Abstract

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that an accurate metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats and FEC overheads, in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the thresholds from optical transmission measurements is also given.

© 2016 CCBY

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Schmalen, A. Alvarado, and R. Rios-Müller, “Predicting the performance of nonbinary forward error correction in optical transmission experiments,” in Proc. Opt. Fiber Commun. Conf., 2016, paper M2A.2.
  2. S. Beppu, K. Kasai, M. Yoshida, and M. Nakazawa, “2048 QAM (66 Gbit/s) single-carrier coherent optical transmission over 150 km with a potential SE of 15.3 bit/s/Hz,” Opt. Express, vol. 23, no. 4, pp. 4960–4969, 2015.
  3. D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.
  4. A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.
  5. A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.
  6. A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.
  7. L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design. Chichester, UK: Wiley, 2015.
  8. H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.
  9. A. Alvarado and E. Agrell, “Four-dimensional coded modulation with bit-wise decoders for future optical communications,” J. Lightw. Technol., vol. 33, no. 10, pp. 1993–2003, 2015.
  10. I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224–2226, 2005.
  11. L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.
  12. U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.
  13. A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.
  14. G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106–1109, 2012.
  15. M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.
  16. M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.
  17. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423 and 623–656, , 1948.
  18. A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.
  19. K. Brueninghauset al., “Link performance models for system level simulations of broadband radio access systems,” in Proc. IEEE Int. Symp. Personal, Indoor Mobile Commun., Berlin, Germany, 2006, pp. 2306–2311.
  20. L. Wan, S. Tsai, and M. Almgren, “A fading-insensitive performance metric for a unified link quality model,” in Proc. IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, USA, 2006, pp. 2110–2114.
  21. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.
  22. T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.
  23. T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.
  24. T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.
  25. 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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.
  26. 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.
  27. T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.
  28. E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .
  29. W. Ryan and S. Lin, Channel Codes: Classical and Modern. Cambridge, U.K.: Cambridge Univ. Press, 2009.
  30. N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.
  31. P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightw. Technol., vol. 30, no. 24, pp. 3857–3879, 2012.
  32. M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.
  33. I. Sason and B. Shuval, “On universal LDPC code ensembles over memoryless symmetric channels,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5182–5202, 2011.
  34. A. Sanaei, M. Ramezani, and M. Ardakani, “On the design of universal LDPC codes,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 802–806.
  35. L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.
  36. S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.
  37. E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, 2009.
  38. S. Verdú and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1147–1157, 1994.
  39. E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.
  40. G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689
  41. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.
  42. A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.
  43. W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 3rd ed. Pacific Grove, CA, USA: Brooks/Cole, 1994.
  44. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY, USA: Wiley, 2006.
  45. M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.
  46. T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.
  47. B. W. Silverman, Density Estimation for Statistics and Data Analysis. CRC Press, 1986, vol. 26.
  48. D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.
  49. T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.
  50. M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.
  51. J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.
  52. X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997.
  53. S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.
  54. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.
  55. H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.
  56. H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.
  57. H. Bülow and E. Masalkina, “Coded modulation in optical communications,” in Proc. Opt. Fiber Commun. Conf., Los Angeles, CA, USA, 2011, paper OThO1.
  58. L. Schmalen, “Energy efficient FEC for optical transmission systems,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M3A.1.
  59. L. Schmalen, S. ten Brink, and A. Leven, “Spatially-coupled LDPC protograph codes for universal phase slip-tolerant differential decoding,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2015, paper Th3E.6.
  60. L. Schmalen, S. ten Brink, and A. Leven, “Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, Eds., Hoboken, NJ, USA: Wiley, 2016, pp. 65–122.
  61. L. Schmalen and R. Dischler, “Experimental evaluation of coded modulation for a coherent PDM system with high spectral efficiency,” in Proc. Opt. Fiber Commun. Conf., 2012, paper OW1H.1.
  62. L. Schmalen and S. ten Brink, “Combining spatially coupled LDPC codes with modulation and detection,” in Proc. Int. ITG Conf. Syst., Commun. Coding, Munich, Germany, 2013.
  63. R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.
  64. R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.
  65. L. Geller and D. Burshtein, “Bounds on the belief propagation threshold of non-binary LDPC codes,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2639–2657, 2016.
  66. L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.
  67. N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

2016 (6)

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .

