Abstract

The probabilistic constellation shaping (PCS) technology has recently gained a great deal of attention for coherent optical communication systems since it allows us to approach the Shannon capacity limit by varying the symbol distribution adaptively to the signal-to-noise ratio (SNR). However, there is a lack of literature on how to apply this technology to intensity modulation (IM)/direct detection (DD) systems. In this paper, we propose and demonstrate an efficient way to apply the PCS technology for IM/DD systems. In the mapping of forward error correction-encoded bits onto the pulse amplitude modulation (PAM) symbols, we assign the uniformly distributed bits to the least significant bit of binary reflected Gray coding. Then, we have a pairwise distribution of symbol amplitude, where two adjacent symbols have the same probability. Although this distribution deviates from the optimum distribution (such as Maxwell-Boltzmann distribution), we show that the SNR penalty caused by this discrepancy is negligible. We evaluate the performance of the proposed scheme through simulation by measuring the achievable rate and frame error ratios after inverse distribution matcher. The results show that the proposed scheme provides a shaping gain larger than the time-division hybrid modulation. We also carry out the experimental demonstration of the proposed scheme using a 10-Gbaud PAM-8 signal. By using the proposed scheme, we improve the receiver sensitivity by 0.9 dB when compared with the uniformly distributed PAM-8 signal.

© 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. P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
    [Crossref]
  2. G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
    [Crossref]
  3. T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
    [Crossref]
  4. F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
    [Crossref]
  5. F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
    [Crossref]
  6. T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
    [Crossref]
  7. T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
    [Crossref]
  8. S. Varughese, J. Lavrencik, and S. E. Ralph, “Probabilistic shaping for VCSEL-MMF links,” in IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (2018).
  9. X. Han and I. B. Djordjevic, “Probabilistically shaped 8-PAM suitable for data centers communication,” in International Conference on Transparent Optical Networks (2018).
    [Crossref]
  10. F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
    [Crossref]
  11. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 2006), Chap. 12.
  12. D. Dowson and A. Wragg, “Maximum-entropy distributions having prescribed first and second moments,” IEEE Trans. Inf. Theory 19(5), 689–693 (1973).
    [Crossref]
  13. A. Wragg and D. Dowson, “Fitting continuous probability density functions over [0, ∞) using information theory ideas,” IEEE Trans. Inf. Theory 16(2), 226–230 (1970).
    [Crossref]
  14. Digital video broadcasting (DVB): 2nd generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications (DVB-S2), European Telecommun. Standards Inst. (ETSI) Standard EN 30 2 307, Rev. 1.2.1 (2009).
  15. G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic shaping and forward error correction for fiber-optic communication systems,” J. Lightwave Technol. 37(2), 230–244 (2019).
    [Crossref]
  16. G. Böcherer, “Achievable rates for probabilistic shaping,” arXiv, 1707.01134 (2017).
  17. F. Steiner, P. Schulte, and G. Böcherer, “Blind decoding-metric estimation for probabilistic shaping via expectation maximization,” in Proceedings of European Conference on Optical Communication (2018).
    [Crossref]

2019 (1)

2016 (2)

2015 (1)

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

1973 (1)

D. Dowson and A. Wragg, “Maximum-entropy distributions having prescribed first and second moments,” IEEE Trans. Inf. Theory 19(5), 689–693 (1973).
[Crossref]

1970 (1)

A. Wragg and D. Dowson, “Fitting continuous probability density functions over [0, ∞) using information theory ideas,” IEEE Trans. Inf. Theory 16(2), 226–230 (1970).
[Crossref]

Alvarado, A.

T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
[Crossref]

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
[Crossref]

Böcherer, G.

G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic shaping and forward error correction for fiber-optic communication systems,” J. Lightwave Technol. 37(2), 230–244 (2019).
[Crossref]

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
[Crossref]

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

F. Steiner, P. Schulte, and G. Böcherer, “Blind decoding-metric estimation for probabilistic shaping via expectation maximization,” in Proceedings of European Conference on Optical Communication (2018).
[Crossref]

Buchali, F.

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
[Crossref]

Djordjevic, I. B.

X. Han and I. B. Djordjevic, “Probabilistically shaped 8-PAM suitable for data centers communication,” in International Conference on Transparent Optical Networks (2018).
[Crossref]

Dowson, D.

D. Dowson and A. Wragg, “Maximum-entropy distributions having prescribed first and second moments,” IEEE Trans. Inf. Theory 19(5), 689–693 (1973).
[Crossref]

A. Wragg and D. Dowson, “Fitting continuous probability density functions over [0, ∞) using information theory ideas,” IEEE Trans. Inf. Theory 16(2), 226–230 (1970).
[Crossref]

Eriksson, T. A.

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

Fehenberger, T.

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
[Crossref]

T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
[Crossref]

Han, X.

X. Han and I. B. Djordjevic, “Probabilistically shaped 8-PAM suitable for data centers communication,” in International Conference on Transparent Optical Networks (2018).
[Crossref]

Hanik, N.

T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
[Crossref]

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
[Crossref]

Idler, W.

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
[Crossref]

Lavrencik, J.

S. Varughese, J. Lavrencik, and S. E. Ralph, “Probabilistic shaping for VCSEL-MMF links,” in IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (2018).

Ralph, S. E.

S. Varughese, J. Lavrencik, and S. E. Ralph, “Probabilistic shaping for VCSEL-MMF links,” in IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (2018).

Schmalen, L.

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

Schuh, K.

F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
[Crossref]

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

Schulte, P.

