Abstract

This paper is concerned with investigating the performance of regular and irregular, randomlike and structured generalized low-density parity-check (GLDPC) codes for long-haul transmission. The proposed GLDPC codes outperform currently known turbo and low-density parity-check (LDPC) coding schemes with comparable parameters utilized in optical communication systems. For a GLDPC coding scheme with 23.6% redundancy, the largest so far reported coding gain of at least 11dB (at 40 Gb/s) is demonstrated.

© 2005 IEEE

PDF Article

References

  • View by:
  • |

  1. K. Azadet, et al. "Equalization and FEC techniques for optical transceivers", IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 317-327, Mar. 2002.
  2. C. Howland and A. Blanksby, "A 220 mW 1 Gb/s 1024-bit rate-1/2 low density parity check code decoder", in IEEE Conf. Custom Integrated Circuits, 2001, pp. 293-296.
  3. A. J. Blanksby and C. J. Howland, "A 690-mW 1-Gb/s 1024-b, rate-1/2 low-density parity-check code encoder", IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 404-412, Mar. 2001.
  4. T. Richardson and R. Urbanke, "The renaissance of Gallager's low-density parity-check codes", IEEE Commun. Mag., vol. 41, no. 8, pp. 126-131, Aug. 2003.
  5. T. Mizouchi, 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. Topics Quantum Electron., vol. 10, no. 2, pp. 376-386, Mar./Apr. 2004.
  6. I. B. Djordjevic, S. Sankaranarayanan and B. Vasic, "Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems", J. Lightw. Technol., vol. 22, no. 3, pp. 695-702, Mar. 2004.
  7. I. B. Djordjevic and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems", IEEE Commun. Lett., vol. 8, no. 8, pp. 538-540, Aug. 2004.
  8. W. E. Ryan, "An introduction to LDPC codes," in CRC Handbook for Coding and Signal Processing for Recording Systems, B. Vasic, and E. M. Kurtas, Eds. Boca Raton, FL: CRC, 2005.
  9. R. M. Tanner, "A recursive approach to low complexity codes", IEEE Trans. Inf. Theory, vol. IT-27, no. 5, pp. 533-547, Sep. 1981.
  10. J. Boutros, O. Pothier and G. Zemor, "Generalized low density (Tanner) codes", in Proc. 1999 IEEE Int. Conf. Communication (ICC 1999), vol. 1, 1999, pp. 441-445.
  11. M. Lentmaier and K. S. Zigangirov, "On generalized low-density parity-check codes based on Hamming component codes", IEEE Commun. Lett., vol. 3, no. 8, pp. 248-250, Aug. 1999.
  12. O. Pothier, L. Brunel and J. Boutros, "A low complexity FEC scheme based on the intersection of interleaved block codes", in Proc. 49th IEEE Vehicular Technol. Conf. , vol. 1, 1999, pp. 274-278.
  13. T. Zhang and K. K. Parhi, "High-performance, low-complexity decoding of generalized low-density parity-check codes", in Proc. IEEE Global Telecommunications Conf. 2001 (IEEE GLOBECOM), vol. 1, 2001, pp. 181-185.
  14. T. Zhang and K. K. Parhi, "A class of efficient-encoding generalized low-density parity-check codes", in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP 2001), vol. 4, 2001, pp. 2477-2480.
  15. T. M. N. Ngatched and F. Takawira, "Efficient decoding of generalized low-density parity-check codes based on long-component codes", in Proc. Wireless Communication Networking Conf. (WCNC 2003), vol. 1, 2003, pp. 705-710.
  16. S. Hirst and B. Honary, "Application of efficient chase algorithm in decoding of generalized low-density parity-check codes", IEEE Commun. Lett. , vol. 6, no. 9, pp. 385-387, Sep. 2002.
  17. L. R. 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. 284-287, Mar. 1974.
  18. A. Ashikhmin and S. Litsyn, "Simple MAP decoding of first order Reed-Muller and Hamming codes", IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1812-1818, Aug. 2003.
  19. I. B. Djordjevic and B. Vasic, "An advanced direct detection receiver model", J. Opt. Commun., vol. 20, pp. 6-9, Feb. 2004.
  20. F. McWilliams and N. Sloane, The Theory of Error Correcting Codes, New York: North Holland, 1977.
  21. V. Nagarajan, N. Jayakumar, S. Khatri and O. Milenkovic, "High-throughput VLSI implementations of iterative decoders and related code construction problems", in Proc. IEEE GLOBECOM 2004, vol. 1, Dec. 2004, pp. 361-365.
  22. R. G. Gallager, Low-Density Parity-Check Codes, Cambridge, MA: MIT, 1963.
  23. O. A. Sab and V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems", in Proc. Optical Fiber Communication Conf. (OFC), vol. 3, 2001, pp. 280-282.
  24. S. Sankaranarayanan and B. Vasic, "Iterative decoding of linear block codes", IEEE Trans. Inf. Theory,
  25. S. Dolinar and D. Dilvasar, "Weight Distributions for Turbo Codes using Random and Nonrandom Permutations", Progr. Rep., JPL TDA, 42-122, 1995.
  26. N. Ehtiati, et al. "Improved interleaver design for turbo coded intersymbol interference channels", in Proc. IEEE 58th Conf. Vehicular Technol. (VTC 2003), Oct. 2003, pp. 327-331.
  27. H. Zhang and J. Moura, "The design of structured regular LDPC codes with large girth", in Proc. IEEE GLOBECOM 2003, vol. 7, 2003, pp. 4022-4027.
  28. O. Milenkovic and S. Laendner, "Analysis of the cycle-structure of LDPC codes based on Latin squares", in Proc. 2004 IEEE Int. Conf. Communications , vol. 2, Jun. 2004, pp. 777-781.
  29. R. Lidle and H. Niederreiter, Finite Fields, CA: Academic Press, 1997.
  30. J. Fan, "Array codes as LDPC codes", in Proc. 2nd Int. Symp. Turbo Codes, 2000, pp. 543-546.
  31. A. Ashikhmin, G. Kramer and S. ten Brink, "Extrinsic information transfer functions: Model and erasure channel properties", IEEE Trans. Inf. Theory, vol. 50, no. 11, pp. 2657-2673, Nov. 2004.
  32. P. A. Humblet, et al. "On the bit error rate of lightwave systems with optical amplifiers", J. Lightw. Technol., vol. 9, no. 11, pp. 1576-1582, Nov. 1991.
  33. I. B. Djordjevic and B. Vasic, "High code rate low-density parity-check codes for optical communication systems", IEEE Photon. Technol. Lett., vol. 16, no. 6, pp. 1600-1602, Jun. 2004.
  34. R. Koetter, "Iterative coding techniques, pseudocodewords and their relationship", presented at the LANL Workshop on Applications of Statistical Physics to Coding Theory, Santa Fe, NM, Jan. 10-12, 2005.
  35. T. Richardson, "Error floors of LDPC codes", presented at the 41st Allerton Conf. Communications, Control and Computing, Allerton, IL, Oct. 2003.