L. Geller and D. Burshtein, “Bounds on the belief propagation threshold of non-binary LDPC codes,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2639–2657, 2016.

2015 (7)

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

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.

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

S. Beppu, K. Kasai, M. Yoshida, and M. Nakazawa, “2048 QAM (66 Gbit/s) single-carrier coherent optical transmission over 150 km with a potential SE of 15.3 bit/s/Hz,” Opt. Express, vol. 23, no. 4, pp. 4960–4969, 2015.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

A. Alvarado and E. Agrell, “Four-dimensional coded modulation with bit-wise decoders for future optical communications,” J. Lightw. Technol., vol. 33, no. 10, pp. 1993–2003, 2015.

2014 (4)

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

2013 (3)

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.

S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

2012 (3)

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightw. Technol., vol. 30, no. 24, pp. 3857–3879, 2012.

G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106–1109, 2012.

2011 (2)

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

I. Sason and B. Shuval, “On universal LDPC code ensembles over memoryless symmetric channels,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5182–5202, 2011.

2010 (1)

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

2009 (3)

E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, 2009.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

2008 (1)

A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.

2007 (1)

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

2006 (2)

M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

2005 (2)

J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224–2226, 2005.

2000 (1)

A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.

1999 (1)

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.

1998 (1)

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.

1997 (1)

X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997.

1994 (2)

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

S. Verdú and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1147–1157, 1994.

1948 (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423 and 623–656, , 1948.

Abay, Ü.

H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.

Agrell, E.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

A. Alvarado and E. Agrell, “Four-dimensional coded modulation with bit-wise decoders for future optical communications,” J. Lightw. Technol., vol. 33, no. 10, pp. 1993–2003, 2015.

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689

Almgren, M.

L. Wan, S. Tsai, and M. Almgren, “A fading-insensitive performance metric for a unified link quality model,” in Proc. IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, USA, 2006, pp. 2110–2114.

Alvarado, A.

E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

A. Alvarado and E. Agrell, “Four-dimensional coded modulation with bit-wise decoders for future optical communications,” J. Lightw. Technol., vol. 33, no. 10, pp. 1993–2003, 2015.

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design. Chichester, UK: Wiley, 2015.

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689

L. Schmalen, A. Alvarado, and R. Rios-Müller, “Predicting the performance of nonbinary forward error correction in optical transmission experiments,” in Proc. Opt. Fiber Commun. Conf., 2016, paper M2A.2.

Andrekson, P. A.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

Ardakani, M.

A. Sanaei, M. Ramezani, and M. Ardakani, “On the design of universal LDPC codes,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 802–806.

Aref, V.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Arikan, E.

E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, 2009.

Arnold, D. M.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

Awais, M.

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

Batshon, H. B.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

Bayvel, P.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689

Beck, N.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

Beermann, M.

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

Beppu, S.

Beygi, L.

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

Bisplinghoff, A.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

Böcherer, G.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

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.

Brink, S. ten

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.

L. Schmalen and S. ten Brink, “Combining spatially coupled LDPC codes with modulation and detection,” in Proc. Int. ITG Conf. Syst., Commun. Coding, Munich, Germany, 2013.

L. Schmalen, S. ten Brink, and A. Leven, “Spatially-coupled LDPC protograph codes for universal phase slip-tolerant differential decoding,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2015, paper Th3E.6.

L. Schmalen, S. ten Brink, and A. Leven, “Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, Eds., Hoboken, NJ, USA: Wiley, 2016, pp. 65–122.

Brueninghaus, K.

K. Brueninghauset al., “Link performance models for system level simulations of broadband radio access systems,” in Proc. IEEE Int. Symp. Personal, Indoor Mobile Commun., Berlin, Germany, 2006, pp. 2306–2311.

Buchali, F.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

Bülow, H.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.

H. Bülow and E. Masalkina, “Coded modulation in optical communications,” in Proc. Opt. Fiber Commun. Conf., Los Angeles, CA, USA, 2011, paper OThO1.

Burshtein, D.

L. Geller and D. Burshtein, “Bounds on the belief propagation threshold of non-binary LDPC codes,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2639–2657, 2016.

Caire, G.

A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.

Chang, D.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

Charlet, G.

R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.

R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.

Cheney, W.

W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 3rd ed. Pacific Grove, CA, USA: Brooks/Cole, 1994.

