Abstract

We propose a rate-adaptive optical transmission scheme using variable-size constellations at a fixed symbol rate and variable-rate forward error correction (FEC) codes with soft-decision decoding (SDD), quantifying how achievable bit rates vary with transmission distance. The scheme uses outer Reed–Solomon codes and inner extended irregular repeat-accumulate low-density parity-check (LDPC) codes to vary the code rate, combined with single-carrier polarization-multiplexed M-ary quadrature amplitude modulation with variable M and digital coherent detection. LDPC codes are decoded iteratively using belief propagation. Employing M=4,8,16, the scheme achieves a maximum bit rate of 200 Gbit/s in a nominal 50-GHz channel bandwidth. A rate adaptation algorithm uses the signal-to-noise ratio (SNR) or the FEC decoder input bit-error ratio (BER) estimated by a receiver to determine the FEC code rate and constellation size that maximize the information bit rate while yielding a target FEC decoder output BER and a specified SNR margin. We simulate single-channel transmission through long-haul fiber systems with or without inline chromatic dispersion compensation, incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, we achieve bit rates of 200/100/50/20 Gbit/s over distances of 960/2800/4400/9680 km and 1920/4960/8160/19,360 km in dispersion-compensated and -uncompensated systems, respectively, corresponding to an increase of about 50% in reach compared to a reference system that uses a hard-decision FEC scheme. Compared to an ideal coding scheme, the proposed scheme exhibits a performance gap ranging from about 4.0 dB at 960 km to 2.7 dB at 9680 km in compensated systems, and from about 3.9 dB at 1920 km to 2.9 dB at 19,360 km in uncompensated systems. Observed performance gaps are about 2.5 dB smaller than for the reference hard-decision FEC scheme, close to the improvement expected when using SDD.

© 2012 OSA

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2012 (3)

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photon. Technol. Lett., vol. 24, pp. 1402–1404, Aug.2012.
[CrossRef]

O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, pp. 12–20, Feb.2012.
[CrossRef]

G. Gho and J. M. Kahn, “Rate-adaptive modulation and coding for optical fiber transmission systems,” J. Lightwave Technol., vol. 30, no. 12, pp. 1818–1828, June2012.
[CrossRef]

2011 (1)

2010 (1)

2009 (1)

E. Ip and J. Kahn, “Addendum to feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol., vol. 27, no. 13, pp. 2552–2553, July2009.
[CrossRef]

2008 (1)

2007 (3)

2005 (1)

P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 3039–3050, Nov.2005.
[CrossRef]

2004 (2)

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

J. Ha, J. Kim, and S. W. McLaughlin, “Rate-compatible puncturing of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. IT-50, pp. 2824–2836, Nov.2004.
[CrossRef]

2003 (1)

2002 (1)

B. Vasic and I. Djordjevic, “Low-density parity-check codes for long-haul optical communication systems,” IEEE Photon. Technol. Lett., vol. 14, pp. 1208–1210, Aug.2002.
[CrossRef]

1999 (1)

D. J. C. MacKay, “Good error correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399–431, Mar.1999.
[CrossRef]

1998 (1)

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May1998.
[CrossRef]

1992 (1)

G. D. Forney, “Trellis shaping,” IEEE Trans. Inf. Theory, vol. 38, pp. 281–300, Mar.1992.
[CrossRef]

1990 (1)

A. R. Calderbank and L. H. Ozarow, “Nonequiprobable signaling on the Gaussian channel,” IEEE Trans. Inf. Theory, vol. 36, pp. 726–740, July1990.
[CrossRef]

Akita, M.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Alouini, M.-S.

P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 3039–3050, Nov.2005.
[CrossRef]

Arabaci, M.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photon. Technol. Lett., vol. 24, pp. 1402–1404, Aug.2012.
[CrossRef]

M. Arabaci, I. B. Djordjevic, T. Schmidt, R. Saunders, and R. M. Marcoccia, “Rate-adaptive nonbinary-LDPC-coded modulation with backpropagation for long-haul optical transport networks,” in Int. Conf. on Transparent Optical Networks, Munich, Germany, June 27–July 1, 2010, We.D1.5.

Ben Yoo, S. J.

O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, pp. 12–20, Feb.2012.
[CrossRef]

Benedetto, S.

S. Benedetto and G. Bosco, “Channel coding for optical communications,” in Optical Communication: Theory and Techniques. E. Forestieri, Ed., Springer, New York, 2005, pp. 63–78, ch. 8.

Biglieri, E.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May1998.
[CrossRef]

Bosco, G.

S. Benedetto and G. Bosco, “Channel coding for optical communications,” in Optical Communication: Theory and Techniques. E. Forestieri, Ed., Springer, New York, 2005, pp. 63–78, ch. 8.

Caire, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May1998.
[CrossRef]

Calderbank, A. R.

A. R. Calderbank and L. H. Ozarow, “Nonequiprobable signaling on the Gaussian channel,” IEEE Trans. Inf. Theory, vol. 36, pp. 726–740, July1990.
[CrossRef]

Djordjevic, I.

