Abstract

A maximum a posteriori probability (MAP) symbol decoding supplemented with iterative decoding is proposed as an effective mean for suppression of intrachannel nonlinearities. The MAP detector, based on Bahl-Cocke-Jelinek-Raviv algorithm, operates on the channel trellis, a dynamical model of intersymbol interference, and provides soft-decision outputs processed further in an iterative decoder. A dramatic performance improvement is demonstrated. The main reason is that the conventional maximum-likelihood sequence detector based on Viterbi algorithm provides hard-decision outputs only, hence preventing the soft iterative decoding. The proposed scheme operates very well in the presence of strong intrachannel intersymbol interference, when other advanced forward error correction schemes fail, and it is also suitable for 40 Gb/s upgrade over existing 10 Gb/s infrastructure.

© 2006 Optical Society of America

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  1. I. B. Djordjevic, and B. Vasic, "Constrained coding techniques for suppression of Intrachannel Nonlinear effects in high-speed optical transmission," J. Lightwave Technology 24, 411-419 (2006).
    [CrossRef]
  2. R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
    [CrossRef]
  3. M. J. Ablowitz, and T. Hirooka, "Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems," Opt. Lett. 24, 1750-1752 (2000).
    [CrossRef]
  4. X. Liu, X. Wei, A. H. Gnauck, C. Xu, and L. K. Wickham, "Suppression of interchannel four-wave-mixing-induced ghost pulses in high-speed transmissions by phase inversion between adjacent marker blocks," Opt. Lett. 27, 1177-1179 (2000).
    [CrossRef]
  5. P. V. Mamyshev, and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing," Opt. Lett. 24, 1454 -1456 (1999).
    [CrossRef]
  6. N. Alic, and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-14 (2004).
    [CrossRef]
  7. J. H. Winters, "Equalization in coherent lightwave systems using a fractionally spaced equalizer," J. Lightwave Technol. 7, 813-815 (1989).
    [CrossRef]
  8. S. Kasturia and J. H. Winters, "Techniques for high-speed implementation of nonlinear cancellation," IEEE J. Sel. Areas Commun. 9, 711-717 (1991).
    [CrossRef]
  9. C. Xia, and W. Rosenkranz, "Performance enhancement for duobinary modulation through nonlinear electrical equalization," in Proc. 31st European Conference on Optical Communications (ECOC 2005), 2, 257-258 (2005).
  10. O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, "Maximum-likelihood sequence estimation in dispersive optical channels," J. Lightwave Technol. 23, 749-763 (2005).
    [CrossRef]
  11. N. Alić, G. Papen, R. Saperstein, L. Milstein, Y. Fainman, "Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical pre-amplifier," Opt. Express 13, 4568-4579 (2005).
    [CrossRef] [PubMed]
  12. C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
    [CrossRef]
  13. S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
    [CrossRef]
  14. B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
    [CrossRef]
  15. L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
    [CrossRef]
  16. I. B. Djordjevic, and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems," IEEE Commun. Lett. 8, 538-540 (2004).
    [CrossRef]
  17. I. B. Djordjevic, S. Sankaranarayanan, and B. Vasic, "Projective plane iteratively decodable block codes for WDM high-speed long-haul transmission systems," J. Lightwave Technol. 22, 695-702 (2004).
    [CrossRef]
  18. B. Vasic, I. B. Djordjevic, and R. Kostuk, "Low-density parity check codes and iterative decoding for long haul optical communication systems," J. Lightwave Technol. 21, 438-446 (2003).
    [CrossRef]
  19. J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft decision outputs and its applications," in Proc. IEEE GLOBECOM, 1680-1686 (1989).
  20. W. E. Ryan, "Concatenated convolutional codes and iterative decoding," in Wiley Encyclopedia of Telecommunications, J. G. Proakis, ed., (John Wiley and Sons, 2002).
  21. S. K. Chilappagari, S. Sankaranarayanan, and B. Vasic, "Error floors of LDPC codes on binary symmetric channel," accepted for presentation at IEEE Int. Conf. Comm. (ICC 2006), Istanbul, Turkey on 11 - 15 June 2006.
  22. B. Vasic, S. K. Chilappagari, and S. Sankaranarayanan, "Error floors of LDPC codes on binary symmetric channel," presented at the IEEE Comm. Theory Workshop, Park City, UT, June 13-15, 2005.
  23. T. Mizuochi et al., "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
    [CrossRef]
  24. M. Mansour, "Implementation of LDPC decoders," presented at the IEEE Comm. Theory Workshop, Park City, UT, June 13-15, 2005.
  25. T. Lee, "80+ Gb/s ETDM systems implementation: an overview of current technology," in Proc. OFC 2006, Paper no. OTuB3.
  26. A. Färbert, "Application of digital equalization in optical transmission systems," in Proc. OFC 2006, Paper no. OTuE5.
  27. S. Sankaranarayanan, I. B. Djordjevic, and B. Vasic, "Iteratively decodable codes on m-flats for WDM high-speed long-haul transmission," J. Lightwave Technol. 23, 3696-3701 (2005).
    [CrossRef]

