Abstract

Coded modulation is a key technique to increase the spectral efficiency of coherent optical communication systems. Two popular strategies for coded modulation are turbo trellis-coded modulation (TTCM) and bit-interleaved coded modulation (BICM) based on low-density parity-check (LDPC) codes. Although BICM LDPC is suboptimal, its simplicity makes it very popular in practice. In this work, we compare the performance of TTCM and BICM LDPC using information-theoretic measures. Our information-theoretic results show that for the same overhead and modulation format only a very small penalty (less than 0.1dB) is to be expected when an ideal BICM LDPC scheme is used. However, the results obtained for the coded modulation schemes implemented in this paper show that the TTCM outperforms BICM LDPC by a larger margin. For a 1000km transmission at 100Gb/s, the observed gain was 0.4dB.

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2016 (5)

D. S. Millaret al., Design of a 1 Tb/s superchannel coherent receiver, J. Lightw. Technol., vol.34, no.6, pp.14531463, 2016.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 2016, Art. no. .

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 2016.

L. Schmalen, A. A. Segovia, and R. Rios-Muller, Performance prediction of nonbinary forward error correction in optical transmission experiments, in J. Lightw. Technol., vol. PP, no. 99, pp. 11, 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.22562266, 2016.

2015 (2)

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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

L. Schmalen, A low-complexity LDPC coding scheme for channels with phase slips, J. Lightw. Technol., vol.33, no.7, pp.13191325, 2015.

2014 (2)

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

R. G. H. van Uden, C. M. Okonkwo, V. A. J. M. Sleiffer, H. de Waardt, and A. M. J. Koonen, MIMO equalization with adaptive step size for few-mode fiber transmission systems, Opt. Express, vol.22, no.1, pp.11926, 2014.

2013 (1)

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.38393852, 2013.

2011 (2)

G. Colavolpe, T. Foggi, A. Modenini, and A. Piemontese, Faster-than-Nyquist and beyond: how to improve spectral efficiency by accepting interference, Opt. Express, vol.19, no.27, pp.2660026609, 2011.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

2010 (1)

B. P. Smith and F. R. Kschischang, Future prospects for FEC in fiber-optic communications, IEEE J. Sel. Topics Quantum Electron., vol.16, no.5, pp.12451257, 2010.

2009 (1)

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

2008 (1)

A. Guilln i Fbregas, A. Martinez, and G. Caire, Bit-Interleaved Coded Modulation, ser. Foundations and trends in communications and information theory. Now Publishers, 2008, vol.5:12.

2007 (1)

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

2006 (1)

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

2001 (1)

S. ten Brink, Convergence behavior of iteratively decoded parallel concatenated codes, IEEE Trans. Commun., vol.49, no.10, pp.17271737, 2001.

2000 (1)

A. Ganti, A. Lapidoth, and I. E. Telatar, Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory, vol.46, no.7, pp.23152328, 2000.

1998 (2)

P. Robertson and T. Worz, Bandwidth-efficient turbo trellis-coded mudulation using punctured component code, IEEE J. Sel. Areas Commun., vol.16, no.2, pp.206218, 1998.

K. Kiasaleh, Turbo-coded optical PPM communication systems, J. Lightw. Technol., vol.16, no.1, pp.1826, 1998.

1992 (1)

E. Zehavi, 8-PSK trellis codes for a Rayleigh channel, IEEE Trans. Commun., vol.40, no.5, pp.873884, 1992.

1982 (1)

G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inf. Theory, vol.28, no.1, pp.5567, 1982.

1974 (1)

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

1948 (1)

C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., vol.27, no.3, pp.379423, 1948.

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.22562266, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

A. Alvarado, F. Brnnstrm, and E. Agrell, High SNR bounds for the BICM capacity, in Proc. 2011 IEEE Inf. Theory Workshop, 2011, pp.360364.

T. Eriksson, E. Agrell, and M. Karlsson, Multidimensional modulation formats for coherent optical communications, in Proc. SPIE Photon. West, Next-Gener. Opt. Commun., p. 977403, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Alvarado, A.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 2016, Art. no. .

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

L. Schmalen, A. Alvarado, and R. Rios-Mller, Predicting the performance of nonbinary forward error correction in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

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

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, On optimal modulation and FEC overhead for future optical networks, in Proc. Opt. Fiber Commun. Conf., 2015, pp.13.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

A. Alvarado, F. Brnnstrm, and E. Agrell, High SNR bounds for the BICM capacity, in Proc. 2011 IEEE Inf. Theory Workshop, 2011, pp.360364.