B. Vasic and I. Djordjevic, “Low-density parity-check codes for long-haul optical communication systems,” IEEE Photon. Technol. Lett., vol. 14, pp. 1208–1210, Aug.2002.
[CrossRef]

Djordjevic, I. B.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photon. Technol. Lett., vol. 24, pp. 1402–1404, Aug.2012.
[CrossRef]

M. Arabaci, I. B. Djordjevic, T. Schmidt, R. Saunders, and R. M. Marcoccia, “Rate-adaptive nonbinary-LDPC-coded modulation with backpropagation for long-haul optical transport networks,” in Int. Conf. on Transparent Optical Networks, Munich, Germany, June 27–July 1, 2010, We.D1.5.

Essiambre, R.-J.

Forney, G. D.

G. D. Forney, “Trellis shaping,” IEEE Trans. Inf. Theory, vol. 38, pp. 281–300, Mar.1992.
[CrossRef]

Foschini, G. J.

Fujita, H.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Gallager, R. G.

R. G. Gallager, Low-Density Parity-Check Codes. MIT Press, Cambridge, MA, 1963.

Gerstel, O.

O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, pp. 12–20, Feb.2012.
[CrossRef]

Gho, G.

Goebel, B.

Ha, J.

J. Ha, J. Kim, and S. W. McLaughlin, “Rate-compatible puncturing of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. IT-50, pp. 2824–2836, Nov.2004.
[CrossRef]

Hall, E. K.

R. Zarubica, R. Hinton, S. G. Wilson, and E. K. Hall, “Efficient quantization schemes for LDPC decoders,” in Proc. of the IEEE Military Communications Conf., San Diego, CA, Nov.2008.

Hinton, R.

R. Zarubica, R. Hinton, S. G. Wilson, and E. K. Hall, “Efficient quantization schemes for LDPC decoders,” in Proc. of the IEEE Military Communications Conf., San Diego, CA, Nov.2008.

Ho, K.-P.

Holzlöhner, R.

Ip, E.

Jinno, M.

O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, pp. 12–20, Feb.2012.
[CrossRef]

Jones, C.

T. Tian, C. Jones, and J. D. Villasenor, “Rate-compatible low-density parity-check codes,” in Proc. of IEEE Int. Symp. on Information Theory, Chicago, IL, June 2004.

Kahn, J.

E. Ip and J. Kahn, “Addendum to feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol., vol. 27, no. 13, pp. 2552–2553, July2009.
[CrossRef]

Kahn, J. M.

Kieffer, J. C.

P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 3039–3050, Nov.2005.
[CrossRef]

Kim, J.

J. Ha, J. Kim, and S. W. McLaughlin, “Rate-compatible puncturing of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. IT-50, pp. 2824–2836, Nov.2004.
[CrossRef]

Klak, L.

Kobayashi, T.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Kramer, G.

Kubo, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Kuno, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Li, J.

J. Li and K. R. Narayanan, “Rate-compatible low-density parity-check codes for capacity-approaching ARQ schemes in packet data communications,” in Proc. of Int. Conf. Communications, Internet, and Information Technology, St. Thomas, Virgin Islands, USA, Nov. 2002, pp. 201–206.

Lord, A.

O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, pp. 12–20, Feb.2012.
[CrossRef]

MacKay, D. J. C.

D. J. C. MacKay, “Good error correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399–431, Mar.1999.
[CrossRef]

Madihian, M.

G. Yue, X. Wang, and M. Madihian, “Design of rate-compatible irregular repeat accumulate codes,” IEEE Trans. Commun., vol. 55, no. 6, pp. 1153–1163, June2007.
[CrossRef]

Marcoccia, R. M.

M. Arabaci, I. B. Djordjevic, T. Schmidt, R. Saunders, and R. M. Marcoccia, “Rate-adaptive nonbinary-LDPC-coded modulation with backpropagation for long-haul optical transport networks,” in Int. Conf. on Transparent Optical Networks, Munich, Germany, June 27–July 1, 2010, We.D1.5.

Matsumoto, W.

Y. Miyata, W. Matsumoto, H. Yoshida, and T. Mizuochi, “Efficient FEC for optical communications using concatenated codes to combat error-floor,” in Optical Fiber Communication Conf./Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, Feb. 24–28, 2008.

McLaughlin, S. W.

J. Ha, J. Kim, and S. W. McLaughlin, “Rate-compatible puncturing of low-density parity-check codes,” IEEE Trans. Inf. Theory, vol. IT-50, pp. 2824–2836, Nov.2004.
[CrossRef]

Menyuk, C. R.

Miyata, Y.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Y. Miyata, W. Matsumoto, H. Yoshida, and T. Mizuochi, “Efficient FEC for optical communications using concatenated codes to combat error-floor,” in Optical Fiber Communication Conf./Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, Feb. 24–28, 2008.

Mizuochi, T.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

T. Mizuochi, “Next generation FEC for optical communication,” in Opt. Fiber Commun. Conf., San Diego, CA, Feb. 2008.

Y. Miyata, W. Matsumoto, H. Yoshida, and T. Mizuochi, “Efficient FEC for optical communications using concatenated codes to combat error-floor,” in Optical Fiber Communication Conf./Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, Feb. 24–28, 2008.