2006 (1)

I. B. Djordjevic, and B. Vasic, "Constrained coding techniques for suppression of Intrachannel Nonlinear effects in high-speed optical transmission," J. Lightwave Technology 24, 411-419 (2006).
[CrossRef]

2005 (3)

2004 (5)

T. Mizuochi et al., "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
[CrossRef]

I. B. Djordjevic, and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems," IEEE Commun. Lett. 8, 538-540 (2004).
[CrossRef]

I. B. Djordjevic, S. Sankaranarayanan, and B. Vasic, "Projective plane iteratively decodable block codes for WDM high-speed long-haul transmission systems," J. Lightwave Technol. 22, 695-702 (2004).
[CrossRef]

N. Alic, and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-14 (2004).
[CrossRef]

2003 (1)

2002 (1)

B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
[CrossRef]

2000 (2)

1999 (2)

P. V. Mamyshev, and N. A. Mamysheva, "Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing," Opt. Lett. 24, 1454 -1456 (1999).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
[CrossRef]

1995 (1)

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

1991 (1)

S. Kasturia and J. H. Winters, "Techniques for high-speed implementation of nonlinear cancellation," IEEE J. Sel. Areas Commun. 9, 711-717 (1991).
[CrossRef]

1989 (1)

J. H. Winters, "Equalization in coherent lightwave systems using a fractionally spaced equalizer," J. Lightwave Technol. 7, 813-815 (1989).
[CrossRef]

1974 (1)

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

Ablowitz, M. J.

Agazzi, O. E.

Alic, N.

Bahl, L. R.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

Berrou, C.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Carrer, H. S.

Cocke, J.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

Crivelli, D. E.

Didier, P.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Djordjevic, I. B.

Douillard, C.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Essiambre, R.-J.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
[CrossRef]

Fainman, Y.

Glavieux, A.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Gnauck, A. H.

Hirooka, T.

Hueda, M. R.

Jelinek, F.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

Jézéquel, M.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Kasturia, S.

S. Kasturia and J. H. Winters, "Techniques for high-speed implementation of nonlinear cancellation," IEEE J. Sel. Areas Commun. 9, 711-717 (1991).
[CrossRef]

Kostuk, R.

Kurkoski, B. M.

B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
[CrossRef]

Liu, X.

Mamyshev, P. V.

Mamysheva, N. A.

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
[CrossRef]

Milstein, L.

Mizuochi, T.

T. Mizuochi et al., "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

Papen, G.

Picart, A.

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

Raviv, J.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

Raybon, G.

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
[CrossRef]

Sankaranarayanan, S.

Saperstein, R.

Siegel, P. H.

B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
[CrossRef]

Singer, A. C.

S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
[CrossRef]

Song, S.

S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
[CrossRef]

Sung, K.-M.

S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
[CrossRef]

Vasic, B.

Wei, X.

Wickham, L. K.

Winters, J. H.

S. Kasturia and J. H. Winters, "Techniques for high-speed implementation of nonlinear cancellation," IEEE J. Sel. Areas Commun. 9, 711-717 (1991).
[CrossRef]

J. H. Winters, "Equalization in coherent lightwave systems using a fractionally spaced equalizer," J. Lightwave Technol. 7, 813-815 (1989).
[CrossRef]

Wolf, J. K.

B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
[CrossRef]

Xu, C.

Electron. Lett. (1)

R.-J. Essiambre, B. Mikkelsen, and G. Raybon, "Intra-channel crossphase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 18, 1576-1578 (1999).
[CrossRef]

Eur. Trans. Telecommun. (1)

C. Douillard, M. Jézéquel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, "Iterative correction of intersymbol interference: turbo equalization’" Eur. Trans. Telecommun. 6, 507-511 (1995).
[CrossRef]

IEEE Commun. Lett. (1)

I. B. Djordjevic, and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems," IEEE Commun. Lett. 8, 538-540 (2004).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

S. Kasturia and J. H. Winters, "Techniques for high-speed implementation of nonlinear cancellation," IEEE J. Sel. Areas Commun. 9, 711-717 (1991).
[CrossRef]