Cho, J.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Christensen, L.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY, USA: Wiley, 2006.

Cvijetic, M.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

Danninger, M.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

Dischler, R.

L. Schmalen and R. Dischler, “Experimental evaluation of coded modulation for a coherent PDM system with high spectral efficiency,” in Proc. Opt. Fiber Commun. Conf., 2012, paper OW1H.1.

Djordjevic, I. B.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224–2226, 2005.

Durisi, G.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

Ene, M.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

Eriksson, T. A.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

Essiambre, R.-J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Fàbregas, A. Guillén i

A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.

Fehenberger, T.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

Feldman, J.

J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.

Ferrari, G.

M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.

Fischer, R. F. H.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.

Forchhammer, S.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

Forestieri, E.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.

Foschini, G. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Franceschini, M.

M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.

Ganti, A.

A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.

Geller, L.

L. Geller and D. Burshtein, “Bounds on the belief propagation threshold of non-binary LDPC codes,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2639–2657, 2016.

Goebel, B.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Han, T. S.

S. Verdú and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1147–1157, 1994.

Hanik, N.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

Huang, M.-F.

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

Huber, J. B.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.

H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.

Idler, W.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

Ip, E.

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

Johannisson, P.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

Kahn, J. M.

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

Kaplan, G.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

Karger, D. R.

J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.

Karlsson, M.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

Kasai, K.

Kavcic, A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

Kincaid, D.

W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 3rd ed. Pacific Grove, CA, USA: Brooks/Cole, 1994.

Klekamp, A.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

Koike-Akino, T.

T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.

Kojima, K.

T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.

Kramer, G.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Kschischang, F. R.

E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .

Kudekar, S.

S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.

Kupfer, T.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

Lapidoth, A.

A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

Larsen, K.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

Lavery, D.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

Leven, A.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

L. Schmalen, S. ten Brink, and A. Leven, “Spatially-coupled LDPC protograph codes for universal phase slip-tolerant differential decoding,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2015, paper Th3E.6.

L. Schmalen, S. ten Brink, and A. Leven, “Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, Eds., Hoboken, NJ, USA: Wiley, 2016, pp. 65–122.

Li, M.-J.

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

Li, X.

X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997.

Liga, G.

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689

Lin, S.

W. Ryan and S. Lin, Channel Codes: Classical and Modern. Cambridge, U.K.: Cambridge Univ. Press, 2009.

Loeliger, H.-A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

Lu, X.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

Maher, R.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

Martina, M.

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

Martinez, A.

A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.

Masalkina, E.

H. Bülow and E. Masalkina, “Coded modulation in optical communications,” in Proc. Opt. Fiber Commun. Conf., Los Angeles, CA, USA, 2011, paper OThO1.

Masera, G.

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

Merhav, N.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

Millar, D. S.

T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.

Montorsi, G.

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106–1109, 2012.

Monzó, E.

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

Nakazawa, M.

Parsons, K.

T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.

Poggiolini, P.

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightw. Technol., vol. 30, no. 24, pp. 3857–3879, 2012.

Prati, G.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.

Qian, D.

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

Raheli, R.

M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.

Ramezani, M.

A. Sanaei, M. Ramezani, and M. Ardakani, “On the design of universal LDPC codes,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 802–806.

Renaudier, J.

R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.

R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.

Richardson, T.

S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.

T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.

Rios-Müller, R.

R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.

R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.

L. Schmalen, A. Alvarado, and R. Rios-Müller, “Predicting the performance of nonbinary forward error correction in optical transmission experiments,” in Proc. Opt. Fiber Commun. Conf., 2016, paper M2A.2.

Ritcey, J. A.

X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997.

Rösener, D.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Ryan, W.

W. Ryan and S. Lin, Channel Codes: Classical and Modern. Cambridge, U.K.: Cambridge Univ. Press, 2009.

Sanaei, A.

A. Sanaei, M. Ramezani, and M. Ardakani, “On the design of universal LDPC codes,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 802–806.

Sason, I.

I. Sason and B. Shuval, “On universal LDPC code ensembles over memoryless symmetric channels,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5182–5202, 2011.

Schenk, A.

H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.

Schmalen, L.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

L. Schmalen, “Energy efficient FEC for optical transmission systems,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M3A.1.