Other (35)

K. Azadet, et al. "Equalization and FEC techniques for optical transceivers", IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 317-327, Mar. 2002.

C. Howland and A. Blanksby, "A 220 mW 1 Gb/s 1024-bit rate-1/2 low density parity check code decoder", in IEEE Conf. Custom Integrated Circuits, 2001, pp. 293-296.

A. J. Blanksby and C. J. Howland, "A 690-mW 1-Gb/s 1024-b, rate-1/2 low-density parity-check code encoder", IEEE J. Solid-State Circuits, vol. 37, no. 3, pp. 404-412, Mar. 2001.

T. Richardson and R. Urbanke, "The renaissance of Gallager's low-density parity-check codes", IEEE Commun. Mag., vol. 41, no. 8, pp. 126-131, Aug. 2003.

T. Mizouchi, 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. Topics Quantum Electron., vol. 10, no. 2, pp. 376-386, Mar./Apr. 2004.

I. B. Djordjevic, S. Sankaranarayanan and B. Vasic, "Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems", J. Lightw. Technol., vol. 22, no. 3, pp. 695-702, Mar. 2004.

I. B. Djordjevic and B. Vasic, "MacNeish-Mann theorem based iteratively decodable codes for optical communication systems", IEEE Commun. Lett., vol. 8, no. 8, pp. 538-540, Aug. 2004.

W. E. Ryan, "An introduction to LDPC codes," in CRC Handbook for Coding and Signal Processing for Recording Systems, B. Vasic, and E. M. Kurtas, Eds. Boca Raton, FL: CRC, 2005.

R. M. Tanner, "A recursive approach to low complexity codes", IEEE Trans. Inf. Theory, vol. IT-27, no. 5, pp. 533-547, Sep. 1981.

J. Boutros, O. Pothier and G. Zemor, "Generalized low density (Tanner) codes", in Proc. 1999 IEEE Int. Conf. Communication (ICC 1999), vol. 1, 1999, pp. 441-445.

