Abstract

In this paper, we propose a rate-adaptive FEC scheme based on LDPC codes together with its software reconfigurable unified FPGA architecture. By FPGA emulation, we demonstrate that the proposed class of rate-adaptive LDPC codes based on shortening with an overhead from 25% to 42.9% provides a coding gain ranging from 13.08 dB to 14.28 dB at a post-FEC BER of 10−15 for BPSK transmission. In addition, the proposed rate-adaptive LDPC coding combined with higher-order modulations have been demonstrated including QPSK, 8-QAM, 16-QAM, 32-QAM, and 64-QAM, which covers a wide range of signal-to-noise ratios. Furthermore, we apply the unequal error protection by employing different LDPC codes on different bits in 16-QAM and 64-QAM, which results in additional 0.5dB gain compared to conventional LDPC coded modulation with the same code rate of corresponding LDPC code.

© 2016 Optical Society of America

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References

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  1. R. Rios-Muller, J. Renaudier, P. Brindel, C. Simonneau, P. Tran, A. Ghazisaeidi, I. Fernandez, L. Schemalen, and G. Charlet, “Optimized spectral efficient transceiver for 400-Gb/s single carrier transport,” in ECOC (2014), paper PD.4.2.
  2. J. Renaudier, R. Rios-Muller, P. Tran, L. Schemalen, and G. Charlet, “Spectrally efficient 1-Tb/s transceivers for long-haul optical systems,” J. Lightwave Technol. 33(7), 1452–1458 (2015).
    [Crossref]
  3. S. Randel, D. Pilori, S. Corteselli, G. Raybon, A. Adamiecki, A. Gnauck, S. Chandrasekhar, P. Winzer, L. Altenhain, A. Bielik, and R. Schemid, “All-electronic flexibly programmable 864-Gb/s single-carrier PDM-64-QAM,” in OFC/NFOEC (2014), paper Th5C.8.
  4. ITU-T G. 975. 1, Forward error correction for high bit-rate DWDM submarine system, 2004.
  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 OFC/NFOEC (2011), paper OTuN2.
  6. 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 OFC/NFOEC (2013), paper OM2B.4.
  7. D. Zou and I. B. Djordjevic, “FPGA implementation of concatenated non-binary QC-LDPC codes for high-speed optical transport,” Opt. Express 23(11), 14501–14509 (2015).
    [Crossref] [PubMed]
  8. A. Leven, V. Aref, J. Cho, D. Suikat, D. Rosener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightwave Technol. 33(5), 1109–1116 (2015).
    [Crossref]
  9. (2015, Jul.). Technology options for 400G implementation [On- line], http://www.oiforum.com/wp-content/uploads/OIF-Tech- Options-400G–01.0.pdf .
  10. R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Modulation order and code rate optimization for digital coherent transceivers using generalized mutual information,” in ECOC (2015), paper Mo. 3.3.4.
  11. T. Koike-Akino, K. Kojima, D. Millar, K. Parsons, T. Yoshida, and T. Sugihara, “Pareto-efficient set of modulation and coding based on RGMI in nonlinear fiber transmissions,” in OFC/NFOEC (2016), paper Th1D.4.
  12. D. Zou and I. B. Djordjevic, “An FPGA design of generalized low-density parity-check codes for rate-adaptive optical transport networks,” Proc. SPIE 9773, 97730M (2016).
    [Crossref]
  13. 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]
  14. 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]

2016 (1)

D. Zou and I. B. Djordjevic, “An FPGA design of generalized low-density parity-check codes for rate-adaptive optical transport networks,” Proc. SPIE 9773, 97730M (2016).
[Crossref]

2015 (3)

2010 (1)

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]

Arabaci, M.

Aref, V.

Charlet, G.

Cho, J.

Djordjevic, I. B.

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]

Leven, A.

Marcoccia, R. M.

Renaudier, J.

Rios-Muller, R.

Rosener, D.

Saunders, R.

Schemalen, L.

Suikat, D.

Tran, P.

Zou, D.

D. Zou and I. B. Djordjevic, “An FPGA design of generalized low-density parity-check codes for rate-adaptive optical transport networks,” Proc. SPIE 9773, 97730M (2016).
[Crossref]

D. Zou and I. B. Djordjevic, “FPGA implementation of concatenated non-binary QC-LDPC codes for high-speed optical transport,” Opt. Express 23(11), 14501–14509 (2015).
[Crossref] [PubMed]

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]

J. Lightwave Technol. (2)

Opt. Express (2)

Proc. SPIE (1)

D. Zou and I. B. Djordjevic, “An FPGA design of generalized low-density parity-check codes for rate-adaptive optical transport networks,” Proc. SPIE 9773, 97730M (2016).
[Crossref]

Other (8)

R. Rios-Muller, J. Renaudier, P. Brindel, C. Simonneau, P. Tran, A. Ghazisaeidi, I. Fernandez, L. Schemalen, and G. Charlet, “Optimized spectral efficient transceiver for 400-Gb/s single carrier transport,” in ECOC (2014), paper PD.4.2.

(2015, Jul.). Technology options for 400G implementation [On- line], http://www.oiforum.com/wp-content/uploads/OIF-Tech- Options-400G–01.0.pdf .

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Modulation order and code rate optimization for digital coherent transceivers using generalized mutual information,” in ECOC (2015), paper Mo. 3.3.4.

T. Koike-Akino, K. Kojima, D. Millar, K. Parsons, T. Yoshida, and T. Sugihara, “Pareto-efficient set of modulation and coding based on RGMI in nonlinear fiber transmissions,” in OFC/NFOEC (2016), paper Th1D.4.

S. Randel, D. Pilori, S. Corteselli, G. Raybon, A. Adamiecki, A. Gnauck, S. Chandrasekhar, P. Winzer, L. Altenhain, A. Bielik, and R. Schemid, “All-electronic flexibly programmable 864-Gb/s single-carrier PDM-64-QAM,” in OFC/NFOEC (2014), paper Th5C.8.

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

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 OFC/NFOEC (2011), paper OTuN2.

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 OFC/NFOEC (2013), paper OM2B.4.

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Figures (4)

Fig. 1
Fig. 1 FPGA architecture of rate-adaptive LDPC-coded modulation: (a) overall architecture, (b) architecture of LDPC decoder, and (c) architecture of check node processor.
Fig. 2
Fig. 2 BER performance curves for LDPC coded modulation with various code rates and modulation formats.
Fig. 3
Fig. 3 BER vs. SNR performance for LDPC coded: (a) uncoded, (b) LDPC-coded cases.
Fig. 4
Fig. 4 BER performance vs. SNR with maximum number of layered iterations set to 45.

Tables (2)

Tables Icon

Table 1 Coding gains (in dB) of LDPC-coded modulation scheme.

Tables Icon

Table 2 Logic Utilization and Power consumption summary of LDPC-coded modulation.

Equations (6)

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LL R s i =log(P( s i |r)/P( s 0 |r))
LL R b j =log( s i ( b j )==0 P( s i |r) / s i ( b j )==1 P( s i |r) )
LL R b j = max * ( s i ( b j )==0 LL R s i ) max * ( s i ( b j )==1 LL R s i )
L v k,l = L v + l ' R cv k, l
L vc k,l = L v + l l R cv k, l
R cv k,l =s× v'v sign( L v'c k,l ) min v'v | L v'c k,l |

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