Abstract

In this paper, we propose a soft-decision-based FEC scheme that is the concatenation of a non-binary LDPC code and hard-decision FEC code. The proposed NB-LDPC + RS with overhead of 27.06% provides a superior NCG of 11.9dB at a post-FEC BER of 10−15. As a result, the proposed NB-LDPC codes represent the strong FEC candidate of soft-decision FEC for beyond 100Gb/s optical transmission systems.

© 2015 Optical Society of America

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References

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  1. ITU-T G. 975. 1, Forward error correction for high bit-rate DWDM submarine system, 2004.
  2. S. Dave, L. Esker, F. Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN Applications,” in Optical Fiber Communication Conference (OFC/NFOEC’2011), paper JWA14.
    [Crossref]
  3. Y. Miyata, W. Matsumoto, H. Yoshida, and T. Mizuochi, “Efficient FEC for optical communications using concatenated codes to combat error-floor,” in Optical Fiber Communication Conference (OFC/NFOEC’2008), paper OTuE4.
  4. N. Kamiya and S. Shioiri, “Concatenated QC-LDPC and SPC codes for 100 Gbps ultra long-haul optical transmission system,” in Optical Fiber Communication Conference (OFC/NFOEC’2010), paper OThL2.
    [Crossref]
  5. D. Chang, F. Yu, Z. Xiao, Y. Li, N. Stojanovic, C. Xie, X. Shi, X. Xu, and Q. Xiong, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” in Optical Fiber Communication Conference (OFC/NFOEC’2011), paper OTuN2.
  6. D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F. N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, and Q. Xiong, “LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission,” in Optical Fiber Communication Conference (OFC/NFOEC’2012), paper OW1H.4.
    [Crossref]
  7. K. Sugihara, Y. Miyata, T. Sugihara, K. Kubo, H. Yoshida, W. Matsumoto, and T. Mizuochi, “A spatially-coupled type LDPC code with an NCG of 12dB for optical transmission beyond 100 Gb/s,” in Optical Fiber Communication Conference (OFC/NFOEC’2013), paper OM2B.4.
  8. D. Zou and I. B. Djordjevic, “FPGA implementation of high-performance QC-LDPC decoder for optical communications,” Proc. SPIE 9388, 93880P (2015).
    [Crossref]
  9. C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.
  10. I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005).
    [Crossref]
  11. M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express 18(3), 1820–1832 (2010).
    [Crossref] [PubMed]
  12. B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
    [Crossref]
  13. B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
    [Crossref]
  14. M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
    [Crossref]
  15. M. Davey and D. MacKay, “Low density parity check codes over GF(q),” IEEE Commun. Lett. 2(6), 165–167 (1998).
    [Crossref]
  16. L. Barnault and D. Declercq, “Fast decoding algorithm for LDPC over GF(2^q),” in Proceedings of IEEE Information Theory Workshop (IEEE, 2003) pp. 70–73.
    [Crossref]
  17. D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
    [Crossref]
  18. C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
    [Crossref]
  19. D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
    [Crossref]
  20. V. Savin, “Min-max decoding for non-binary LDPC codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2008) pp. 960–964.
  21. D. E. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes,” in Proceedings of IEEE Signal Processing Systems (IEEE, 2004) pp. 107–112.
    [Crossref]
  22. Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
    [Crossref]
  23. X. Zhang and F. Cai, “Reduced-complexity decoder architecture for non-binary LDPC codes,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(7), 1229–1238 (2011).
  24. E. D. Mastrovito, “VLSI designs for multiplication over finite fields GF(2m),” in Sixth Symp. Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-6, 1988) pp. 297–309.
  25. H. Lee, “A high-speed low-complexity Reed-Solomon decoder for optical communications,” IEEE Trans. Circ. Syst. 52(8), 461–465 (2005).
    [Crossref]
  26. S. B. Wicker, Error Control Systems for Digital Communication and Storage (Prentice Hall, 1995).

2015 (1)

D. Zou and I. B. Djordjevic, “FPGA implementation of high-performance QC-LDPC decoder for optical communications,” Proc. SPIE 9388, 93880P (2015).
[Crossref]

2013 (1)

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

2011 (1)

X. Zhang and F. Cai, “Reduced-complexity decoder architecture for non-binary LDPC codes,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(7), 1229–1238 (2011).

2010 (1)

2009 (3)

C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
[Crossref]

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

2007 (2)

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

2005 (2)

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005).
[Crossref]

H. Lee, “A high-speed low-complexity Reed-Solomon decoder for optical communications,” IEEE Trans. Circ. Syst. 52(8), 461–465 (2005).
[Crossref]

2004 (1)

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[Crossref]

1998 (1)

M. Davey and D. MacKay, “Low density parity check codes over GF(q),” IEEE Commun. Lett. 2(6), 165–167 (1998).
[Crossref]

Arabaci, M.

