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Sequence-Selection-Based Constellation Shaping for Nonlinear Channels (2307.13292v3)

Published 25 Jul 2023 in cs.IT, eess.SP, and math.IT

Abstract: Probabilistic shaping is a pragmatic approach to improve the performance of coherent optical fiber communication systems. In the nonlinear regime, the advantages offered by probabilistic shaping might increase thanks to the opportunity to obtain an additional nonlinear shaping gain. Unfortunately, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in scenarios of limited practical interest. In this manuscript we use sequence selection to investigate the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 bit/s/Hz gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols: they must be known to compute the selection metric, but there is no need to shape them. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if these are modified. Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC) and complexity. Overall, the single block and the multi block FEC-independent bit scrambling are the best options, with a gain up to 0.08 bit/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included.

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References (41)
  1. S. Civelli, E. Forestieri, and M. Secondini, “Probabilistic shaping methods for linear and nonlinear channels,” in Proc. Optical Fiber Commun. Conf. (OFC), pp. Th3E–5, Optica Publishing Group, 2023.
  2. S. Civelli, E. Forestieri, and M. Secondini, “Practical implementation of sequence selection for nonlinear probabilistic shaping,” in Proc. Optical Fiber Commun. Conf. (OFC), pp. Th3E–2, Optica Publishing Group, 2023.
  3. C. E. Shannon, “A mathematical theory of communication,” Bell System Tech. J., vol. 27, pp. 379–423/623–656, July/Oct. 1948.
  4. C. E. Shannon, “Communication in the presence of noise,” Proceedings of the IRE, vol. 37, no. 1, pp. 10–21, 1949.
  5. A. R. Calderbank and L. H. Ozarow, “Nonequiprobable signaling on the gaussian channel,” IEEE Trans. Inf. Theory, vol. 36, no. 4, pp. 726–740, 1990.
  6. F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 913–929, 1993.
  7. G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun., vol. 63, no. 12, pp. 4651–4665, 2015.
  8. F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: An experimental demonstration,” J. Lightwave Technol., vol. 34, no. 7, pp. 1599–1609, 2016.
  9. J. Cho and P. J. Winzer, “Probabilistic constellation shaping for optical fiber communications,” J. Lightwave Technol., vol. 37, no. 6, pp. 1590–1607, 2019.
  10. P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory, vol. 62, no. 1, pp. 430–434, 2016.
  11. Y. C. Gültekin, T. Fehenberger, A. Alvarado, and F. M. Willems, “Probabilistic shaping for finite blocklengths: Distribution matching and sphere shaping,” Entropy, vol. 22, no. 5, p. 581, 2020.
  12. T. Yoshida, M. Karlsson, and E. Agrell, “Hierarchical distribution matching for probabilistically shaped coded modulation,” J. Lightwave Technol., vol. 37, no. 6, pp. 1579–1589, 2019.
  13. S. Civelli and M. Secondini, “Hierarchical distribution matching for probabilistic amplitude shaping,” Entropy, vol. 22, no. 9, p. 958, 2020.
  14. M. Secondini and E. Forestieri, “Scope and limitations of the nonlinear Shannon limit,” J. Lightwave Technol., vol. 35, pp. 893–902, Feb. 2017.
  15. O. Geller, R. Dar, M. Feder, and M. Shtaif, “A shaping algorithm for mitigating inter-channel nonlinear phase-noise in nonlinear fiber systems,” J. Lightwave Technol., vol. 34, pp. 3884–3889, Aug. 2016.
  16. T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On probabilistic shaping of quadrature amplitude modulation for the nonlinear fiber channel,” J. Lightwave Technol., vol. 34, pp. 5063–5073, Nov. 2016.
  17. J. Cho, X. Chen, G. Raybon, D. Che, E. Burrows, S. Olsson, and R. Tkach, “Shaping lightwaves in time and frequency for optical fiber communication,” Nature communications, vol. 13, no. 1, pp. 1–11, 2022.
  18. S. Civelli, E. Forestieri, A. Lotsmanov, D. Razdoburdin, and M. Secondini, “A sequence selection bound for the capacity of the nonlinear fiber channel,” in Proc. European Conf. Optical Commun. (ECOC), pp. 1–4, IEEE, 2021.
  19. M. Secondini, S. Civelli, E. Forestieri, and L. Z. Khan, “New lower bounds on the capacity of optical fiber channels via optimized shaping and detection,” J. Lightwave Technol., vol. 40, no. 10, pp. 3197–3209, 2022.