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.22562266, 2016.

Aono, Y.

M. F. Huang, S. Zhang, K. Mino, and Y. Aono, Transmission of 400G dual-carrier DP-16QAM and multi-carrier DP-QPSK signals over regional and long-haul distances with span lengths greater than 200 km, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Arnold, D. M.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

Bahl, L.

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

Barreto, A. N.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

Bayvel, P.

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 2016.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, On optimal modulation and FEC overhead for future optical networks, in Proc. Opt. Fiber Commun. Conf., 2015, pp.13.

Beygi, L.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

Brink, S.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

Brink, S. ten

S. ten Brink, Convergence behavior of iteratively decoded parallel concatenated codes, IEEE Trans. Commun., vol.49, no.10, pp.17271737, 2001.

Brnnstrm, F.

A. Alvarado, F. Brnnstrm, and E. Agrell, High SNR bounds for the BICM capacity, in Proc. 2011 IEEE Inf. Theory Workshop, 2011, pp.360364.

Buchali, F.

F. Buchali, A. Klekamp, L. Schmalen, and T. Drenski, Implementation of 64QAM at 42.66 GBaud using 1.5 samples per symbol DAC and demonstration of up to 300 km fiber transmission, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Caire, G.

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

A. Guilln i Fbregas, A. Martinez, and G. Caire, Bit-Interleaved Coded Modulation, ser. Foundations and trends in communications and information theory. Now Publishers, 2008, vol.5:12.

Cocke, J.

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

Colavolpe, G.

De Lima, T. C.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

de Waardt, H.

Divsalar, D.

S. Dolinar and D. Divsalar, Weight distributions for turbo codes using random and nonrandom permutations, The Telecommunications and Data Acquisition Progress Report , Jet Propulsion Laboratory California Inst. Technol., Pasadena, California, 1995.

Dolinar, S.

S. Dolinar and D. Divsalar, Weight distributions for turbo codes using random and nonrandom permutations, The Telecommunications and Data Acquisition Progress Report , Jet Propulsion Laboratory California Inst. Technol., Pasadena, California, 1995.

Drenski, T.

F. Buchali, A. Klekamp, L. Schmalen, and T. Drenski, Implementation of 64QAM at 42.66 GBaud using 1.5 samples per symbol DAC and demonstration of up to 300 km fiber transmission, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Eriksson, T.

T. Eriksson, E. Agrell, and M. Karlsson, Multidimensional modulation formats for coherent optical communications, in Proc. SPIE Photon. West, Next-Gener. Opt. Commun., p. 977403, 2016.

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.22562266, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Fbregas, A. Guilln i

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

A. Guilln i Fbregas, A. Martinez, and G. Caire, Bit-Interleaved Coded Modulation, ser. Foundations and trends in communications and information theory. Now Publishers, 2008, vol.5:12.

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.22562266, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Foggi, T.

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.38393852, 2013.

Ganti, A.

A. Ganti, A. Lapidoth, and I. E. Telatar, Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory, vol.46, no.7, pp.23152328, 2000.

Gray, F.

F. Gray, Pulse code communications, U.S. Patent 2632058, 1953.

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.22562266, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Huang, M. F.

M. F. Huang, S. Zhang, K. Mino, and Y. Aono, Transmission of 400G dual-carrier DP-16QAM and multi-carrier DP-QPSK signals over regional and long-haul distances with span lengths greater than 200 km, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Idler, W.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

Ives, D. J.

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 2016.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, On optimal modulation and FEC overhead for future optical networks, in Proc. Opt. Fiber Commun. Conf., 2015, pp.13.

Jelinek, F.

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

Kahn, J. M.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

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.22562266, 2016.

T. Eriksson, E. Agrell, and M. Karlsson, Multidimensional modulation formats for coherent optical communications, in Proc. SPIE Photon. West, Next-Gener. Opt. Commun., p. 977403, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Kavcic, A.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

Kawanishi, T.

G. W. Lu, T. Sakamoto, and T. Kawanishi, Flexible high-order QAM transmitters for elastic optical networks, in Proc. 2014 13th Int. Conf. Opt. Commun. Netw., 2014, pp.14.

Kiasaleh, K.