Barnault, L.

L. Barnault and D. Declercq, “Fast decoding algorithm for LDPC over GF(2^q),” in Proceedings of IEEE Information Theory Workshop (IEEE, 2003) pp. 70–73.
[Crossref]

Cai, F.

X. Zhang and F. Cai, “Reduced-complexity decoder architecture for non-binary LDPC codes,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(7), 1229–1238 (2011).

Chen, Y.

C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.

Chou, H.

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

Davey, M.

M. Davey and D. MacKay, “Low density parity check codes over GF(q),” IEEE Commun. Lett. 2(6), 165–167 (1998).
[Crossref]

Declercq, D.

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

L. Barnault and D. Declercq, “Fast decoding algorithm for LDPC over GF(2^q),” in Proceedings of IEEE Information Theory Workshop (IEEE, 2003) pp. 70–73.
[Crossref]

Ding, Z.

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

Djordjevic, I. B.

D. Zou and I. B. Djordjevic, “FPGA implementation of high-performance QC-LDPC decoder for optical communications,” Proc. SPIE 9388, 93880P (2015).
[Crossref]

M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express 18(3), 1820–1832 (2010).
[Crossref] [PubMed]

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005).
[Crossref]

Fossorier, M.

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

Fossorier, M. P. C.

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[Crossref]

Ghaffar, K. A.

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

Hocevar, D. E.

D. E. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes,” in Proceedings of IEEE Signal Processing Systems (IEEE, 2004) pp. 107–112.
[Crossref]

Kaneda, N.

C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.

Kang, J.

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

Lee, H.

H. Lee, “A high-speed low-complexity Reed-Solomon decoder for optical communications,” IEEE Trans. Circ. Syst. 52(8), 461–465 (2005).
[Crossref]

C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.

Liao, K.

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

Lin, S.

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

MacKay, D.

M. Davey and D. MacKay, “Low density parity check codes over GF(q),” IEEE Commun. Lett. 2(6), 165–167 (1998).
[Crossref]

Marcoccia, R. M.

Marnane, W.

C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
[Crossref]

Popovici, E.

C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
[Crossref]

Saunders, R.

Savin, V.

V. Savin, “Min-max decoding for non-binary LDPC codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2008) pp. 960–964.

Seok, C.

C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.

Song, S.

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

Spagnol, C.

C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
[Crossref]

Tai, Y.

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

Ueng, Y.

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

Vasic, B.

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005).
[Crossref]

Xu, M.

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

Yang, C.

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

Zhang, X.

X. Zhang and F. Cai, “Reduced-complexity decoder architecture for non-binary LDPC codes,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(7), 1229–1238 (2011).

Zhou, B.

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

Zou, D.

D. Zou and I. B. Djordjevic, “FPGA implementation of high-performance QC-LDPC decoder for optical communications,” Proc. SPIE 9388, 93880P (2015).
[Crossref]

IEEE Commun. Lett. (1)

M. Davey and D. MacKay, “Low density parity check codes over GF(q),” IEEE Commun. Lett. 2(6), 165–167 (1998).
[Crossref]

IEEE Photon. Technol. Lett. (1)

I. B. Djordjevic and B. Vasic, “Nonbinary LDPC codes for optical communication systems,” IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005).
[Crossref]

IEEE Trans. Circ. Syst. (2)

C. Spagnol, E. Popovici, and W. Marnane, “Hardware implementation of GF(2m) LDPC decoders,” IEEE Trans. Circ. Syst. 56(12), 2609–2620 (2009).
[Crossref]

H. Lee, “A high-speed low-complexity Reed-Solomon decoder for optical communications,” IEEE Trans. Circ. Syst. 52(8), 461–465 (2005).
[Crossref]

IEEE Trans. Commun. (4)

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

D. Declercq and M. Fossorier, “Decoding algorithm for nonbinary LDPC codes over GF(q),” IEEE Trans. Commun. 55(4), 633–643 (2007).
[Crossref]

B. Zhou, J. Kang, S. Song, S. Lin, K. A. Ghaffar, and M. Xu, “Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersion,” IEEE Trans. Commun. 57(6), 1652–1662 (2009).
[Crossref]

B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, “High performance non-binary quasi-cyclic LDPC codes on Euclidean geometry,” IEEE Trans. Commun. 57(5), 1298–1311 (2009).
[Crossref]

IEEE Trans. Inf. Theory (1)

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[Crossref]

IEEE Trans. Signal Process. (1)

Y. Ueng, K. Liao, H. Chou, and C. Yang, “A high-throughput trellis-based layered decoding architecture for non-binary LDPC codes using Max-Log-QSPA,” IEEE Trans. Signal Process. 61(11), 2940–2951 (2013).
[Crossref]

IEEE Trans. Very Large Scale Integr. (VLSI) Syst. (1)

X. Zhang and F. Cai, “Reduced-complexity decoder architecture for non-binary LDPC codes,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(7), 1229–1238 (2011).

