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.

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.

(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.

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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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