L. Schmalen, A. Alvarado, and R. Rios-Müller, “Predicting the performance of nonbinary forward error correction in optical transmission experiments,” in Proc. Opt. Fiber Commun. Conf., 2016, paper M2A.2.

L. Schmalen, S. ten Brink, and A. Leven, “Spatially-coupled LDPC protograph codes for universal phase slip-tolerant differential decoding,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2015, paper Th3E.6.

L. Schmalen, S. ten Brink, and A. Leven, “Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, Eds., Hoboken, NJ, USA: Wiley, 2016, pp. 65–122.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.

L. Schmalen and R. Dischler, “Experimental evaluation of coded modulation for a coherent PDM system with high spectral efficiency,” in Proc. Opt. Fiber Commun. Conf., 2012, paper OW1H.1.

L. Schmalen and S. ten Brink, “Combining spatially coupled LDPC codes with modulation and detection,” in Proc. Int. ITG Conf. Syst., Commun. Coding, Munich, Germany, 2013.

Schulte, P.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

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.

Secondini, M.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.

Shamai (Shitz), S.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423 and 623–656, , 1948.

Shuval, B.

I. Sason and B. Shuval, “On universal LDPC code ensembles over memoryless symmetric channels,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5182–5202, 2011.

Silverman, B. W.

B. W. Silverman, Density Estimation for Statistics and Data Analysis. CRC Press, 1986, vol. 26.

Speidel, J.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.

Steiner, F.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

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.

Stojanovic, N.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

Suikat, D.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Szczecinski, L.

L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design. Chichester, UK: Wiley, 2015.

Telatar, I. E.

A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY, USA: Wiley, 2006.

Tran, P.

R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.

Tsai, S.

L. Wan, S. Tsai, and M. Almgren, “A fading-insensitive performance metric for a unified link quality model,” in Proc. IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, USA, 2006, pp. 2110–2114.

Urbanke, R.

S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.

T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.

Vacondio, F.

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

Vary, P.

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

Vasic, B.

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224–2226, 2005.

Verdú, S.

S. Verdú and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1147–1157, 1994.

Vontobel, P. O.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

Wachsmann, U.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.

Wainwright, M. J.

J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.

Wan, L.

L. Wan, S. Tsai, and M. Almgren, “A fading-insensitive performance metric for a unified link quality model,” in Proc. IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, USA, 2006, pp. 2110–2114.

Wang, T.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

Winzer, P. J.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

Xiao, Z.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

Xu, L.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

Yan, R.-H.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.

Yankov, M.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

Yoshida, M.

Yu, F.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

Zeng, W.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

Zhao, Y.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

Zibar, D.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423 and 623–656, , 1948.

Found. Trends Commun. Inf. Theory (1)

A. Guillén i Fàbregas, A. Martinez, and G. Caire, “Bit-interleaved coded modulation,” Found. Trends Commun. Inf. Theory, vol. 5, no. 1–2, pp. 1–153, 2008.

IEE Electron. Lett. (1)

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” IEE Electron. Lett., vol. 34, no. 15, pp. 1459–1460, 1998.

IEEE Commun. Lett. (2)

X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997.

G. Montorsi, “Analog digital belief propagation,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1106–1109, 2012.

IEEE Photon. Technol. Lett. (7)

A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, and W. Idler, “Estimation of soft FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 20, no. 23, pp. 1547–1549, 2011.

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224–2226, 2005.

T. Fehenberger, R. Maher, A. Alvarado, P. Bayvel, and N. Hanik, “Sensitivity gains by mismatched probabilistic shaping for optical communication systems,” IEEE Photon. Technol. Lett., vol. 28, no. 7, pp. 786–789, 2016.

L. Schmalen, F. Buchali, A. Leven, and S. ten Brink, “A generic tool for assessing the soft-FEC performance in optical transmission experiments,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 40–42, 2012.

N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, and F. Yu, “Reusing common uncoded experimental data in performance estimation of different FEC codes,” IEEE Photon. Technol. Lett., vol. 25, no. 24, pp. 2494–2497, 2013.

M. Yankov, D. Zibar, K. Larsen, L. Christensen, and S. Forchhammer, “Constellation shaping for fiber-optic channels with QAM and high spectral efficiency,” IEEE Photon. Technol. Lett., vol. 26, no. 23, pp. 2407–2410, 2014.

