition (OFC).

[20]  Marco Secondini,et al.  On XPM Mitigation in WDM Fiber-Optic Systems , 2014, IEEE Photonics Technology Letters.

[21]  Patrick Schulte,et al.  Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration , 2016, Journal of Lightwave Technology.

[22]  H. Kogelnik,et al.  PMD fundamentals: polarization mode dispersion in optical fibers. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[23]  G. David Forney,et al.  Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations , 1989, IEEE J. Sel. Areas Commun..

[24]  G. David Forney,et al.  Modulation and Coding for Linear Gaussian Channels , 1998, IEEE Trans. Inf. Theory.

[25]  Ronen Dar,et al.  On shaping gain in the nonlinear fiber-optic channel , 2014, 2014 IEEE International Symposium on Information Theory.

[26]  Joseph M. Kahn,et al.  Rate-Adaptive Coded Modulation for Fiber-Optic Communications , 2014, Journal of Lightwave Technology.

[27]  Robert F. H. Fischer,et al.  Precoding and Signal Shaping for Digital Transmission , 2002 .

[28]  Ting Wang,et al.  Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission , 2010, 2010 Conference on Optical Fiber Communication (OFC/NFOEC), collocated National Fiber Optic Engineers Conference.

[29]  Amir K. Khandani,et al.  Shaping multidimensional signal spaces - II: Shell-addressed constellations , 1993, IEEE Trans. Inf. Theory.

[30]  R. Essiambre,et al.  Nonlinear Shannon Limit in Pseudolinear Coherent Systems , 2012, Journal of Lightwave Technology.

[31]  Frank R. Kschischang,et al.  Optimal shaping properties of the truncated polydisc , 1994, IEEE Trans. Inf. Theory.