M. Lentmaier and K. S. Zigangirov, "On generalized low-density parity-check codes based on Hamming component codes", IEEE Commun. Lett., vol. 3, no. 8, pp. 248-250, Aug. 1999.

O. Pothier, L. Brunel and J. Boutros, "A low complexity FEC scheme based on the intersection of interleaved block codes", in Proc. 49th IEEE Vehicular Technol. Conf. , vol. 1, 1999, pp. 274-278.

T. Zhang and K. K. Parhi, "High-performance, low-complexity decoding of generalized low-density parity-check codes", in Proc. IEEE Global Telecommunications Conf. 2001 (IEEE GLOBECOM), vol. 1, 2001, pp. 181-185.

T. Zhang and K. K. Parhi, "A class of efficient-encoding generalized low-density parity-check codes", in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP 2001), vol. 4, 2001, pp. 2477-2480.

T. M. N. Ngatched and F. Takawira, "Efficient decoding of generalized low-density parity-check codes based on long-component codes", in Proc. Wireless Communication Networking Conf. (WCNC 2003), vol. 1, 2003, pp. 705-710.

S. Hirst and B. Honary, "Application of efficient chase algorithm in decoding of generalized low-density parity-check codes", IEEE Commun. Lett. , vol. 6, no. 9, pp. 385-387, Sep. 2002.

L. R. 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. 284-287, Mar. 1974.

A. Ashikhmin and S. Litsyn, "Simple MAP decoding of first order Reed-Muller and Hamming codes", IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1812-1818, Aug. 2003.

I. B. Djordjevic and B. Vasic, "An advanced direct detection receiver model", J. Opt. Commun., vol. 20, pp. 6-9, Feb. 2004.

F. McWilliams and N. Sloane, The Theory of Error Correcting Codes, New York: North Holland, 1977.

V. Nagarajan, N. Jayakumar, S. Khatri and O. Milenkovic, "High-throughput VLSI implementations of iterative decoders and related code construction problems", in Proc. IEEE GLOBECOM 2004, vol. 1, Dec. 2004, pp. 361-365.

R. G. Gallager, Low-Density Parity-Check Codes, Cambridge, MA: MIT, 1963.

O. A. Sab and V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems", in Proc. Optical Fiber Communication Conf. (OFC), vol. 3, 2001, pp. 280-282.

S. Sankaranarayanan and B. Vasic, "Iterative decoding of linear block codes", IEEE Trans. Inf. Theory,

S. Dolinar and D. Dilvasar, "Weight Distributions for Turbo Codes using Random and Nonrandom Permutations", Progr. Rep., JPL TDA, 42-122, 1995.

N. Ehtiati, et al. "Improved interleaver design for turbo coded intersymbol interference channels", in Proc. IEEE 58th Conf. Vehicular Technol. (VTC 2003), Oct. 2003, pp. 327-331.

H. Zhang and J. Moura, "The design of structured regular LDPC codes with large girth", in Proc. IEEE GLOBECOM 2003, vol. 7, 2003, pp. 4022-4027.

O. Milenkovic and S. Laendner, "Analysis of the cycle-structure of LDPC codes based on Latin squares", in Proc. 2004 IEEE Int. Conf. Communications , vol. 2, Jun. 2004, pp. 777-781.

R. Lidle and H. Niederreiter, Finite Fields, CA: Academic Press, 1997.

J. Fan, "Array codes as LDPC codes", in Proc. 2nd Int. Symp. Turbo Codes, 2000, pp. 543-546.

A. Ashikhmin, G. Kramer and S. ten Brink, "Extrinsic information transfer functions: Model and erasure channel properties", IEEE Trans. Inf. Theory, vol. 50, no. 11, pp. 2657-2673, Nov. 2004.

P. A. Humblet, et al. "On the bit error rate of lightwave systems with optical amplifiers", J. Lightw. Technol., vol. 9, no. 11, pp. 1576-1582, Nov. 1991.

I. B. Djordjevic and B. Vasic, "High code rate low-density parity-check codes for optical communication systems", IEEE Photon. Technol. Lett., vol. 16, no. 6, pp. 1600-1602, Jun. 2004.

R. Koetter, "Iterative coding techniques, pseudocodewords and their relationship", presented at the LANL Workshop on Applications of Statistical Physics to Coding Theory, Santa Fe, NM, Jan. 10-12, 2005.

T. Richardson, "Error floors of LDPC codes", presented at the 41st Allerton Conf. Communications, Control and Computing, Allerton, IL, Oct. 2003.

Cited By

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