Abstract

The deep learning-based decoder of polar codes is investigated over free space optical (FSO) turbulence channel for the first time. The feedforward neural networks (NN) are adopted to establish the decoder and some custom layers are designed to train the NN decoder over the turbulence channel. The tanh-based modified log-likelihood ratio (LLR) is proposed as the input of NN decoder, which has faster convergence and better bit error rate (BER) performance compared with the standard LLR input. The simulation results show that the BER performance of NN decoder with tanh-based modified LLR is close to the conventional successive cancellation list (SCL) decoder over the turbulence channel, which verifies that the NN decoder with tanh-based modified LLR can learn the encoding rule of polar codes and the characteristics of turbulence channel. Furthermore, the turbulence-stability is investigated and the trained NN decoder in a fixed turbulence condition also has stable performance in other turbulence conditions.

© 2020 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. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).
  2. T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
    [Crossref]
  3. T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
    [Crossref]
  4. J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Trans. Inf. Theory 35(5), 976–987 (1989).
    [Crossref]
  5. E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
    [Crossref]
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    [Crossref]
  7. 3GPP TS 38.212 Technical Specification Group Radio Access Network, NR, Multiplexing and Channel Coding, 2017.
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    [Crossref]
  12. J. Li and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003- Fall Vehicular Technology Conference 2003 IEEE 58th, 168–172 (2003).
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    [Crossref]
  14. J. Fang, M. Bi, S. Xiao, G. Yang, C. Li, Y. Zhang, T. Huang, and W. Hu, “Performance investigation of the polar coded FSO communication system over turbulence channel,” Appl. Opt. 57(25), 7378–7384 (2018).
    [Crossref]
  15. J. Fang, M. Bi, S. Xiao, G. Yang, L. Liu, Y. Zhang, and W. Hu, “Polar-coded MIMO FSO communication system over gamma-gamma turbulence channel with spatially correlated fading,” J. Opt. Commun. Netw. 10(11), 915–923 (2018).
    [Crossref]
  16. I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
    [Crossref]
  17. L. C. Andrews and R. L. Phillips, Laser beam propagation through random media, (SPIE Press, 1998).
  18. Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012).
  19. X. Zhu and J. Kahn, “Free-space optical communication through atomospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
    [Crossref]

2018 (4)

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

J. Fang, M. Bi, S. Xiao, G. Yang, C. Li, Y. Zhang, T. Huang, and W. Hu, “Performance investigation of the polar coded FSO communication system over turbulence channel,” Appl. Opt. 57(25), 7378–7384 (2018).
[Crossref]

J. Fang, M. Bi, S. Xiao, G. Yang, L. Liu, Y. Zhang, and W. Hu, “Polar-coded MIMO FSO communication system over gamma-gamma turbulence channel with spatially correlated fading,” J. Opt. Commun. Netw. 10(11), 915–923 (2018).
[Crossref]

2017 (1)

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

2015 (1)

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

2014 (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

2009 (1)

E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

2007 (1)

2002 (1)

X. Zhu and J. Kahn, “Free-space optical communication through atomospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

1989 (1)

J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Trans. Inf. Theory 35(5), 976–987 (1989).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser beam propagation through random media, (SPIE Press, 1998).

Arikan, E.

E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

Bi, M.

Blaum, M.

J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Trans. Inf. Theory 35(5), 976–987 (1989).
[Crossref]

Brind, S. t.

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brind, “On deep learning-based channel decoding,” in Proc. Annual Conference on Information Sciences and Systems 2017 IEEE 51st1–6 (2017).

S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brind, “Scaling deep learning-based decoding of polar codes via partitioning,” in Proc. IEEE Global Commun. Conf. (GLOBECOM)1–6 (2017).

Bruck, J.

J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Trans. Inf. Theory 35(5), 976–987 (1989).
[Crossref]

Burshtein, D.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

Cambria, E.

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

Cammerer, S.

S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brind, “Scaling deep learning-based decoding of polar codes via partitioning,” in Proc. IEEE Global Commun. Conf. (GLOBECOM)1–6 (2017).

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brind, “On deep learning-based channel decoding,” in Proc. Annual Conference on Information Sciences and Systems 2017 IEEE 51st1–6 (2017).

Djordjevic, I. B.

Doan, N.

N. Doan, S. A. Hashemi, and W. J. Gross, “Neural successive cancellation decoding of polar codes,” in Proc. International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2018 IEEE 19th1–5 (2018).

Doulamis, A.

A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).

Doulamis, N.

A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).

ery, Y. B.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

Fang, J.

Gao, F.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Ghassemlooy, Z.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012).

Gross, W. J.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

N. Doan, S. A. Hashemi, and W. J. Gross, “Neural successive cancellation decoding of polar codes,” in Proc. International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2018 IEEE 19th1–5 (2018).

Gruber, T.

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brind, “On deep learning-based channel decoding,” in Proc. Annual Conference on Information Sciences and Systems 2017 IEEE 51st1–6 (2017).

S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brind, “Scaling deep learning-based decoding of polar codes via partitioning,” in Proc. IEEE Global Commun. Conf. (GLOBECOM)1–6 (2017).

Hashemi, S. A.

N. Doan, S. A. Hashemi, and W. J. Gross, “Neural successive cancellation decoding of polar codes,” in Proc. International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2018 IEEE 19th1–5 (2018).

Hazarika, D.

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

Hoydis, J.

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brind, “On deep learning-based channel decoding,” in Proc. Annual Conference on Information Sciences and Systems 2017 IEEE 51st1–6 (2017).