Opt. Express (1)

Proc. SPIE (1)

D. Zou and I. B. Djordjevic, “FPGA implementation of high-performance QC-LDPC decoder for optical communications,” Proc. SPIE 9388, 93880P (2015).
[Crossref]

Other (13)

C. Seok, H. Lee, N. Kaneda, and Y. Chen, “Concatenated non-binary LDPC and HD-FEC codes for 100 Gb/s optical transport system,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2012), pp. 1783–1786.

ITU-T G. 975. 1, Forward error correction for high bit-rate DWDM submarine system, 2004.

S. Dave, L. Esker, F. Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN Applications,” in Optical Fiber Communication Conference (OFC/NFOEC’2011), paper JWA14.
[Crossref]

Y. Miyata, W. Matsumoto, H. Yoshida, and T. Mizuochi, “Efficient FEC for optical communications using concatenated codes to combat error-floor,” in Optical Fiber Communication Conference (OFC/NFOEC’2008), paper OTuE4.

N. Kamiya and S. Shioiri, “Concatenated QC-LDPC and SPC codes for 100 Gbps ultra long-haul optical transmission system,” in Optical Fiber Communication Conference (OFC/NFOEC’2010), paper OThL2.
[Crossref]

D. Chang, F. Yu, Z. Xiao, Y. Li, N. Stojanovic, C. Xie, X. Shi, X. Xu, and Q. Xiong, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” in Optical Fiber Communication Conference (OFC/NFOEC’2011), paper OTuN2.

D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F. N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, and Q. Xiong, “LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission,” in Optical Fiber Communication Conference (OFC/NFOEC’2012), paper OW1H.4.
[Crossref]

K. Sugihara, Y. Miyata, T. Sugihara, K. Kubo, H. Yoshida, W. Matsumoto, and T. Mizuochi, “A spatially-coupled type LDPC code with an NCG of 12dB for optical transmission beyond 100 Gb/s,” in Optical Fiber Communication Conference (OFC/NFOEC’2013), paper OM2B.4.

L. Barnault and D. Declercq, “Fast decoding algorithm for LDPC over GF(2^q),” in Proceedings of IEEE Information Theory Workshop (IEEE, 2003) pp. 70–73.
[Crossref]

V. Savin, “Min-max decoding for non-binary LDPC codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2008) pp. 960–964.

D. E. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes,” in Proceedings of IEEE Signal Processing Systems (IEEE, 2004) pp. 107–112.
[Crossref]

E. D. Mastrovito, “VLSI designs for multiplication over finite fields GF(2m),” in Sixth Symp. Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-6, 1988) pp. 297–309.

S. B. Wicker, Error Control Systems for Digital Communication and Storage (Prentice Hall, 1995).

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Figures (6)

Fig. 1
Fig. 1 Fixed-point simulation over BI-AWGN.
Fig. 2
Fig. 2 Non-binary LDPC decoder architecture: (a) overall architecture, (b) architecture of CNU, and (c) architecture of BCJR-based min-max processor.
Fig. 3
Fig. 3 Overall architecture of Reed-Solomon decoder.
Fig. 4
Fig. 4 BER performances of various non-binary LDPC decoders.
Fig. 5
Fig. 5 Error bits histogram of the post-LDPC decoder.
Fig. 6
Fig. 6 BER performances of concatenated non-binary LDPC codes.

Tables (2)

Tables Icon

Table 1 Utilization Summary of LDPC Decoders and Reed-Solomon Decoder.

Tables Icon

Table 2 Utilization Summary of Proposed Concatenated Decoder.

Equations (6)

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

H NB,γp×ρp = W γp×ρp H B,γp×ρp =( w 0,0 w 0,ρ1 w γ1,0 w γ1,ρ1 )( A 0,0 A 0,ρ1 A γ1,0 A γ1,ρ1 ).
L v k,l ( a )= L v ( a )+ l' R cv k,l' ( a ) .
c ^ v =arg min aGF( q ) L v k,l ( a ).
L vc k,l ( a )= L v ( a )+ l'l R cv k,l' ( a ) .
L vc k,l ( a )= L vc k,l ( a ) min a'GF( q ) ( L vc k,l ( a' ) ).
R cv k,l ( a )= min a v' L( c| a v =a ) ( max v'N( c )/v L v'c k,l ( a v' ) ).

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