Abstract

In this paper, with the aid of mutual information and generalized mutual information (GMI) capacity analyses, it is shown that the geometrically shaped APSK that mimics an optimal Gaussian distribution with equiprobable signaling together with the corresponding gray-mapping rules can approach the Shannon limit closer than conventional quadrature amplitude modulation (QAM) at certain range of FEC overhead for both 16-APSK and 64-APSK. The field programmable gate array (FPGA) based LDPC-coded APSK emulation is conducted on block interleaver-based and bit interleaver-based systems; the results verify a significant improvement in hardware efficient bit interleaver-based systems. In bit interleaver-based emulation, the LDPC-coded 64-APSK outperforms 64-QAM, in terms of symbol signal-to-noise ratio (SNR), by 0.1 dB, 0.2 dB, and 0.3 dB at spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz, respectively. It is found by emulation that LDPC-coded 64-APSK for spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz is 1.6 dB, 1.7 dB, and 2.2 dB away from the GMI capacity.

© 2017 Optical Society of America

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References

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2016 (2)

2015 (3)

2012 (1)

Q. Xie, Z. Wang, and Z. Yang, “Simplified soft demmapper for APSK with product constellation labeling,” IEEE Trans. Wirel. Commun. 11(7), 2649–2657 (2012).
[Crossref]

2011 (1)

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

2010 (2)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photonics J. 2(4), 593–599 (2010).
[Crossref]

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]

1999 (1)

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999).
[Crossref]

1998 (2)

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” Electron. Lett. 34(15), 1459–1460 (1998).
[Crossref]

G. Caire, G. Tarrico, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).

Agrell, E.

Alvarado, A.

Arabaci, M.

Aref, V.

Batshon, H. G.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photonics J. 2(4), 593–599 (2010).
[Crossref]

Bayvel, P.

Biglieri, E.

G. Caire, G. Tarrico, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).

Caire, G.

G. Caire, G. Tarrico, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).

Charlet, G.

Chen, J.

Cho, J.

Cui, X.

Ding, T.

Djordjevic, I. B.

Fischer, R. F. H.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999).
[Crossref]

Huber, J. B.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999).
[Crossref]

Lavery, D.

Leven, A.

Li, C.

Li, L.

Liu, Z.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

Maher, R.

Marcoccia, R. M.

Peng, K.

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

Renaudier, J.

Rios-Muller, R.

Rosener, D.

Saunders, R.

Schemalen, L.

Schmalen, L.

Si, M.

Speidel, J.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” Electron. Lett. 34(15), 1459–1460 (1998).
[Crossref]

Suikat, D.

Tarrico, G.

G. Caire, G. Tarrico, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).

ten Brink, S.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” Electron. Lett. 34(15), 1459–1460 (1998).
[Crossref]

Tran, P.

Wachsmann, U.

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999).
[Crossref]

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photonics J. 2(4), 593–599 (2010).
[Crossref]

Wang, Y.

Wang, Z.

Q. Xie, Z. Wang, and Z. Yang, “Simplified soft demmapper for APSK with product constellation labeling,” IEEE Trans. Wirel. Commun. 11(7), 2649–2657 (2012).
[Crossref]

Xiang, H.

Xiao, Z.

Xie, Q.

Q. Xie, Z. Wang, and Z. Yang, “Simplified soft demmapper for APSK with product constellation labeling,” IEEE Trans. Wirel. Commun. 11(7), 2649–2657 (2012).
[Crossref]

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photonics J. 2(4), 593–599 (2010).
[Crossref]

Yan, R.-H.

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” Electron. Lett. 34(15), 1459–1460 (1998).
[Crossref]

Yang, Z.

Q. Xie, Z. Wang, and Z. Yang, “Simplified soft demmapper for APSK with product constellation labeling,” IEEE Trans. Wirel. Commun. 11(7), 2649–2657 (2012).
[Crossref]

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

Zhang, Z.