H. B. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett., vol. 21, no. 16, pp. 1139–1141, 2009.

IEEE Signal Process. Mag. (1)

L. Beygi, E. Agrell, J. M. Kahn, and M. Karlsson, “Coded modulation for fiber-optic networks: Toward better tradeoff between signal processing complexity and optical transparent reach,” IEEE Signal Process. Mag., vol. 31, no. 2, pp. 93–103, 2014.

IEEE Trans. Commun. (2)

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.

M. Franceschini, G. Ferrari, and R. Raheli, “Does the performance of LDPC codes depend on the channel?” IEEE Trans. Commun., vol. 54, no. 12, pp. 2129–2132, 2006.

IEEE Trans. Inf. Theory (10)

I. Sason and B. Shuval, “On universal LDPC code ensembles over memoryless symmetric channels,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5182–5202, 2011.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” IEEE Trans. Inf. Theory, vol. 40, no. 6, pp. 1953–1967, 1994.

S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” IEEE Trans. Inf. Theory, vol. 59, no. 12, pp. 7761–7813, 2013.

E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, 2009.

S. Verdú and T. S. Han, “A general formula for channel capacity,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1147–1157, 1994.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: Theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1361–1391, 1999.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006.

A. Ganti, A. Lapidoth, and İ. E. Telatar, “Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit,” IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2315–2328, 2000.

L. Geller and D. Burshtein, “Bounds on the belief propagation threshold of non-binary LDPC codes,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2639–2657, 2016.

J. Feldman, M. J. Wainwright, and D. R. Karger, “Using linear programming to decode binary linear codes,” IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 954–972, 2005.

IEEE Trans. Signal Process. (1)

M. Awais, G. Masera, M. Martina, and G. Montorsi, “VLSI implementation of a non-binary decoder based on the analog digital belief propagation,” IEEE Trans. Signal Process., vol. 62, no. 15, pp. 3965–3975, 2014.

J. Lightw. Technol. (12)

A. Alvarado and E. Agrell, “Four-dimensional coded modulation with bit-wise decoders for future optical communications,” J. Lightw. Technol., vol. 33, no. 10, pp. 1993–2003, 2015.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems (Invited Paper),” J. Lightw. Technol., vol. 33, no. 20, pp. 4338–4352, 2015.

A. Alvarado, E. Agrell, D. Lavery, R. Maher, and P. Bayvel, “Corrections to “Replacing the soft-decision FEC limit paradigm in the design of optical communication systems”,” J. Lightw. Technol., vol. 34, no. 2, p. 722, 2016.

E. Agrell, A. Alvarado, G. Durisi, and M. Karlsson, “Capacity of a nonlinear optical channel with finite memory (Invited Paper),” J. Lightw. Technol., vol. 32, no. 16, pp. 2862–2876, 2014.

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightw. Technol., vol. 30, no. 24, pp. 3857–3879, 2012.

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. Lightw. Technol., vol. 34, no. 7, pp. 1599–1609, 2016.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

T. A. Eriksson, T. Fehenberger, P. A. Andrekson, M. Karlsson, N. Hanik, and E. Agrell, “Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments,” J. Lightw. Technol., vol. 34, no. 9, pp. 2256–2266, 2016.

M. Secondini, E. Forestieri, and G. Prati, “Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps,” J. Lightw. Technol., vol. 31, no. 23, pp. 3839–3852, 2013.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra highspeed optical transmission,” J. Lightw. Technol., vol. 25, no. 11, pp. 3619–3625, 2007.

L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701, 2010.

J. Signal Process. Syst. (1)

M. Beermann, E. Monzó, L. Schmalen, and P. Vary, “GPU accelerated belief propagation decoding of non-binary LDPC codes with parallel and sequential scheduling,” J. Signal Process. Syst., vol. 78, no. 1, pp. 21–34, 2015.

Opt. Express (1)

Optics Express (1)

T. Fehenberger, A. Alvarado, P. Bayvel, and N. Hanik, “On achievable rates for long-haul fiber-optic communications,” Optics Express, vol. 23, no. 7, pp. 9183–9191, 2015.

Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci. (1)

E. Agrell, A. Alvarado, and F. R. Kschischang, “Implications of information theory in optical fibre communications (Invited Paper),” Philos. Trans. Roy. Soc. A, Math. Phys. Eng. Sci., Vol. 374, no. 2062, 2016, Art. no. .