S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brind, “Scaling deep learning-based decoding of polar codes via partitioning,” in Proc. IEEE Global Commun. Conf. (GLOBECOM)1–6 (2017).

Hu, W.

Huang, T.

Jiang, T.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Jin, S.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Kahn, J.

X. Zhu and J. Kahn, “Free-space optical communication through atomospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

Li, C.

Li, J.

J. Li and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003- Fall Vehicular Technology Conference 2003 IEEE 58th, 168–172 (2003).

Liu, L.

Lugosch, L.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

Marciano, E.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

Nachmani, E.

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser beam propagation through random media, (SPIE Press, 1998).

Popoola, W.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012).

Poria, S.

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

Protopapadakis, E.

A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).

Rajbhandari, S.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012).

Tal, I.

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

J. Li and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003- Fall Vehicular Technology Conference 2003 IEEE 58th, 168–172 (2003).

Vardy, A.

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

Voulodimos, A.

A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).

Wang, H.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Wang, T.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Wen, C. K.

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

Xiao, S.

Yang, G.

Young, T.

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

Zhang, Y.

Zhu, X.

X. Zhu and J. Kahn, “Free-space optical communication through atomospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

Appl. Opt. (1)

China Commun. (1)

T. Wang, C. K. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep learning for wireless physical layer: Opportunities and challenges,” China Commun. 14(11), 92–111 (2017).
[Crossref]

IEEE Commun. Surv. Tutorials (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

IEEE Comput. Intell. Mag. (1)

T. Young, D. Hazarika, S. Poria, and E. Cambria, “Recent trends in deep learning based natural language processing [review article],” IEEE Comput. Intell. Mag. 13(3), 55–75 (2018).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

E. Nachmani, E. Marciano, L. Lugosch, W. J. Gross, D. Burshtein, and Y. B. ery, “Deep learning methods for improved decoding of linear codes,” IEEE J. Sel. Top. Signal Process. 12(1), 119–131 (2018).
[Crossref]

IEEE Trans. Commun. (1)

X. Zhu and J. Kahn, “Free-space optical communication through atomospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[Crossref]

IEEE Trans. Inf. Theory (3)

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Trans. Inf. Theory 35(5), 976–987 (1989).
[Crossref]

J. Opt. Commun. Netw. (1)

Opt. Express (1)

Other (8)

A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep learning for computer vision: A brief review,” Computational intelligence and neuroscience, (2018).

3GPP TS 38.212 Technical Specification Group Radio Access Network, NR, Multiplexing and Channel Coding, 2017.

T. Gruber, S. Cammerer, J. Hoydis, and S. t. Brind, “On deep learning-based channel decoding,” in Proc. Annual Conference on Information Sciences and Systems 2017 IEEE 51st1–6 (2017).

S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brind, “Scaling deep learning-based decoding of polar codes via partitioning,” in Proc. IEEE Global Commun. Conf. (GLOBECOM)1–6 (2017).

N. Doan, S. A. Hashemi, and W. J. Gross, “Neural successive cancellation decoding of polar codes,” in Proc. International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2018 IEEE 19th1–5 (2018).

L. C. Andrews and R. L. Phillips, Laser beam propagation through random media, (SPIE Press, 1998).

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling with MATLAB (CRC Press, 2012).

J. Li and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003- Fall Vehicular Technology Conference 2003 IEEE 58th, 168–172 (2003).

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Figures (8)

Fig. 1.
Fig. 1. Block diagrams of deep learning-based decoding of polar coded FSO communication system
Fig. 2.
Fig. 2. NN decoder and some custom layers designed for training the network
Fig. 3.
Fig. 3. BER performance of (16, 8) polar codes over weak turbulence (standard LLR is input into the NN decoder)
Fig. 4.
Fig. 4. Probability distribution of LLR over weak turbulence channel with different SNR
Fig. 5.
Fig. 5. Example of the tanh function with scale parameter s (s = 10)
Fig. 6.
Fig. 6. NN decoder training loss with and without tanh-based modified LLR over weak turbulence channel
Fig. 7.
Fig. 7. BER performance of NN decoder with tanh-based modified LLR over (a) weak, (b) moderate, and (c) strong turbulence conditions respectively.
Fig. 8.
Fig. 8. Turbulence-stability of NN decoder with tanh-based modified LLR over (a) weak, (b) moderate, and (c) strong turbulence conditions respectively.

Tables (3)

Tables Icon

Table 1. Turbulence conditions

Tables Icon

Table 2. Layout of the 128-64-32 decoder

Tables Icon

Table 3. Custom layers for training the NN decoder

Equations (14)

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

y(t)=ηI(t)x(t)+n(t),
f(I)=2(αβ)(α+β)/2Γ(α)Γ(β)I(α+β)/21Kαβ(2αβI),
α = [exp(0.49σR2(1+1.11σR12/5)7/6)1]1,
β = [exp(0.51σR2(1+0.69σR12/5)5/6)1]1,
σR2=1.23Cn2k7/6D11/6,
σI2=E[I2]E[I]21=1α+1β+1αβ,
LLR[x(t)]=lnp[x(t)=0|y(t)]p[x(t)=1|y(t)]=2y(t)I(t)+I(t)22σ2.
GN=Fn,n=log2N,
F=[1011].
c1N=u1NGN,
y=g(iθixi + θ0).
w = f(v;θ) = out(f(Q1)((f(0)(v)))),
LMSE=1ki(bib^i)2,
v=tanh(LLR/s)s,

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