Abstract

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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  1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol. 28, 662–701 (2010).
    [Crossref]
  2. D. J. Costello and G. D. Forney, “Channel coding: The road to channel capacity,” Proc. IEEE 95, 1150–1177 (2007).
    [Crossref]
  3. B. Smith and F. R. Kschischang, “A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications,” J. Lightw. Technol. 30, 2047–2053 (2012).
    [Crossref]
  4. I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
    [Crossref]
  5. L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
    [Crossref]
  6. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
    [Crossref]
  7. J. Thorpe, “Low-density parity-check (LDPC) codes constructed from protographs,” IPN Progress Report 42-154, JPL (2005).
  8. L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
    [Crossref]
  9. D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).
  10. A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
    [Crossref]
  11. A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45, 2181–2191 (1999).
    [Crossref]
  12. S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
    [Crossref]
  13. T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
    [Crossref]
  14. G. Richter, A. Hof, and M. Bossert, “On the mapping of low-density parity-check codes for bit-interleaved coded modulation,” in “Proc. IEEE Int. Symp. Information Theory (ISIT),” (Nice, Italy, 2007).
  15. D. Divsalar and C. Jones, “Protograph based low error floor LDPC coded modulation,” in “Proc. IEEE Military Communications Conf. (MILCOM),” (Atlantic City, NJ, 2005).
  16. Y. Jin, M. Jiang, and C. Zhao, “Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM,” in “Proc. Int. Symp. Turbo Codes and Iterative Information Processing (ISTC),” (Brest, France, 2010).
  17. T. Van Nguyen, A. Nosratinia, and D. Divsalar, “Threshold of protograph-based LDPC coded BICM for Rayleigh fading,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Houston, TX, 2011).
  18. T. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
    [Crossref]
  19. G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Washington, DC, 2007).
  20. C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).
  21. G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley-Interscience, 2005).
    [Crossref]
  22. M. Secondini and E. Forestieri, “The nonlinear Schrödinger equation in fiber-optic systems,” Riv. Mat. Univ. Parma 8, 69–98 (2008).
  23. J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
    [Crossref]
  24. W. Ryan and S. Lin, Channel Codes Classical and Modern (Cambridge University, 2009).
    [Crossref]
  25. D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, “AWGN channel analysis of terminated LDPC convolutional codes,” in “Proc. Information Theory and Applications Workshop (ITA),” (La Jolla, CA, 2011).
  26. R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
    [Crossref]
  27. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
    [Crossref]
  28. R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Opt. 11, 341–359 (1997).
    [Crossref]
  29. D. Kaufman and R. Smith, “Direction choice for accelerated convergence in hit-and-run sampling,” Operations Research 46, 84–95 (1998).
    [Crossref]
  30. G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
    [Crossref]

2013 (1)

L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
[Crossref]

2012 (5)

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

B. Smith and F. R. Kschischang, “A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications,” J. Lightw. Technol. 30, 2047–2053 (2012).
[Crossref]

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

2011 (1)

S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
[Crossref]

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. 28, 662–701 (2010).
[Crossref]

2009 (1)

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
[Crossref]

2008 (1)

M. Secondini and E. Forestieri, “The nonlinear Schrödinger equation in fiber-optic systems,” Riv. Mat. Univ. Parma 8, 69–98 (2008).

2007 (1)

D. J. Costello and G. D. Forney, “Channel coding: The road to channel capacity,” Proc. IEEE 95, 1150–1177 (2007).
[Crossref]

2006 (1)

R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
[Crossref]

2003 (1)

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

2001 (2)

T. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[Crossref]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[Crossref]

1999 (1)

A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45, 2181–2191 (1999).
[Crossref]

1998 (2)

D. Kaufman and R. Smith, “Direction choice for accelerated convergence in hit-and-run sampling,” Operations Research 46, 84–95 (1998).
[Crossref]

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
[Crossref]

1997 (1)

R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Opt. 11, 341–359 (1997).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley-Interscience, 2005).
[Crossref]

Agrell, E.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

Alvarado, A.

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

Arabaci, M.

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
[Crossref]

Beygi, L.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

Biglieri, E.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
[Crossref]

Bosco, G.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

Bossert, M.

G. Richter, A. Hof, and M. Bossert, “On the mapping of low-density parity-check codes for bit-interleaved coded modulation,” in “Proc. IEEE Int. Symp. Information Theory (ISIT),” (Nice, Italy, 2007).

Brännström, F.

