Abstract

We present forward error correction systems based on soft-decision low-density parity check (LDPC) codes for applications in 100–400-Gbps optical transport networks. These systems are based on the low-complexity “adaptive degeneration” decoding algorithm, which we introduce in this paper, along with randomly-structured LDPC codes with block lengths from 30 000 to 60 000 bits and overhead (OH) from 6.7% to 33%. We also construct a 3600-bit prototype LDPC code with 20% overhead, and experimentally show that it has no error floor above a bit error rate (BER) of 10−15 using a field-programmable gate array (FPGA)-based hardware emulator. The projected net coding gain at a BER of 10−15 ranges from 9.6 dB at 6.7% OH to 11.2 dB at 33% OH. We also present application-specific integrated circuit synthesis results for these decoders in 28 nm fully depleted silicon on insulator technology, which show that they are capable of 400-Gbps operation with energy consumption of under 3 pJ per information bit.

© 2016 OAPA

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  1. A. Leven and L. Schmalen, “Status and recent advances on forward error correction technologies for lightwave systems,” J. Lightw. Technol., vol. 32, no. 16, pp. 2735–2750, 2014.
  2. K. Onoharaet al., “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1258–1267, 2010.
  3. T. J. Richardson, “Error-floors of LDPC codes,” in Proc. 41st Annu. Allerton Conf. Commun. Control Comput., Oct. 2003, pp. 1426–1435.
  4. D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.
  5. M. Liet al., “Low-overhead low-power-consumption LDPC-based FEC solution for next-generation high-speed optical systems,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.
  6. L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.
  7. B. S. G. Pillaiet al., “End-to-end energy modeling and analysis of long-haul coherent transmission systems,” J. Lightw. Technol., vol. 32, no. 18, pp. 3093–3111, 2014.
  8. A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.
  9. T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.
  10. F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.
  11. S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.
  12. F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.
  13. T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.
  14. G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.
  15. K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.
  16. K. Cushon, P. Larsson-Edefors, and P. Andrekson, “Energy-efficient soft-decision LDPC FEC for long-haul optical communication,” in Proc. Eur. Conf. Opt. Commun., Sep. 2015, pp. 1–3.
  17. L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.
  18. D. Changet al., “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.
  19. D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999.
  20. D. J. C. MacKay. (2002) “Gallager code resources,” [Online]. Available: http://www.inference.phy.cam.ac.uk/mackay/CodesFiles.html
  21. T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.
  22. E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.
  23. M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.
  24. Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.
  25. Xilinx Inc., 7 Series FPGAs Overview, 2015, v1.17.
  26. G. Marsaglia, “Xorshift RNGs,” J. Statist. Softw., vol. 8, no. 1, pp. 1–6, 2003.
  27. S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.
  28. D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.
  29. Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.
  30. L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightw. Technol., vol. 32, no. 10, pp. 1999–2002, 2014.
  31. C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

2016 (1)

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

2015 (2)

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Xilinx Inc., 7 Series FPGAs Overview, 2015, v1.17.

2014 (6)

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

B. S. G. Pillaiet al., “End-to-end energy modeling and analysis of long-haul coherent transmission systems,” J. Lightw. Technol., vol. 32, no. 18, pp. 3093–3111, 2014.

A. Leven and L. Schmalen, “Status and recent advances on forward error correction technologies for lightwave systems,” J. Lightw. Technol., vol. 32, no. 16, pp. 2735–2750, 2014.

G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightw. Technol., vol. 32, no. 10, pp. 1999–2002, 2014.

2010 (6)

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

K. Onoharaet al., “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1258–1267, 2010.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.

2009 (1)

E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.

2008 (1)

A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.

2006 (1)

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

2004 (1)

M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.

2003 (1)

G. Marsaglia, “Xorshift RNGs,” J. Statist. Softw., vol. 8, no. 1, pp. 1–6, 2003.

2001 (1)

T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.

1999 (1)

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999.

Agazzi, O. E.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Agrell, E.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Aguirre, A.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

Almenar, V.

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

Alvarado, A.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Anantharam, V.

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

Andrekson, P.

K. Cushon, P. Larsson-Edefors, and P. Andrekson, “Energy-efficient soft-decision LDPC FEC for long-haul optical communication,” in Proc. Eur. Conf. Opt. Commun., Sep. 2015, pp. 1–3.

Angarita, F.

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

Aref, V.

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Baas, B. M.

T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.

Boutillon, E.

G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.

Brännström, F.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Castrillon, M. A.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Cavus, E.

E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.

Chan Carusone, A.

A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.

Chang, D.

D. Changet al., “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Chen, Lei

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

Cho, Junho

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Cushon, K.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

K. Cushon, P. Larsson-Edefors, and P. Andrekson, “Energy-efficient soft-decision LDPC FEC for long-haul optical communication,” in Proc. Eur. Conf. Opt. Commun., Sep. 2015, pp. 1–3.