Other (25)

W. Ryan and S. Lin, Channel Codes: Classical and Modern. Cambridge, U.K.: Cambridge Univ. Press, 2009.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andrekson, and M. Karlsson, “Biorthogonal modulation in 8 dimensions experimentally implemented as 2PPM-PS-QPSK,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper W1A.5.

T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, “Eight-dimensional modulation for coherent optical communications,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Tu.3.C.3.

A. Sanaei, M. Ramezani, and M. Ardakani, “On the design of universal LDPC codes,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 802–806.

G. Liga, A. Alvarado, E. Agrell, and P. Bayvel, “Information rates of next-generation long-haul optical fiber systems using coded modulation,” submitted to IEEE/OSAJ. Lightw. Technol., preprint available at https://arxiv.org/abs/1606.01689

D. Qian, E. Ip, M.-F. Huang, M.-J. Li, and T. Wang, “698.5-Gb/s PDM-2048QAM transmission over 3km multicore fiber,” in Proc. Eur. Conf. Opt. Commun., London, U.K., 2013, paper Th.1.C.5.

K. Brueninghauset al., “Link performance models for system level simulations of broadband radio access systems,” in Proc. IEEE Int. Symp. Personal, Indoor Mobile Commun., Berlin, Germany, 2006, pp. 2306–2311.

L. Wan, S. Tsai, and M. Almgren, “A fading-insensitive performance metric for a unified link quality model,” in Proc. IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, USA, 2006, pp. 2110–2114.

L. Szczecinski and A. Alvarado, Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design. Chichester, UK: Wiley, 2015.

H. Bülow, Ü. Abay, A. Schenk, and J. B. Huber, “Coded modulation of polarization- and space-multiplexed signals,” in Proc. Asia Commun. Photon. Conf. Exhib., Shanghai, China, 2011, pp. 1–10.

A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, and T. Kupfer, “Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2016, paper M3A.2.

T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.

B. W. Silverman, Density Estimation for Statistics and Data Analysis. CRC Press, 1986, vol. 26.

W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 3rd ed. Pacific Grove, CA, USA: Brooks/Cole, 1994.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York, NY, USA: Wiley, 2006.

H. Bülow, X. Lu, L. Schmalen, A. Klekamp, and F. Buchali, “Experimental performance of 4D optimized constellation alternatives for PM-8QAM and PM-16QAM,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M2A.6.

H. Bülow and E. Masalkina, “Coded modulation in optical communications,” in Proc. Opt. Fiber Commun. Conf., Los Angeles, CA, USA, 2011, paper OThO1.

L. Schmalen, “Energy efficient FEC for optical transmission systems,” in Proc. Opt. Fiber Commun. Conf., San Francisco, CA, USA, 2014, paper M3A.1.

L. Schmalen, S. ten Brink, and A. Leven, “Spatially-coupled LDPC protograph codes for universal phase slip-tolerant differential decoding,” in Proc. Opt. Fiber Commun. Conf., Optical Society of America, 2015, paper Th3E.6.

L. Schmalen, S. ten Brink, and A. Leven, “Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs,” in Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, X. Zhou and C. Xie, Eds., Hoboken, NJ, USA: Wiley, 2016, pp. 65–122.

L. Schmalen and R. Dischler, “Experimental evaluation of coded modulation for a coherent PDM system with high spectral efficiency,” in Proc. Opt. Fiber Commun. Conf., 2012, paper OW1H.1.

L. Schmalen and S. ten Brink, “Combining spatially coupled LDPC codes with modulation and detection,” in Proc. Int. ITG Conf. Syst., Commun. Coding, Munich, Germany, 2013.

R. Rios-Müller, J. Renaudier, L. Schmalen, and G. Charlet, “Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information,” in Proc. Opt. Fiber Commun. Conf., 2015, paper W3K.4.

R. Rios-Müller, J. Renaudier, P. Tran, and G. Charlet, “Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-Haul transmission link,” in Proc. Eur. Conf. Opt. Commun., Cannes, France, 2014, paper P.5.1.

L. Schmalen, A. Alvarado, and R. Rios-Müller, “Predicting the performance of nonbinary forward error correction in optical transmission experiments,” in Proc. Opt. Fiber Commun. Conf., 2016, paper M2A.2.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.