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

Caire, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
[Crossref]

Carena, A.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

Cheng, T.

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

Chiani, M.

G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Washington, DC, 2007).

Corazza, G. E.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

Costello, D. J.

D. J. Costello and G. D. Forney, “Channel coding: The road to channel capacity,” Proc. IEEE 95, 1150–1177 (2007).
[Crossref]

D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, “AWGN channel analysis of terminated LDPC convolutional codes,” in “Proc. Information Theory and Applications Workshop (ITA),” (La Jolla, CA, 2011).

Curri, V.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

de Lind van Wijngaarden, A. J.

L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
[Crossref]

Divsalar, D.

D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).

D. Divsalar and C. Jones, “Protograph based low error floor LDPC coded modulation,” in “Proc. IEEE Military Communications Conf. (MILCOM),” (Atlantic City, NJ, 2005).

T. Van Nguyen, A. Nosratinia, and D. Divsalar, “Threshold of protograph-based LDPC coded BICM for Rayleigh fading,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Houston, TX, 2011).

Djordjevic, I. B.

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
[Crossref]

Dolinar, S.

D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).

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. 28, 662–701 (2010).
[Crossref]

Felström, A. J.

A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45, 2181–2191 (1999).
[Crossref]

Forestieri, E.

M. Secondini and E. Forestieri, “The nonlinear Schrödinger equation in fiber-optic systems,” Riv. Mat. Univ. Parma 8, 69–98 (2008).

Forghieri, F.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

Forney, G. D.

D. J. Costello and G. D. Forney, “Channel coding: The road to channel capacity,” Proc. IEEE 95, 1150–1177 (2007).
[Crossref]

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. 28, 662–701 (2010).
[Crossref]

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. 28, 662–701 (2010).
[Crossref]

Graell i Amat, A.

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

Häger, C.

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

Hof, A.

G. Richter, A. Hof, and M. Bossert, “On the mapping of low-density parity-check codes for bit-interleaved coded modulation,” in “Proc. IEEE Int. Symp. Information Theory (ISIT),” (Nice, Italy, 2007).

Hou, J.

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

Iyengar, A. R.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

Jiang, M.

Y. Jin, M. Jiang, and C. Zhao, “Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM,” in “Proc. Int. Symp. Turbo Codes and Iterative Information Processing (ISTC),” (Brest, France, 2010).

Jin, Y.

Y. Jin, M. Jiang, and C. Zhao, “Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM,” in “Proc. Int. Symp. Turbo Codes and Iterative Information Processing (ISTC),” (Brest, France, 2010).

Johannisson, P.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

Jones, C.

D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).

D. Divsalar and C. Jones, “Protograph based low error floor LDPC coded modulation,” in “Proc. IEEE Military Communications Conf. (MILCOM),” (Atlantic City, NJ, 2005).

Karlsson, M.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

Kaufman, D.

D. Kaufman and R. Smith, “Direction choice for accelerated convergence in hit-and-run sampling,” Operations Research 46, 84–95 (1998).
[Crossref]

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. 28, 662–701 (2010).
[Crossref]

Kschischang, F. R.

B. Smith and F. R. Kschischang, “A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications,” J. Lightw. Technol. 30, 2047–2053 (2012).
[Crossref]

Kudekar, S.

S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
[Crossref]

Lentmaier, M.

D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, “AWGN channel analysis of terminated LDPC convolutional codes,” in “Proc. Information Theory and Applications Workshop (ITA),” (La Jolla, CA, 2011).

Lin, S.

W. Ryan and S. Lin, Channel Codes Classical and Modern (Cambridge University, 2009).
[Crossref]

Liu, R.

R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
[Crossref]

Liva, G.

G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Washington, DC, 2007).

Milstein, L. B.

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

Minkov, L. L.

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
[Crossref]

Mitchell, D. G. M.

D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, “AWGN channel analysis of terminated LDPC convolutional codes,” in “Proc. Information Theory and Applications Workshop (ITA),” (La Jolla, CA, 2011).

Nosratinia, A.

T. Van Nguyen, A. Nosratinia, and D. Divsalar, “Threshold of protograph-based LDPC coded BICM for Rayleigh fading,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Houston, TX, 2011).

Papaleo, M.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

Peng, K.

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

Pfister, H. D.

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

Poggiolini, P.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

Price, K.

R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Opt. 11, 341–359 (1997).
[Crossref]

Richardson, T.

S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
[Crossref]

T. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[Crossref]

Richardson, T. J.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[Crossref]

Richter, G.