K. Kiasaleh, Turbo-coded optical PPM communication systems, J. Lightw. Technol., vol.16, no.1, pp.1826, 1998.

Klekamp, A.

F. Buchali, A. Klekamp, L. Schmalen, and T. Drenski, Implementation of 64QAM at 42.66 GBaud using 1.5 samples per symbol DAC and demonstration of up to 300 km fiber transmission, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Koike-Akino, T.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Kojima, K.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Koonen, A. M. J.

Kschischang, F. R.

B. P. Smith and F. R. Kschischang, Future prospects for FEC in fiber-optic communications, IEEE J. Sel. Topics Quantum Electron., vol.16, no.5, pp.12451257, 2010.

Lapidoth, A.

A. Ganti, A. Lapidoth, and I. E. Telatar, Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory, vol.46, no.7, pp.23152328, 2000.

Lassing, J.

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

Lavery, D.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

Leven, A.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

Loeliger, H. A.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

Lu, G. W.

G. W. Lu, T. Sakamoto, and T. Kawanishi, Flexible high-order QAM transmitters for elastic optical networks, in Proc. 2014 13th Int. Conf. Opt. Commun. Netw., 2014, pp.14.

Maher, R.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

Martinez, A.

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

A. Guilln i Fbregas, A. Martinez, and G. Caire, Bit-Interleaved Coded Modulation, ser. Foundations and trends in communications and information theory. Now Publishers, 2008, vol.5:12.

Mello, D. A. A.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

Millar, D.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Millar, D. S.

D. S. Millaret al., Design of a 1 Tb/s superchannel coherent receiver, J. Lightw. Technol., vol.34, no.6, pp.14531463, 2016.

Mino, K.

M. F. Huang, S. Zhang, K. Mino, and Y. Aono, Transmission of 400G dual-carrier DP-16QAM and multi-carrier DP-QPSK signals over regional and long-haul distances with span lengths greater than 200 km, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Modenini, A.

Okonkwo, C. M.

Ottosson, T.

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

Pajovic, M.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Parsons, K.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Piemontese, A.

Portela, T. F.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

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.38393852, 2013.

Raviv, J.

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

Rios-Mller, R.

L. Schmalen, A. Alvarado, and R. Rios-Mller, Predicting the performance of nonbinary forward error correction in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Rios-Muller, R.

L. Schmalen, A. A. Segovia, and R. Rios-Muller, Performance prediction of nonbinary forward error correction in optical transmission experiments, in J. Lightw. Technol., vol. PP, no. 99, pp. 11, 2016.

Robertson, P.

P. Robertson and T. Worz, Bandwidth-efficient turbo trellis-coded mudulation using punctured component code, IEEE J. Sel. Areas Commun., vol.16, no.2, pp.206218, 1998.

Sakamoto, T.

G. W. Lu, T. Sakamoto, and T. Kawanishi, Flexible high-order QAM transmitters for elastic optical networks, in Proc. 2014 13th Int. Conf. Opt. Commun. Netw., 2014, pp.14.

Savory, S.

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 2016.

Savory, S. J.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, On optimal modulation and FEC overhead for future optical networks, in Proc. Opt. Fiber Commun. Conf., 2015, pp.13.

Schmalen, L.

L. Schmalen, A. A. Segovia, and R. Rios-Muller, Performance prediction of nonbinary forward error correction in optical transmission experiments, in J. Lightw. Technol., vol. PP, no. 99, pp. 11, 2016.

L. Schmalen, A low-complexity LDPC coding scheme for channels with phase slips, J. Lightw. Technol., vol.33, no.7, pp.13191325, 2015.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

L. Schmalen, A. Alvarado, and R. Rios-Mller, Predicting the performance of nonbinary forward error correction in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

F. Buchali, A. Klekamp, L. Schmalen, and T. Drenski, Implementation of 64QAM at 42.66 GBaud using 1.5 samples per symbol DAC and demonstration of up to 300 km fiber transmission, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

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.38393852, 2013.

Segovia, A. A.

L. Schmalen, A. A. Segovia, and R. Rios-Muller, Performance prediction of nonbinary forward error correction in optical transmission experiments, in J. Lightw. Technol., vol. PP, no. 99, pp. 11, 2016.

Shannon, C. E.

C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., vol.27, no.3, pp.379423, 1948.