  20. S. Civelli, E. Parente, E. Forestieri, and M. Secondini, “On the nonlinear shaping gain with probabilistic shaping and carrier phase recovery,” J. Lightwave Technol., 2023.
  21. A. Alvarado, T. Fehenberger, B. Chen, and F. M. Willems, “Achievable information rates for fiber optics: Applications and computations,” J. Lightwave Technol., vol. 36, no. 2, pp. 424–439, 2018.
  22. T. Fehenberger, D. S. Millar, T. Koike-Akino, K. Kojima, and K. Parsons, “Multiset-partition distribution matching,” IEEE Trans. Commun., vol. 67, no. 3, pp. 1885–1893, 2018.
  23. T. M. Cover and J. A. Thomas, Elements of Information Theory. Hoboken, NJ: Wiley, 2nd ed., 2006.
  24. Y. Gültekin, W. van Houtum, and F. Willems, “On constellation shaping for short block lengths,” in 2018 Symposium on Information Theory and Signal Processing in the Benelux (SITB 2018), pp. 86–96, University of Twente, 2018.
  25. Y. C. Gültekin, W. J. van Houtum, S. Şerbetli, and F. M. Willems, “Constellation shaping for IEEE 802.11,” in 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), pp. 1–7, IEEE, 2017.
  26. Y. C. Gültekin, F. M. Willems, W. J. van Houtum, and S. Şerbetli, “Approximate enumerative sphere shaping,” in Proc. IEEE Symposium on Information Theory, pp. 676–680, IEEE, 2018.
  27. S. Civelli and M. Secondini, “Hierarchical distribution matching: a versatile tool for probabilistic shaping,” in Proc. Optical Fiber Commun. Conf. (OFC), p. Th1G.4, Optical Society of America, 2020.
  28. A. Amari, S. Goossens, Y. C. Gültekin, O. Vassilieva, I. Kim, T. Ikeuchi, C. M. Okonkwo, F. M. Willems, and A. Alvarado, “Introducing enumerative sphere shaping for optical communication systems with short blocklengths,” J. Lightwave Technol., vol. 37, no. 23, pp. 5926–5936, 2019.
  29. T. Fehenberger, H. Griesser, and J.-P. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Proc. Optical Fiber Commun. Conf. (OFC), pp. Th1I–2, Optical Society of America, 2020.
  30. R. R. Borujeny and F. R. Kschischang, “Why constant-composition codes reduce nonlinear interference noise,” J. Lightwave Technol., 2023.
  31. Y. C. Gültekin, A. Alvarado, O. Vassilieva, I. Kim, P. Palacharla, C. M. Okonkwo, and F. M. Willems, “Mitigating nonlinear interference by limiting energy variations in sphere shaping,” in Proc. Optical Fiber Commun. Conf. (OFC), pp. Th3F–2, Optica Publishing Group, 2022.
  32. Y. C. Gültekin, A. Alvarado, O. Vassilieva, I. Kim, P. Palacharla, C. M. Okonkwo, and F. M. Willems, “Kurtosis-limited sphere shaping for nonlinear interference noise reduction in optical channels,” J. Lightwave Technol., vol. 40, no. 1, pp. 101–112, 2021.
  33. K. Wu, G. Liga, A. Sheikh, F. M. Willems, and A. Alvarado, “Temporal energy analysis of symbol sequences for fiber nonlinear interference modelling via energy dispersion index,” J. Lightwave Technol., vol. 39, no. 18, pp. 5766–5782, 2021.
  34. K. Wu, G. Liga, Y. C. Gültekin, and A. Alvarado, “Exponentially-weighted energy dispersion index for the nonlinear interference analysis of finite-blocklength shaping,” in Proc. European Conf. Optical Commun. (ECOC), IEEE, 2021.
  35. M. T. Askari, L. Lampe, and J. Mitra, “Probabilistic amplitude shaping and nonlinearity tolerance: Analysis and sequence selection method,” J. Lightwave Technol., 2023.
  36. A. D. Jayalath and C. Tellambura, “Reducing the peak-to-average power ratio of orthogonal frequency division multiplexing signal through bit or symbol interleaving,” Electronics Letters, vol. 36, no. 13, pp. 1161–1163, 2000.
  37. K. Wu, G. Liga, A. Sheikh, Y. C. Gültekin, F. M. Willems, and A. Alvarado, “List-encoding CCDM: A nonlinearity-tolerant shaper aided by energy dispersion index,” J. Lightwave Technol., vol. 40, no. 4, pp. 1064–1071, 2022.
  38. M. T. Askari, L. Lampe, and J. Mitra, “Nonlinearity tolerant shaping with sequence selection,” in Proc. European Conf. Optical Commun. (ECOC), IEEE, 2022.
  39. G. Böcherer and R. Mathar, “Operating LDPC codes with zero shaping gap,” in 2011 IEEE Information Theory Workshop, pp. 330–334, IEEE, 2011.
  40. S. Civelli, E. Forestieri, and M. Secondini, “Interplay of probabilistic shaping and carrier phase recovery for nonlinearity mitigation,” in Proc. European Conf. Optical Commun. (ECOC), IEEE, 2020.
  41. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for m𝑚mitalic_m-qam constellations,” J. Lightwave Technol., vol. 27, no. 8, pp. 989–999, 2009.
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