G. Richter, A. Hof, and M. Bossert, “On the mapping of low-density parity-check codes for bit-interleaved coded modulation,” in “Proc. IEEE Int. Symp. Information Theory (ISIT),” (Nice, Italy, 2007).

Ryan, W.

W. Ryan and S. Lin, Channel Codes Classical and Modern (Cambridge University, 2009).
[Crossref]

Schmalen, L.

L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
[Crossref]

Secondini, M.

M. Secondini and E. Forestieri, “The nonlinear Schrödinger equation in fiber-optic systems,” Riv. Mat. Univ. Parma 8, 69–98 (2008).

Shokrollahi, M. A.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[Crossref]

Siegel, P. H.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

Smith, B.

B. Smith and F. R. Kschischang, “A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications,” J. Lightw. Technol. 30, 2047–2053 (2012).
[Crossref]

Smith, R.

D. Kaufman and R. Smith, “Direction choice for accelerated convergence in hit-and-run sampling,” Operations Research 46, 84–95 (1998).
[Crossref]

Soljanin, E.

R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
[Crossref]

Song, J.

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

Spasojevic, P.

R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
[Crossref]

Storn, R.

R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Opt. 11, 341–359 (1997).
[Crossref]

Taricco, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
[Crossref]

ten Brink, S.

L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
[Crossref]

Thorpe, J.

J. Thorpe, “Low-density parity-check (LDPC) codes constructed from protographs,” IPN Progress Report 42-154, JPL (2005).

D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).

Urbanke, R.

S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
[Crossref]

T. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[Crossref]

Urbanke, R. L.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[Crossref]

Van Nguyen, T.

T. Van Nguyen, A. Nosratinia, and D. Divsalar, “Threshold of protograph-based LDPC coded BICM for Rayleigh fading,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Houston, TX, 2011).

Vanelli-coralli, A.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

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. 28, 662–701 (2010).
[Crossref]

Wolf, J. K.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

Wymeersch, H.

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

Yan, K.

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

Zhao, C.

Y. Jin, M. Jiang, and C. Zhao, “Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM,” in “Proc. Int. Symp. Turbo Codes and Iterative Information Processing (ISTC),” (Brest, France, 2010).

Zigangirov, K. S.

A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45, 2181–2191 (1999).
[Crossref]

Bell Labs Tech. J (1)

L. Schmalen, A. J. de Lind van Wijngaarden, and S. ten Brink, “Forward error correction in optical core and optical access networks,” Bell Labs Tech. J 18, 39–66 (2013).
[Crossref]

IEEE Commun. Lett. (1)

T. Cheng, K. Peng, J. Song, and K. Yan, “EXIT-aided bit mapping design for LDPC coded modulation with APSK constellations,” IEEE Commun. Lett. 16, 777–780 (2012).
[Crossref]

IEEE Trans. Commun. (1)

L. Beygi, E. Agrell, P. Johannisson, M. Karlsson, and H. Wymeersch, “A discrete-time model for uncompensated single-channel fiber-optical links,” IEEE Trans. Commun. 60, 3440–3450 (2012).
[Crossref]

IEEE Trans. Inf. Theory (8)

T. Richardson and R. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[Crossref]

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58, 2303–2320 (2012).
[Crossref]

A. J. Felström and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45, 2181–2191 (1999).
[Crossref]

S. Kudekar, T. Richardson, and R. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57, 803–834 (2011).
[Crossref]

J. Hou, P. H. Siegel, L. B. Milstein, and H. D. Pfister, “Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes,” IEEE Trans. Inf. Theory 49, 2141–2155 (2003).
[Crossref]

R. Liu, P. Spasojevic, and E. Soljanin, “Reliable channel regions for good binary codes transmitted over parallel channels,” IEEE Trans. Inf. Theory 52, 1405–1424 (2006).
[Crossref]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[Crossref]

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44, 927–946 (1998).
[Crossref]

J. Global Opt. (1)

R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Opt. 11, 341–359 (1997).
[Crossref]

J. Lightw. Technol. (4)

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightw. Technol. 30, 1524–1539 (2012).
[Crossref]

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol. 28, 662–701 (2010).
[Crossref]

B. Smith and F. R. Kschischang, “A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications,” J. Lightw. Technol. 30, 2047–2053 (2012).
[Crossref]

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightw. Technol. 27, 3518–3530 (2009).
[Crossref]

Operations Research (1)

D. Kaufman and R. Smith, “Direction choice for accelerated convergence in hit-and-run sampling,” Operations Research 46, 84–95 (1998).
[Crossref]

Proc. IEEE (1)

D. J. Costello and G. D. Forney, “Channel coding: The road to channel capacity,” Proc. IEEE 95, 1150–1177 (2007).
[Crossref]

Riv. Mat. Univ. Parma (1)

M. Secondini and E. Forestieri, “The nonlinear Schrödinger equation in fiber-optic systems,” Riv. Mat. Univ. Parma 8, 69–98 (2008).

