Abstract

Codes on graphs of interest for next generation forward error correction (FEC) in high-speed optical networks, namely turbo codes and low-density parity-check (LDPC) codes, are described in this invited paper. We describe both binary and nonbinary LDPC codes, their design, and decoding. We also discuss an FPGA implementation of decoders for binary LDPC codes. We then explain how to combine multilevel modulation and channel coding optimally by using coded modulation. Also, we describe an LDPC-coded turbo-equalizer as a candidate for dealing simultaneously with fiber nonlinearities, PMD, and residual chromatic dispersion.

© 2009 IEEE

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  7. O. A. Sab, V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems," Proc. OFC (2001) pp. 280-282.
  8. T. Mizuochi, "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Sel. Topics Quantum Electron. 10, 376-386 (2004).
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  12. D. J. C. MacKay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory 45, 399-431 (1999).
  13. S. Chung, "On the design of low-density parity-check codes within 0.0045 dB of the Shannon Limit," IEEE Commun. Lett. 5, 58-60 (2001).
  14. I. B. Djordjevic, L. Xu, T. Wang, M. Cvijetic, "Large girth low-density parity-check codes for long-haul high-speed optical communications," Proc. OFC/NFOEC (2008).
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  18. H. Xiao-Yu, E. Eleftheriou, D.-M. Arnold, A. Dholakia, "Efficient implementations of the sum-product algorithm for decoding of LDPC codes," Proc. IEEE Globecom (2001) pp. 1036-1036E.
  19. Y. Miyata, R. Sakai, W. Matsumoto, H. Yoshida, T. Mizuochi, "Reduced-complexity decoding algorithm for LDPC codes for practical circuit implementation in optical communications," Optical Fiber Communication Conf. OWE5.
  20. M. Arabaci, I. B. Djordjevic, "An alternative FPGA implementation of decoders for quasi-cyclic LDPC codes," Proc. TELFOR (2008) pp. 351-354.
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  27. J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, X.-Y. Hu, "Reduced-complexity decoding of LDPC codes," IEEE Trans. Commun. 53, 1288-1299 (2005).
  28. I. B. Djordjevic, B. Vasic, "Multilevel coding in ${\rm M}$-ary DPSK/differential QAM high-speed optical transmission with direct detection," IEEE/OSA J. Lightw. Technol. 24, 420-428 (2006).
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  31. J. Hou, P. H. Siegel, L. B. Milstein, H. D. Pfitser, "Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes," IEEE Trans. Inf. Theory 49, 2141-2155 (2003).
  32. I. B. Djordjevic, L. Xu, T. Wang, "PMD compensation in coded-modulation schemes with coherent detection using alamouti-type polarization-time coding," Opt. Exp. 16, 14163-14172.
  33. E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, H. V. Poor, MIMO Wireless Communications (Cambridge Univ. Press, 2007).
  34. I. B. Djordjevic, L. Xu, T. Wang, "PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation," Opt. Exp. 16, 14845-14852 (2008).
  35. I. B. Djordjevic, L. Xu, T. Wang, "Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection," IEEE J. Sel. Areas Commun., Optical Commun., Netw. 27, (2009).
  36. I. B. Djordjevic, L. L. Minkov, H. G. Batshon, "Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization," IEEE J. Sel. Areas Comm., Opt. Commun., Netw. 26, 73-83 (2008).
  37. L. R. Bahl, J. Cocke, F. Jelinek, J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate," IEEE Trans. Inf. Theory IT-20, 284-287 (1974).
  38. M. Ivkovic, I. Djordjevic, P. Rajkovic, B. Vasic, "Pulse energy probability density Functions for long-haul optical fiber transmission systems by using instantons and edgeworth expansion," IEEE Photon. Technol. Lett. 19, 1604-1606 (2007).
  39. J. G. Proakis, Digital Communications (McGraw-Hill, 2001).

2009 (1)

I. B. Djordjevic, L. Xu, T. Wang, "Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection," IEEE J. Sel. Areas Commun., Optical Commun., Netw. 27, (2009).

2008 (3)

I. B. Djordjevic, L. L. Minkov, H. G. Batshon, "Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization," IEEE J. Sel. Areas Comm., Opt. Commun., Netw. 26, 73-83 (2008).

I. B. Djordjevic, B. Vasic, "LDPC-coded OFDM in fiber-optics communication systems [Invited]," OSA J. Opt. Netw. 7, 217-226 (2008).