Motoshima, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Narayanan, K. R.

J. Li and K. R. Narayanan, “Rate-compatible low-density parity-check codes for capacity-approaching ARQ schemes in packet data communications,” in Proc. of Int. Conf. Communications, Internet, and Information Technology, St. Thomas, Virgin Islands, USA, Nov. 2002, pp. 201–206.

Ouchi, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Ozarow, L. H.

A. R. Calderbank and L. H. Ozarow, “Nonequiprobable signaling on the Gaussian channel,” IEEE Trans. Inf. Theory, vol. 36, pp. 726–740, July1990.
[CrossRef]

Richardson, T.

T. Richardson, “Error floors of LDPC codes,” in Proc. of the Allerton Conf. on Communications, Control, and Computing, Monticello, IL, Oct. 1–3, 2003.

Ryan, W. E.

M. Yang and W. E. Ryan, “Lowering the error-rate floors of moderate-length high-rate irregular LDPC codes,” in IEEE Int. Symp. on Information Theory, Yokohama, Japan, June 2003.

Saunders, R.

M. Arabaci, I. B. Djordjevic, T. Schmidt, R. Saunders, and R. M. Marcoccia, “Rate-adaptive nonbinary-LDPC-coded modulation with backpropagation for long-haul optical transport networks,” in Int. Conf. on Transparent Optical Networks, Munich, Germany, June 27–July 1, 2010, We.D1.5.

Schmidt, T.

M. Arabaci, I. B. Djordjevic, T. Schmidt, R. Saunders, and R. M. Marcoccia, “Rate-adaptive nonbinary-LDPC-coded modulation with backpropagation for long-haul optical transport networks,” in Int. Conf. on Transparent Optical Networks, Munich, Germany, June 27–July 1, 2010, We.D1.5.

Shieh, W.

Shimizu, K.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Sinkin, O. V.

Tagami, H.

T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron., vol. 10, no. 2, pp. 376–386, Mar./Apr.2004.
[CrossRef]

Taricco, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927–946, May1998.
[CrossRef]

Tian, T.

T. Tian, C. Jones, and J. D. Villasenor, “Rate-compatible low-density parity-check codes,” in Proc. of IEEE Int. Symp. on Information Theory, Chicago, IL, June 2004.

Vasic, B.

B. Vasic and I. Djordjevic, “Low-density parity-check codes for long-haul optical communication systems,” IEEE Photon. Technol. Lett., vol. 14, pp. 1208–1210, Aug.2002.
[CrossRef]

Villasenor, J. D.

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Figures (8)

Fig. 1
Fig. 1

QAM constellations with bit-to-symbol mappings. (a) Square 4-QAM. (b) Cross 8-QAM. (c) Square 16-QAM.

Fig. 2
Fig. 2

Performance of inner LDPC codes on an AWGN channel with six different rates, in terms of LDPC decoder output BER versus SNR per symbol. The BP algorithm uses 50 iterations. The SNR per symbol is measured at the equalizer output (i.e., the LDPC decoder input) and P b , out , LDPC is measured at the LDPC decoder output (i.e., the RS-encoder input). (a) M = 4 . (b) M = 8 . (c) M = 16 .

Fig. 3
Fig. 3

Performance of outer RS codes with six different rates, in terms of input and output BERs of the RS decoder. The P b , in,RS and P b , out,RS values are measured at the input and output of the RS decoder, respectively.

Fig. 4
Fig. 4

Constructing variable-rate inner RS and outer LDPC codes by shortening the mother codes. The overall RS–LDPC encoding process is also illustrated.

Fig. 5
Fig. 5

Information bit rate versus threshold SNR per symbol for PM-M-QAM on an AWGN channel. Information bit rates are computed using Eq. (1), while SNR values are obtained by combining Figs. 2 and 3. The set of filled (M, code) combinations represent a possible choice of modes for rate-adaptive transmission.

Fig. 6
Fig. 6

FEC chain for encoding and decoding concatenated RS–LDPC codes.

Fig. 7
Fig. 7

Achievable information bit rates versus transmission distance for different SNR margins. The set (M, code) denotes the modulation order and type of RS–LDPC code. (a) Dispersion-compensated system. (b) Dispersion-uncompensated system.

Fig. 8
Fig. 8

Two different measures of SNR compared to the SNR required for an ideal capacity-achieving coding scheme to achieve error-free transmission at the information bit rate R b achieved by the proposed rate-adaptive scheme. (a) Dispersion-compensated system. (b) Dispersion-uncompensated system.

Tables (2)

Tables Icon

Table I RS and LDPC Code Parameters: Lengths of Message Word and Codeword

Tables Icon

Table II Comparison of Gaps to Capacity for Different FEC Schemes, Channel Types, and Residual Dispersion Values

Equations (5)

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R b = 2 r L r C R s   log 2   M ,
C = 2 R s   log 2   ( 1 + SNR ) .
SNR AWGN = P t P n .
SNR AWGN, best-fit = { A c L 1 . 40 , 3.1% RDPS A u L 1 . 15 , 100% RDPS .
SNR required,ideal = 2 R b 2 R s 1 .