G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic shaping and forward error correction for fiber-optic communication systems,” J. Lightwave Technol. 37(2), 230–244 (2019).
[Crossref]

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

F. Steiner, P. Schulte, and G. Böcherer, “Blind decoding-metric estimation for probabilistic shaping via expectation maximization,” in Proceedings of European Conference on Optical Communication (2018).
[Crossref]

Steiner, F.

G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic shaping and forward error correction for fiber-optic communication systems,” J. Lightwave Technol. 37(2), 230–244 (2019).
[Crossref]

F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, and W. Idler, “Rate adaptation and reach increase by probabilistically shaped 64-QAM: an experimental demonstration,” J. Lightwave Technol. 34(7), 1599–1609 (2016).
[Crossref]

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

F. Steiner, P. Schulte, and G. Böcherer, “Blind decoding-metric estimation for probabilistic shaping via expectation maximization,” in Proceedings of European Conference on Optical Communication (2018).
[Crossref]

ten Brink, S.

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

Varughese, S.

S. Varughese, J. Lavrencik, and S. E. Ralph, “Probabilistic shaping for VCSEL-MMF links,” in IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (2018).

Wragg, A.

D. Dowson and A. Wragg, “Maximum-entropy distributions having prescribed first and second moments,” IEEE Trans. Inf. Theory 19(5), 689–693 (1973).
[Crossref]

A. Wragg and D. Dowson, “Fitting continuous probability density functions over [0, ∞) using information theory ideas,” IEEE Trans. Inf. Theory 16(2), 226–230 (1970).
[Crossref]

IEEE Trans. Commun. (1)

G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015).
[Crossref]

IEEE Trans. Inf. Theory (3)

D. Dowson and A. Wragg, “Maximum-entropy distributions having prescribed first and second moments,” IEEE Trans. Inf. Theory 19(5), 689–693 (1973).
[Crossref]

A. Wragg and D. Dowson, “Fitting continuous probability density functions over [0, ∞) using information theory ideas,” IEEE Trans. Inf. Theory 16(2), 226–230 (1970).
[Crossref]

P. Schulte and G. Böcherer, “Constant composition distribution matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016).
[Crossref]

J. Lightwave Technol. (2)

Other (11)

Digital video broadcasting (DVB): 2nd generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications (DVB-S2), European Telecommun. Standards Inst. (ETSI) Standard EN 30 2 307, Rev. 1.2.1 (2009).

T. Fehenberger, G. Böcherer, A. Alvarado, and N. Hanik, “LDPC coded modulation with probabilistic shaping for optical fiber systems,” in Optical Fiber Communications Conference (2015).
[Crossref]

F. Buchali, G. Böcherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” in Proceedings of European Conference on Optical Communication (2015).
[Crossref]

G. Böcherer, “Achievable rates for probabilistic shaping,” arXiv, 1707.01134 (2017).

F. Steiner, P. Schulte, and G. Böcherer, “Blind decoding-metric estimation for probabilistic shaping via expectation maximization,” in Proceedings of European Conference on Optical Communication (2018).
[Crossref]

T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On the impact of probabilistic shaping on SNR and information rates in multi-span WDM systems,” in Optical Fiber Communications Conference (2017).
[Crossref]

T. A. Eriksson, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proceedings of European Conference on Optical Communication (2017).
[Crossref]

S. Varughese, J. Lavrencik, and S. E. Ralph, “Probabilistic shaping for VCSEL-MMF links,” in IEEE Avionics and Vehicle Fiber-Optics and Photonics Conference (2018).

X. Han and I. B. Djordjevic, “Probabilistically shaped 8-PAM suitable for data centers communication,” in International Conference on Transparent Optical Networks (2018).
[Crossref]

F. Buchali, L. Schmalen, K. Schuh, and W. Idler, “Optimization of time-division hybrid-modulation and its application to rate adaptive 200Gb transmission,” in Proceedings of European Conference on Optical Communication (2014).
[Crossref]

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 2006), Chap. 12.

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Figures (8)

Fig. 1
Fig. 1 Block diagram of the proposed PS IM/DD system. The insets show the amplitude probabilities of the symbols when PAM-8 signal is used.
Fig. 2
Fig. 2 BRGC mapping table for PAM-8 constellation.
Fig. 3
Fig. 3 Simulation setup.
Fig. 4
Fig. 4 PMFs of (a) PS, (b) PS-TDHM, and (c) UD PAM-8 signals.
Fig. 5
Fig. 5 Achievable rate as a function of SNR.
Fig. 6
Fig. 6 BER and FER as a function of SNR.
Fig. 7
Fig. 7 Experimental setup. Eye diagrams of (a) UD and (b) PS signals.
Fig. 8
Fig. 8 Measured BER and FER performance.

Equations (8)

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

P X (x)= e v x 2 x'X e vx ' 2 ,x0
P X (x)= e vx x'X e vx' ,x0
R= [ log 2 | S | n U( q,X,Y ) ] +
log 2 |S| n = log 2 2 n 2 k n =1+ k n =1+ R dm
U( q bmd , B 1 ... B m ,y )= i=1 m H( B i |Y ) = i=1 m E[ log 2 { 1+exp[ (12 B i ) L i ] } ]
L i =log P B i |Y (0|y) P B i |Y (1|y) =log x X i 0 P Y|X (y|x) P X (x) x X i 1 P Y|X (y|x) P X (x)
P Y|X (y|x)= 1 2π σ 2 exp( ( yΔx ) 2 2 σ 2 )
R= [ log 2 | S | n 1 n s k=1 m l=1 n s log 2 [ 1+exp{ (12 b k,l ) L k,l } ] ] +

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