Other (11)

W. Ryan and S. Lin, Channel Codes Classical and Modern (Cambridge University, 2009).
[Crossref]

D. G. M. Mitchell, M. Lentmaier, and D. J. Costello, “AWGN channel analysis of terminated LDPC convolutional codes,” in “Proc. Information Theory and Applications Workshop (ITA),” (La Jolla, CA, 2011).

J. Thorpe, “Low-density parity-check (LDPC) codes constructed from protographs,” IPN Progress Report 42-154, JPL (2005).

D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (St. Louis, Missouri, 2005).

G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Washington, DC, 2007).

C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, and E. Agrell, “Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels,” in “Proc. IEEE Int. Conf. Communications (ICC),” (Sydney, Australia, 2014).

G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley-Interscience, 2005).
[Crossref]

G. Richter, A. Hof, and M. Bossert, “On the mapping of low-density parity-check codes for bit-interleaved coded modulation,” in “Proc. IEEE Int. Symp. Information Theory (ISIT),” (Nice, Italy, 2007).

D. Divsalar and C. Jones, “Protograph based low error floor LDPC coded modulation,” in “Proc. IEEE Military Communications Conf. (MILCOM),” (Atlantic City, NJ, 2005).

Y. Jin, M. Jiang, and C. Zhao, “Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM,” in “Proc. Int. Symp. Turbo Codes and Iterative Information Processing (ISTC),” (Brest, France, 2010).

T. Van Nguyen, A. Nosratinia, and D. Divsalar, “Threshold of protograph-based LDPC coded BICM for Rayleigh fading,” in “Proc. IEEE Glob. Communication Conf. (GLOBECOM),” (Houston, TX, 2011).

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Figures (7)

Fig. 1
Fig. 1 Block diagram of the consider fiber-optical transmission system.
Fig. 2
Fig. 2 (a) BICM block diagram including the channel symmetrization technique. (b) Approximate model with parallel Gaussian LLR channels.
Fig. 3
Fig. 3 The considered signal constellations in each dimension.
Fig. 4
Fig. 4 Comparison of the LLR channels for PM-64-QAM including channel symmetrization (solid lines) with the Gaussian LLR channels that have the same MI (dashed lines).
Fig. 5
Fig. 5 Block diagram illustrating the purpose of the bit mapper.
Fig. 6
Fig. 6 Comparison of the optimized bit mappers (blue) with the baseline bit mappers (red) for the linear transmission scenario. Dashed lines correspond to P-EXIT analysis and solid lines to simulation results. In (b), solid green lines correspond to the P-EXIT analysis for V = 6.
Fig. 7
Fig. 7 Comparison of the optimized bit mappers (blue) with the baseline bit mappers (red) for the nonlinear transmission scenario.

Tables (2)

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Algorithm 1: P-EXIT analysis of the WD for a (J, K) regular SC-LDPC protograph.

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Table 1 System parameters

Equations (7)

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v ( t , z ) z = α g ( z ) 2 v ( t , z ) j β 2 2 2 v ( t , z ) t 2 + j γ v ( t , z ) v ( t , z ) 2 + w ( t , z ) ,
f R k | S k ( r k | s k ) = 1 ( π P N ) 2 exp ( r k ζ s k 2 P N ) ,
l i , k log f R k | B i , k ( r k | 0 ) f R k | B i , k ( r k | 1 ) = log s 𝒳 i , 0 f R k | S k ( r k | s ) s 𝒳 i , 1 f R k | S k ( r k | s ) ,
P ( ) = ( P ( ) | 0 0 3 1 1 3 ) , P ( = 0 ) = ( 1 2 0 0 0 0 3 1 1 1 0 1 2 2 1 )
P [ T ] = ( P 0 P 1 P 0 P m s P 1 P m s ) T times .
A opt = argmin A 𝒜 m × n ρ * ( A ) ,
A * = argmin A 𝒜 m × n l s ( A , ρ ) .

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