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E. Sillekenset al., Experimental demonstration of 8 state turbo trellis coded modulation employing 8 phase shift keying, in Proc. Eur. Conf. Opt. Commun., 2015, pp.13.

Sleiffer, V. A. J. M.

Smith, B. P.

B. P. Smith and F. R. Kschischang, Future prospects for FEC in fiber-optic communications, IEEE J. Sel. Topics Quantum Electron., vol.16, no.5, pp.12451257, 2010.

Strm, E. G.

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

Sugihara, K.

K. Sugiharaet al., A spatially-coupled type LDPC code with an ncg of 12 dB for optical transmission beyond 100 Gb/s, in Proc. Opt. Fiber Commun. Conf., 2013, pp.13.

Szczecinski, L.

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

Telatar, I. E.

A. Ganti, A. Lapidoth, and I. E. Telatar, Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory, vol.46, no.7, pp.23152328, 2000.

Ungerboeck, G.

G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inf. Theory, vol.28, no.1, pp.5567, 1982.

Vacondio, F.

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

van Uden, R. G. H.

Vontobel, P. O.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

Willems, F. M. J.

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

Worz, T.

P. Robertson and T. Worz, Bandwidth-efficient turbo trellis-coded mudulation using punctured component code, IEEE J. Sel. Areas Commun., vol.16, no.2, pp.206218, 1998.

Xia, T. J.

T. J. Xiaet al., Transmission of 400G PM-16QAM channels over long-haul distance with commercial all-distributed Raman amplification system and aged standard SMF in field, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Yoshida, T.

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

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E. Zehavi, 8-PSK trellis codes for a Rayleigh channel, IEEE Trans. Commun., vol.40, no.5, pp.873884, 1992.

Zeng, W.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

Zhang, S.

M. F. Huang, S. Zhang, K. Mino, and Y. Aono, Transmission of 400G dual-carrier DP-16QAM and multi-carrier DP-QPSK signals over regional and long-haul distances with span lengths greater than 200 km, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

Bell Syst. Tech. J. (1)

C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., vol.27, no.3, pp.379423, 1948.

Bit-Interleaved Coded Modulation (1)

A. Guilln i Fbregas, A. Martinez, and G. Caire, Bit-Interleaved Coded Modulation, ser. Foundations and trends in communications and information theory. Now Publishers, 2008, vol.5:12.

IEEE J. Sel. Areas Commun. (1)

P. Robertson and T. Worz, Bandwidth-efficient turbo trellis-coded mudulation using punctured component code, IEEE J. Sel. Areas Commun., vol.16, no.2, pp.206218, 1998.

IEEE J. Sel. Topics Quantum Electron. (1)

B. P. Smith and F. R. Kschischang, Future prospects for FEC in fiber-optic communications, IEEE J. Sel. Topics Quantum Electron., vol.16, no.5, pp.12451257, 2010.

IEEE Photon. Technol. Lett. (1)

A. Leven, F. Vacondio, L. Schmalen, S. Brink, and W. Idler, Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett., vol.23, no.20, pp.15471549, 2011.

IEEE Trans. Commun. (2)

S. ten Brink, Convergence behavior of iteratively decoded parallel concatenated codes, IEEE Trans. Commun., vol.49, no.10, pp.17271737, 2001.

E. Zehavi, 8-PSK trellis codes for a Rayleigh channel, IEEE Trans. Commun., vol.40, no.5, pp.873884, 1992.

IEEE Trans. Inf. Theory (6)

A. Ganti, A. Lapidoth, and I. E. Telatar, Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory, vol.46, no.7, pp.23152328, 2000.

D. M. Arnold, H. A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, Simulation-based computation of information rates for channels with memory, IEEE Trans. Inf. Theory, vol.52, no.8, pp.34983508, 2006.

A. Guilln i Fbregas, A. Martinez, G. Caire, and F. M. J. Willems, Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory, vol.55, no.6, pp.27562765, 2009.

L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inf. Theory, vol.20, no.2, pp.284287, 1974.

E. Agrell, J. Lassing, E. G. Strm, and T. Ottosson, Gray coding for multilevel constellations in gaussian noise, IEEE Trans. Inf. Theory, vol.53, no.1, pp.224235, 2007.

G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inf. Theory, vol.28, no.1, pp.5567, 1982.

J. Lightw. Technol. (9)

A. Alvarado, D. J. Ives, S. Savory, and P. Bayvel, On the impact of optimal modulation and FEC overhead on future optical networks, J. Lightw. Technol., vol.34, no.9, pp.23392352, 2016.