Daneshrad, B.

E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.

Darabiha, A.

A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.

Dave, S.

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Dolecek, L.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

Esker, L.

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Fong, W. H.

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

Fuerst, R.

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Funahashi, Y.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Giard, P.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

Goette, T. A.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Graell i Amat, A.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Gross, W. J.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

Häger, C.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Haymes, C. L.

E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.

Hemati, S.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

Hueda, M. R.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Kamendje, G.-A.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

Keszenheimer, J.

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Kschischang, F. R.

L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightw. Technol., vol. 32, no. 10, pp. 1999–2002, 2014.

A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.

Larsson-Edefors, P.

K. Cushon, P. Larsson-Edefors, and P. Andrekson, “Energy-efficient soft-decision LDPC FEC for long-haul optical communication,” in Proc. Eur. Conf. Opt. Commun., Sep. 2015, pp. 1–3.

Leduc-Primeau, F.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

Leroux, C.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

Leven, A.

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

A. Leven and L. Schmalen, “Status and recent advances on forward error correction technologies for lightwave systems,” J. Lightw. Technol., vol. 32, no. 16, pp. 2735–2750, 2014.

Li, M.

M. Liet al., “Low-overhead low-power-consumption LDPC-based FEC solution for next-generation high-speed optical systems,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Li, Yan

M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.

Li, Zongwang

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

Lin, S.

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

MacKay, D. J. C.

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999.

D. J. C. MacKay. (2002) “Gallager code resources,” [Online]. Available: http://www.inference.phy.cam.ac.uk/mackay/CodesFiles.html

Mannor, S.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

Marsaglia, G.

G. Marsaglia, “Xorshift RNGs,” J. Statist. Softw., vol. 8, no. 1, pp. 1–6, 2003.

Mo, Fan

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Mohsenin, T.

T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.

Morero, D. A.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Naderi, A.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

Nakamura, K.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Nikolic, B.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

Onohara, K.

K. Onoharaet al., “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1258–1267, 2010.

Pfister, H. D.

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

Pillai, B. S. G.

B. S. G. Pillaiet al., “End-to-end energy modeling and analysis of long-haul coherent transmission systems,” J. Lightw. Technol., vol. 32, no. 18, pp. 3093–3111, 2014.

Ramos, F. A.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

Raymond, A. J.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

Richardson, T. J.

T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.

T. J. Richardson, “Error-floors of LDPC codes,” in Proc. 41st Annu. Allerton Conf. Commun. Control Comput., Oct. 2003, pp. 1426–1435.

Rosener, D.

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Ryan, W. E.

M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.

Schmalen, L.

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

A. Leven and L. Schmalen, “Status and recent advances on forward error correction technologies for lightwave systems,” J. Lightw. Technol., vol. 32, no. 16, pp. 2735–2750, 2014.

Sharifi Tehrani, S.

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

Suikat, D.

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

Sundararajan, G.

G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.

Takumi, I.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Thesling, W.

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

Thibeault, C.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

Torres, V.

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

Truong, D. N.

T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.

Urbanke, R. L.

T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.

Usami, S.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Valls, J.

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

Wadayama, T.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Wainwright, M. J.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

Winstead, C.

G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.

Yagita, M.

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

Yang, M.

M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.

Zeng, Lingqi

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

Zhang, L. M.

L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightw. Technol., vol. 32, no. 10, pp. 1999–2002, 2014.

Zhang, Z.

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

Zhang, Zhengya

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

7 Series FPGAs Overview (1)

Xilinx Inc., 7 Series FPGAs Overview, 2015, v1.17.

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

K. Onoharaet al., “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 5, pp. 1258–1267, 2010.

IEEE J. Solid-State Circuits (2)

A. Darabiha, A. Chan Carusone, and F. R. Kschischang, “Power reduction techniques for LDPC decoders,” IEEE J. Solid-State Circuits, vol. 43, no. 8, pp. 1835–1845, 2008.

Z. Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “An efficient 10GBASE-T ethernet LDPC decoder design with low error floors,” IEEE J. Solid-State Circuits, vol. 45, no. 4, pp. 843–855, 2010.

IEEE Trans. Circuits Syst. I (1)

F. Angarita, J. Valls, V. Almenar, and V. Torres, “Reduced-complexity min-sum algorithm for decoding LDPC codes with low error-floor,” IEEE Trans. Circuits Syst. I, vol. 61, no. 7, pp. 2150–2158, 2014.

IEEE Trans. Circuits Syst. I Reg. Papers (1)

T. Mohsenin, D. N. Truong, and B. M. Baas, “A low-complexity message-passing algorithm for reduced routing congestion in LDPC decoders,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 57, no. 5, pp. 1048–1061, 2010.