Zou, D.

Electron. Lett. (1)

S. ten Brink, J. Speidel, and R.-H. Yan, “Iterative demapping for QPSK modulation,” Electron. Lett. 34(15), 1459–1460 (1998).
[Crossref]

IEEE Commun. Lett. (1)

Z. Liu, Q. Xie, K. Peng, and Z. Yang, “APSK constellation with gray mapping,” IEEE Commun. Lett. 15(12), 1271–1273 (2011).
[Crossref]

IEEE Photonics J. (1)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photonics J. 2(4), 593–599 (2010).
[Crossref]

IEEE Trans. Inf. Theory (2)

U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999).
[Crossref]

G. Caire, G. Tarrico, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).

IEEE Trans. Wirel. Commun. (1)

Q. Xie, Z. Wang, and Z. Yang, “Simplified soft demmapper for APSK with product constellation labeling,” IEEE Trans. Wirel. Commun. 11(7), 2649–2657 (2012).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (3)

Other (6)

J. Zhang and I. B. Djordjevic, “Optimum Signal Constellation Design for Rotationally Symmetric Optical Channel with Coherent Detection,” in OFC/NFOEC (2011), paper OThO3.

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.

F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped-64-QAM,” in ECOC (2015), paper We.4.D.5.

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

C. A. S. Diniz, J. H. C. Junior, A. L. N. Souza, T. C. Lima, R. R. Lopez, S. M. Rossi, M. Garrich, J. D. Reis, D. S. Arantes, J. R. F. Oliveira, and D. A. A. Mello, “Network cost savings enabled by probabilistic shaping in DP-16QAM 200-Gb/s systems,” in OFC/NFOEC (2016), paper Tu3F.7.

S. Zhang, F. Yaman, Y. Huang, J. D. Downie, D. Zou, W. A. Wood, A. Zakharian, R. Khrapko, S. Mishara, V. Nazarov, J. Hurley, I. B. Djordjevic, E. Mateo, and Y. Inada, “Capacity-approaching transmission over 6375 km at spectral efficiency of 9.3 bit/s/Hz,” in OFC/NFOEC (2016), paper PDP Th5C.2.

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Figures (7)

Fig. 1
Fig. 1 LDPC-coded Gray mapping APSK scheme.
Fig. 2
Fig. 2 APSK constellation: (a) Gray-mapping 16-APSK, (b) Gray-mapping 64-APSK, (c) Pseudo gray-mapping 16-APSK, (d) Pseudo gray-mapping 32-APSK.
Fig. 3
Fig. 3 MI/GMI for APSK and QAM constellations for: (a) 16-point constellations and (b) 64-point constellations.
Fig. 4
Fig. 4 Decomposed GMI vs. SNR for Gray-mapping-based 16-APSK, pseudo-Gray-mapping-based 16-APSK and Gray-mapping-based 16-QAM.
Fig. 5
Fig. 5 Decomposed GMI vs. SNR for Gray-mapping-based 64-APSK and Gray-mapping-based 64-QAM.
Fig. 6
Fig. 6 BER vs. SNR performance for LDPC-coded 16-APSK and 16-QAM when: (a) block interleaver and (b) bit interleaver is used.
Fig. 7
Fig. 7 BER vs. SNR performance for LDPC-coded 64-APSK and 64-QAM when: (a) block interleaver and (b) bit interleaver is used.

Equations (3)

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C MI =maxI(S;Y)=m Ε s,y [ log 2 zχ p(y|z) p(y|s) ]
C GMI =max i=0 m1 I( b i ;Y) =m Ε b,y [ log 2 zχ p(y|z) z χ b i p(y|z) ]
χ={ r 1 exp(j( 2π n 1 i+ θ 1 )),i=0,..., n 1 1 r 2 exp(j( 2π n 2 i+ θ 2 )),i=0,..., n 2 1 r R exp(j( 2π n R i+ θ R )),i=0,..., n R 1

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