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

T. Mizuochi et al., "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Sel. Top. Quantum Electron. 10, 376-386 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Alic, and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-14 (2004).
[CrossRef]

IEEE Trans. Inf. Theory (2)

B. M. Kurkoski, P. H. Siegel, and J. K. Wolf, "Joint Message-Passing decoding of LDPC codes and partial-response channels," IEEE Trans. Inf. Theory 48, 1410-1422 (2002).
[CrossRef]

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory,  IT-20, 284-287 (1974).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. Song, A. C. Singer, and K.-M. Sung, "Soft input channel estimation for turbo equalization," IEEE Trans. Signal Process. 522885-2894 (2004).
[CrossRef]

J. Lightwave Technol. (5)

J. Lightwave Technology (1)

I. B. Djordjevic, and B. Vasic, "Constrained coding techniques for suppression of Intrachannel Nonlinear effects in high-speed optical transmission," J. Lightwave Technology 24, 411-419 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (8)

M. Mansour, "Implementation of LDPC decoders," presented at the IEEE Comm. Theory Workshop, Park City, UT, June 13-15, 2005.

T. Lee, "80+ Gb/s ETDM systems implementation: an overview of current technology," in Proc. OFC 2006, Paper no. OTuB3.

A. Färbert, "Application of digital equalization in optical transmission systems," in Proc. OFC 2006, Paper no. OTuE5.

C. Xia, and W. Rosenkranz, "Performance enhancement for duobinary modulation through nonlinear electrical equalization," in Proc. 31st European Conference on Optical Communications (ECOC 2005), 2, 257-258 (2005).

J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft decision outputs and its applications," in Proc. IEEE GLOBECOM, 1680-1686 (1989).

W. E. Ryan, "Concatenated convolutional codes and iterative decoding," in Wiley Encyclopedia of Telecommunications, J. G. Proakis, ed., (John Wiley and Sons, 2002).

S. K. Chilappagari, S. Sankaranarayanan, and B. Vasic, "Error floors of LDPC codes on binary symmetric channel," accepted for presentation at IEEE Int. Conf. Comm. (ICC 2006), Istanbul, Turkey on 11 - 15 June 2006.

B. Vasic, S. K. Chilappagari, and S. Sankaranarayanan, "Error floors of LDPC codes on binary symmetric channel," presented at the IEEE Comm. Theory Workshop, Park City, UT, June 13-15, 2005.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Pulses at positions 2, 3, and -1 give rise to a ghost pulse at position 0; (b) cumulative effect of resonance positions on position 0.

Fig. 2.
Fig. 2.

(a) Estimated conditional PDFs for states s=1110111 and s=0001000 and for different number of spans. Eye diagrams after 10 (b), and 30 spans (c) of dispersion map from Fig. 3.

Fig. 3.
Fig. 3.

Dispersion map under study

Fig. 4.
Fig. 4.

(a) Trellis used by BCJR (for 2m+1=5), (b) the forward step of BCJR, and (c) the backward step of BCJR

Fig. 5.
Fig. 5.

Receiver configuration

Fig. 6.
Fig. 6.

BER performance of combined BCJR-LDPC scheme (a), and BER performance comparison for different LDPC codes (b).

Fig. 7.
Fig. 7.

Semi-analytic method (SAM) for frame-error rate analysis of projective geometry codes for hard-decision decoding using Gallager B algorithm

Tables (2)

Tables Icon

Table 1 Fiber parameters

Tables Icon

Table 2 Coding gains of combined BCJR-LDPC scheme for different channel memories at BER of 1·10-6

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

L ( u j ) = max * ( s ' , s ) : u j = 0 [ α j 1 ( s ' ) + γ j ( s ' , s ) + β j ( s ) ] max * ( s ' , s ) : u j = 1 [ α j 1 ( s ' ) + γ j ( s ' , s ) + β j ( s ) ] .
α j ( s ) = max * s [ α j 1 ( s ) + γ j ( s , s ) ] ,
β j 1 ( s ' ) = max * s [ β j ( s ) + γ j ( s ' , s ) ] ,
γ j ( s ' , s ) = log p ( s j = s , y j s j 1 = s ' ) = log p ( y j u j ) p ( u j ) .
α 0 ( s ) = { 0 , s = s 0 , s s 0 and β n ( s ) = { 0 , s = s 0 , s s 0 .
max * ( x , y ) = max ( x , y ) + log ( 1 + e x y ) .
L ( u j ) = log p ( u j = 0 y j ) p ( u j = 1 y j ) ,
p ( y j u j = 0 , 1 ) = s : u j = 0 , 1 p ( y j s ) p ( s ) .

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