IEEE Trans. Commun. (5)

T. Wadayama, K. Nakamura, M. Yagita, Y. Funahashi, S. Usami, and I. Takumi, “Gradient descent bit flipping algorithms for decoding LDPC codes,” IEEE Trans. Commun., vol. 58, no. 6, pp. 1610–1614, 2010.

G. Sundararajan, C. Winstead, and E. Boutillon, “Noisy gradient descent bit-flip decoding for LDPC codes,” IEEE Trans. Commun., vol. 62, no. 10, pp. 3385–3400, 2014.

E. Cavus, C. L. Haymes, and B. Daneshrad, “Low BER performance estimation of LDPC codes via application of importance sampling to trapping sets,” IEEE Trans. Commun., vol. 57, no. 7, pp. 1886–1888, 2009.

M. Yang, W. E. Ryan, and Yan Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Trans. Commun., vol. 52, no. 4, pp. 564–571, 2004.

Zongwang Li, Lei Chen, Lingqi Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, 2006.

IEEE Trans. Inf. Theory (3)

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399–431, 1999.

T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.

L. Dolecek, Zhengya Zhang, V. Anantharam, M. J. Wainwright, and B. Nikolic, “Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes,” IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 181–201, 2010.

IEEE Trans. Signal Process. (2)

S. Sharifi Tehrani, A. Naderi, G.-A. Kamendje, S. Hemati, S. Mannor, and W. J. Gross, “Majority-based tracking forecast memories for stochastic LDPC decoding,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4883–4896, 2010.

K. Cushon, S. Hemati, C. Leroux, S. Mannor, and W. J. Gross, “High-throughput energy-efficient LDPC decoders using differential binary message passing,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 619–631, 2014.

J. Lightw. Technol. (5)

L. Schmalen, V. Aref, Junho Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightw. Technol., vol. 33, no. 5, pp. 1109–1116, 2015.

B. S. G. Pillaiet al., “End-to-end energy modeling and analysis of long-haul coherent transmission systems,” J. Lightw. Technol., vol. 32, no. 18, pp. 3093–3111, 2014.

A. Leven and L. Schmalen, “Status and recent advances on forward error correction technologies for lightwave systems,” J. Lightw. Technol., vol. 32, no. 16, pp. 2735–2750, 2014.

L. M. Zhang and F. R. Kschischang, “Staircase codes with 6% to 33% overhead,” J. Lightw. Technol., vol. 32, no. 10, pp. 1999–2002, 2014.

D. A. Morero, M. A. Castrillon, A. Aguirre, M. R. Hueda, and O. E. Agazzi, “Design tradeoffs and challenges in practical coherent optical transceiver implementations,” J. Lightw. Technol., vol. 34, no. 1, pp. 121–136, 2016.

J. Statist. Softw. (1)

G. Marsaglia, “Xorshift RNGs,” J. Statist. Softw., vol. 8, no. 1, pp. 1–6, 2003.

Other (9)

S. Dave, L. Esker, Fan Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision forward error correction in a 40-nm ASIC for 100-Gbps OTN applications,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

D. J. C. MacKay. (2002) “Gallager code resources,” [Online]. Available: http://www.inference.phy.cam.ac.uk/mackay/CodesFiles.html

C. Häger, A. Graell i Amat, H. D. Pfister, A. Alvarado, F. Brännström, and E. Agrell, “On parameter optimization for staircase codes,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

T. J. Richardson, “Error-floors of LDPC codes,” in Proc. 41st Annu. Allerton Conf. Commun. Control Comput., Oct. 2003, pp. 1426–1435.

D. A. Morero, M. A. Castrillon, F. A. Ramos, T. A. Goette, O. E. Agazzi, and M. R. Hueda, “Non-concatenated FEC codes for ultra-high speed optical transport networks,” in Proc. IEEE Global Telecommun. Conf., Dec. 2011, pp. 1–5.

M. Liet al., “Low-overhead low-power-consumption LDPC-based FEC solution for next-generation high-speed optical systems,” in Proc. Opt. Fiber Commun. Conf. Exhib., Mar. 2015, pp. 1–3.

K. Cushon, P. Larsson-Edefors, and P. Andrekson, “Energy-efficient soft-decision LDPC FEC for long-haul optical communication,” in Proc. Eur. Conf. Opt. Commun., Sep. 2015, pp. 1–3.

F. Leduc-Primeau, A. J. Raymond, P. Giard, K. Cushon, C. Thibeault, and W. J. Gross, “High-throughput LDPC decoding using the RHS algorithm,” in Proc. Conf. Des. Archit. Signal Image Process., Oct. 2012, pp. 1–6.

D. Changet al., “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” in Proc. Opt. Fiber Commun. Conf. Expo. Nat. Fiber Opt. Eng. Conf., Mar. 2011, pp. 1–3.

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