D. A. A. Mello, A. N. Barreto, T. C. De Lima, T. F. Portela, L. Beygi, and J. M. Kahn, Optical networking with variable-code-rate transceivers, J. Lightw. Technol., vol.32, no.2, pp.257266, 2014.

D. S. Millaret al., Design of a 1 Tb/s superchannel coherent receiver, J. Lightw. Technol., vol.34, no.6, pp.14531463, 2016.

K. Kiasaleh, Turbo-coded optical PPM communication systems, J. Lightw. Technol., vol.16, no.1, pp.1826, 1998.

L. Schmalen, A low-complexity LDPC coding scheme for channels with phase slips, J. Lightw. Technol., vol.33, no.7, pp.13191325, 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, J. Lightw. Technol., vol.33, no.20, pp.43384352, 2015.

L. Schmalen, A. A. Segovia, and R. Rios-Muller, Performance prediction of nonbinary forward error correction in optical transmission experiments, in J. Lightw. Technol., vol. PP, no. 99, pp. 11, 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.22562266, 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.38393852, 2013.

Opt. Express (2)

Sci. Rep. (1)

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, Increasing the information rates of optical communications via coded modulation: A study of transceiver performance, Sci. Rep., vol.6, pp.110, 2016, Art. no. .

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F. Buchali, A. Klekamp, L. Schmalen, and T. Drenski, Implementation of 64QAM at 42.66 GBaud using 1.5 samples per symbol DAC and demonstration of up to 300 km fiber transmission, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

G. W. Lu, T. Sakamoto, and T. Kawanishi, Flexible high-order QAM transmitters for elastic optical networks, in Proc. 2014 13th Int. Conf. Opt. Commun. Netw., 2014, pp.14.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, On optimal modulation and FEC overhead for future optical networks, in Proc. Opt. Fiber Commun. Conf., 2015, pp.13.

T. J. Xiaet al., Transmission of 400G PM-16QAM channels over long-haul distance with commercial all-distributed Raman amplification system and aged standard SMF in field, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

M. F. Huang, S. Zhang, K. Mino, and Y. Aono, Transmission of 400G dual-carrier DP-16QAM and multi-carrier DP-QPSK signals over regional and long-haul distances with span lengths greater than 200 km, in Proc. Opt. Fiber Commun. Conf., 2014, pp.13.

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

K. Kojima, T. Koike-Akino, D. Millar, M. Pajovic, K. Parsons, and T. Yoshida, Investigation of low code rate DP-8PSK as an alternative to DP-QPSK, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

E. Sillekenset al., Experimental demonstration of 8 state turbo trellis coded modulation employing 8 phase shift keying, in Proc. Eur. Conf. Opt. Commun., 2015, pp.13.

S. Dolinar and D. Divsalar, Weight distributions for turbo codes using random and nonrandom permutations, The Telecommunications and Data Acquisition Progress Report , Jet Propulsion Laboratory California Inst. Technol., Pasadena, California, 1995.

L. Schmalen, A. Alvarado, and R. Rios-Mller, Predicting the performance of nonbinary forward error correction in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

Digital Video Broadcasting (DVB); Second Generation Framing Structure, Channel Coding and Modulation Systems for Broadcasting, Interactive Services, News Gathering and Other Broadband Satellite Applications. (DVB-S2), European Standard , V1.4.1, 2014.

K. Sugiharaet al., A spatially-coupled type LDPC code with an ncg of 12 dB for optical transmission beyond 100 Gb/s, in Proc. Opt. Fiber Commun. Conf., 2013, pp.13.

F. Gray, Pulse code communications, U.S. Patent 2632058, 1953.

A. Alvarado, F. Brnnstrm, and E. Agrell, High SNR bounds for the BICM capacity, in Proc. 2011 IEEE Inf. Theory Workshop, 2011, pp.360364.

T. Eriksson, E. Agrell, and M. Karlsson, Multidimensional modulation formats for coherent optical communications, in Proc. SPIE Photon. West, Next-Gener. Opt. Commun., p. 977403, 2016.

T. Fehenberger, T. A. Eriksson, A. Alvarado, M. Karlsson, E. Agrell, and N. Hanik, Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments, in Proc. Opt. Fiber Commun. Conf., 2016, pp.13.

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