Abstract

In this paper, we propose a unified field-programmable gate array (FPGA) structure for a rate-adaptive forward error correction (FEC) scheme based on spatially coupled (SC) LDPC codes derived from quasi-cyclic (QC) LDPC codes. We described the unified decoder structure in detail and showed that the rate adaptation can be achieved by a controller on-the-fly. By FPGA based emulation, the results show that, with comparable complexity, the SC codes provide larger coding gain. The implemented unified structure can be employed for any template QC-LDPC code to achieve a spatially-coupling based code-rate adaptation scheme.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999).
    [Crossref]
  2. M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
    [Crossref]
  3. S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
    [Crossref]
  4. 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.
  5. 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 OFC/NFOEC (2012), pp. 1−3.
  6. A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
    [Crossref]
  7. L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, and A. Leven, “Spatially coupled soft-decision error correction for future lightwave systems,” J. Lightwave Technol. 33(5), 1109–1116 (2015).
    [Crossref]
  8. C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
    [Crossref]
  9. V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
    [Crossref]
  10. X. Sun, D. Zou, Z. Qu, and I. B. Djordjevic, “Run-time reconfigurable adaptive LDPC coding for optical channels,” Opt. Express 26(22), 29319–29329 (2018).
    [Crossref] [PubMed]
  11. 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]
  12. C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
    [Crossref]

2018 (1)

2015 (1)

2014 (1)

V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
[Crossref]

2013 (1)

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

2012 (1)

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

2011 (1)

S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
[Crossref]

2010 (1)

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

2008 (1)

C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
[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]

1999 (1)

A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999).
[Crossref]

Aref, V.

Chandrasetty, V. A.

V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
[Crossref]

Chen, X.

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

Cho, J.

Corazza, G. E.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Costello, D. J.

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

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]

Iyengar, A. R.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Jimenez Felstrom, A.

A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999).
[Crossref]

Johnson, S. J.

V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
[Crossref]

Kudekar, S.

S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
[Crossref]

Lau, F. C.

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

Lechner, G.

V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
[Crossref]

Lentmaier, M.

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

Leven, A.

Lin, S. Y.

C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
[Crossref]

Papaleo, M.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Qu, Z.

Richardson, T. J.

S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
[Crossref]

Rösener, D.

Schmalen, L.

Sham, C. W.

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

Shieh, M. D.

C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
[Crossref]

Siegel, P. H.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Sridharan, A.

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

Suikat, D.

Sun, X.

Tam, W. M.

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

Urbanke, R. L.

S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
[Crossref]

Vanelli-Coralli, A.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Wey, C. L.

C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
[Crossref]

Wolf, J. K.

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

Zhao, Y.

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

Zigangirov, K. S.

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999).
[Crossref]

Zou, D.

IEEE Trans. Circuits Syst. I Regul. Pap. (2)

C. W. Sham, X. Chen, F. C. Lau, Y. Zhao, and W. M. Tam, “A 2.0 Gb/s throughput decoder for QC-LDPC convolutional codes,” IEEE Trans. Circuits Syst. I Regul. Pap. 60(7), 1857–1869 (2013).
[Crossref]

C. L. Wey, M. D. Shieh, and S. Y. Lin, “Algorithms of finding the first two minimum values and their hardware implementation,” IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3430–3437 (2008).
[Crossref]

IEEE Trans. Inf. Theory (5)

A. R. Iyengar, M. Papaleo, P. H. Siegel, J. K. Wolf, A. Vanelli-Coralli, and G. E. Corazza, “Windowed decoding of protograph-based LDPC convolutional codes over erasure channels,” IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012).
[Crossref]

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]

A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix,” IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999).
[Crossref]

M. Lentmaier, A. Sridharan, D. J. Costello, and K. S. Zigangirov, “Iterative decoding threshold analysis for LDPC convolutional codes,” IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010).
[Crossref]

S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC,” IEEE Trans. Inf. Theory 57(2), 803–834 (2011).
[Crossref]

IET Commun. (1)

V. A. Chandrasetty, S. J. Johnson, and G. Lechner, “Memory-efficient quasi-cyclic spatially coupled low-density parity-check and repeat-accumulate codes,” IET Commun. 8(17), 3179–3188 (2014).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Other (2)

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.

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 OFC/NFOEC (2012), pp. 1−3.

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Figures (5)

Fig. 1
Fig. 1 High-level schematic diagram of the emulation platform.
Fig. 2
Fig. 2 FPGA architecture diagram of the unified QC/SC-LDPC decoder.
Fig. 3
Fig. 3 Hsc representation of the example SC code consisting of three (3,15,1129) QC codes with coupling length of m = 5.
Fig. 4
Fig. 4 The lcvBRAM organization for the SC-LDPC code.
Fig. 5
Fig. 5 FPGA emulation BER performance of proposed SC-LDPC codes.

Equations (2)

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H QC =[ I( O 0,0 ) I( O 0,1 ) I( O 0,K1 ) I( O 1,0 ) I( O 1,1 ) I( O 1,K1 ) I( O J1,0 ) I( O J1,1 ) I( O J1,K1 ) ],
H SC =[ I( O 0,0 ) I( O 0,10 ) I( O 0,14 ) I( O 1,0 ) I( O 1,10 ) I( O 1,14 ) I( O 2,0 ) I( O 2,10 ) I( O 2,14 ) I( O 0,0 ) I( O 0,4 ) I( O 0,10 ) I( O 0,14 ) I( O 1,0 ) I( O 1,4 ) I( O 1,10 ) I( O 1,14 ) I( O 2,0 ) I( O 2,4 ) I( O 2,10 ) I( O 2,14 ) I( O 0,0 ) I( O 0,4 ) I( O 0,14 ) I( O 1,0 ) I( O 1,4 ) I( O 1,14 ) I( O 2,0 ) I( O 2,4 ) I( O 2,14 ) ].

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