I. B. Djordjevic, L. Xu, T. Wang, "PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation," Opt. Exp. 16, 14845-14852 (2008).

2007 (3)

I. B. Djordjevic, M. Cvijetic, L. Xu, T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," IEEE/OSA J. Lightw. Technol. 25, 3619-3625 (2007).

L. Lan, L. Zeng, Y. Y. Tai, L. Chen, S. Lin, K. Abdel-Ghaffar, "Construction of quasi-cyclic LDPC codes for AWGN and binary erasure channels: A finite field approach," IEEE Trans. Inf. Theory 53, 2429-2458 (2007).

M. Ivkovic, I. Djordjevic, P. Rajkovic, B. Vasic, "Pulse energy probability density Functions for long-haul optical fiber transmission systems by using instantons and edgeworth expansion," IEEE Photon. Technol. Lett. 19, 1604-1606 (2007).

2006 (1)

I. B. Djordjevic, B. Vasic, "Multilevel coding in ${\rm M}$-ary DPSK/differential QAM high-speed optical transmission with direct detection," IEEE/OSA J. Lightw. Technol. 24, 420-428 (2006).

2005 (1)

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, X.-Y. Hu, "Reduced-complexity decoding of LDPC codes," IEEE Trans. Commun. 53, 1288-1299 (2005).

2004 (3)

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

M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices," IEEE Trans. Inf. Theory 50, 1788-1793 (2004).

O. Milenkovic, I. B. Djordjevic, B. Vasic, "Block-circulant low-density parity-check codes for optical communication systems," IEEE/LEOS J. Sel. Topics Quantum Electron. 10, 294-299 (2004).

2003 (1)

J. Hou, P. H. Siegel, L. B. Milstein, H. D. Pfitser, "Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes," IEEE Trans. Inf. Theory 49, 2141-2155 (2003).

2001 (2)

S. Chung, "On the design of low-density parity-check codes within 0.0045 dB of the Shannon Limit," IEEE Commun. Lett. 5, 58-60 (2001).

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).

1999 (1)

D. J. C. MacKay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory 45, 399-431 (1999).

1998 (1)

R. M. Pyndiah, "Near optimum decoding of product codes," IEEE Trans. Commun. 46, 1003-1010 (1998).

1996 (1)

C. Berrou, A. Glavieux, "Near optimum error correcting coding and decoding: turbo codes," IEEE Trans. Commun. 1261-1271 (1996).

1981 (1)

R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory IT-27, 533-547 (1981).

1974 (1)

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

IEEE Commun. Lett. (1)

S. Chung, "On the design of low-density parity-check codes within 0.0045 dB of the Shannon Limit," IEEE Commun. Lett. 5, 58-60 (2001).

IEEE J. Sel. Areas Comm., Opt. Commun., Netw. (1)

I. B. Djordjevic, L. L. Minkov, H. G. Batshon, "Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization," IEEE J. Sel. Areas Comm., Opt. Commun., Netw. 26, 73-83 (2008).

IEEE J. Sel. Areas Commun., Optical Commun., Netw. (1)

I. B. Djordjevic, L. Xu, T. Wang, "Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection," IEEE J. Sel. Areas Commun., Optical Commun., Netw. 27, (2009).

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

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

IEEE Photon. Technol. Lett. (1)

M. Ivkovic, I. Djordjevic, P. Rajkovic, B. Vasic, "Pulse energy probability density Functions for long-haul optical fiber transmission systems by using instantons and edgeworth expansion," IEEE Photon. Technol. Lett. 19, 1604-1606 (2007).

IEEE Trans. Commun. (3)

R. M. Pyndiah, "Near optimum decoding of product codes," IEEE Trans. Commun. 46, 1003-1010 (1998).

C. Berrou, A. Glavieux, "Near optimum error correcting coding and decoding: turbo codes," IEEE Trans. Commun. 1261-1271 (1996).

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, X.-Y. Hu, "Reduced-complexity decoding of LDPC codes," IEEE Trans. Commun. 53, 1288-1299 (2005).

IEEE Trans. Inf. Theory (7)

R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory IT-27, 533-547 (1981).

D. J. C. MacKay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory 45, 399-431 (1999).

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

F. R. Kschischang, B. J. Frey, H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory 47, 498-519 (2001).

L. Lan, L. Zeng, Y. Y. Tai, L. Chen, S. Lin, K. Abdel-Ghaffar, "Construction of quasi-cyclic LDPC codes for AWGN and binary erasure channels: A finite field approach," IEEE Trans. Inf. Theory 53, 2429-2458 (2007).

J. Hou, P. H. Siegel, L. B. Milstein, H. D. Pfitser, "Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes," IEEE Trans. Inf. Theory 49, 2141-2155 (2003).

M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices," IEEE Trans. Inf. Theory 50, 1788-1793 (2004).

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

O. Milenkovic, I. B. Djordjevic, B. Vasic, "Block-circulant low-density parity-check codes for optical communication systems," IEEE/LEOS J. Sel. Topics Quantum Electron. 10, 294-299 (2004).

IEEE/OSA J. Lightw. Technol. (2)

I. B. Djordjevic, B. Vasic, "Multilevel coding in ${\rm M}$-ary DPSK/differential QAM high-speed optical transmission with direct detection," IEEE/OSA J. Lightw. Technol. 24, 420-428 (2006).

I. B. Djordjevic, M. Cvijetic, L. Xu, T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," IEEE/OSA J. Lightw. Technol. 25, 3619-3625 (2007).

Opt. Exp. (2)

I. B. Djordjevic, L. Xu, T. Wang, "PMD compensation in coded-modulation schemes with coherent detection using alamouti-type polarization-time coding," Opt. Exp. 16, 14163-14172.

I. B. Djordjevic, L. Xu, T. Wang, "PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation," Opt. Exp. 16, 14845-14852 (2008).

OSA J. Opt. Netw. (1)

I. B. Djordjevic, B. Vasic, "LDPC-coded OFDM in fiber-optics communication systems [Invited]," OSA J. Opt. Netw. 7, 217-226 (2008).

Other (18)

I. B. Djordjevic, L. Xu, T. Wang, M. Cvijetic, "Large girth low-density parity-check codes for long-haul high-speed optical communications," Proc. OFC/NFOEC (2008).

W. E. Ryan, CRC Handbook for Coding and Signal Processing for Recording Systems (CRC, 2004).

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, H. V. Poor, MIMO Wireless Communications (Cambridge Univ. Press, 2007).

H. Xiao-Yu, E. Eleftheriou, D.-M. Arnold, A. Dholakia, "Efficient implementations of the sum-product algorithm for decoding of LDPC codes," Proc. IEEE Globecom (2001) pp. 1036-1036E.

Y. Miyata, R. Sakai, W. Matsumoto, H. Yoshida, T. Mizuochi, "Reduced-complexity decoding algorithm for LDPC codes for practical circuit implementation in optical communications," Optical Fiber Communication Conf. OWE5.

M. Arabaci, I. B. Djordjevic, "An alternative FPGA implementation of decoders for quasi-cyclic LDPC codes," Proc. TELFOR (2008) pp. 351-354.

Mitrion Users Guide, v1.5.0-001Mitrionics, Inc. (Mitrionics, Inc., 2008).

M. Arabaci, I. B. Djordjevic, R. Saunders, R. Marcoccia, "A class of nonbinary regular Girth-8 LDPC codes for optical communication channels," OFC/NFOEC San DiegoCA (2009) JThA.

M. C. Davey, Error-Correction Using Low-Density Parity-Check Codes Ph.D. dissertation Univ. CambridgeCambridgeU.K. (1999).

C. Spagnol, W. Marnane, E. Popovici, "FPGA implementations of LDPC over ${\rm GF}(2^{m})$ decoders," Proc. IEEE Workshop on Signal Processing Systems (2007) pp. 273-278.

A. Voicila, F. Verdier, D. Declercq, M. Fossorier, P. Urard, "Architecture of a low-complexity non-binary LDPC decoder for high order fields," Proc. ISIT pp. 1201-1206.

W. E. Ryan, Wiley Encyclopedia in Telecommunications (Wiley, 2003).

E.-J. Essiambre, G. Raybon, B. Mikkelsen, Optical Fiber Telecommunications IVB (Academic, 2002) pp. 233-304.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

O. A. Sab, V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems," Proc. OFC (2001) pp. 280-282.

T. Mizuochi, "Next generation FEC for optical transmission systems," Proc. Opt. Fib. Comm. Conf. (2003) pp. 527-528.

R. G. Gallager, Low Density Parity Check Codes (MIT Press, 1963).

J. G. Proakis, Digital Communications (McGraw-Hill, 2001).

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