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Licensed Unlicensed Requires Authentication Published by De Gruyter March 25, 2016

BCH Codes for Coherent Star DQAM Systems with Laser Phase Noise

Miu Yoong Leong, Knud J. Larsen, Gunnar Jacobsen, Darko Zibar, Sergey Sergeyev and Sergei Popov


Coherent optical systems have relatively high laser phase noise, which affects the performance of forward error correction (FEC) codes. In this paper, we propose a method for selecting Bose–Chaudhuri–Hocquenghem (BCH) codes for coherent systems with star-shaped constellations and M-ary differential quadrature amplitude modulation (DQAM). Our method supports constellations of any order M which is a power of 2, and includes differential M-ary phase shift keying as a special case. Our approach is straightforward, requiring only short pre-FEC simulations to parameterize a statistical model, based on which we select codes analytically. It is applicable to pre-FEC bit error rates (BERs) of around 10−3. We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of 10−5, codes selected with our method yield BERs within 2× target. Lastly, we extend our method to systems with interleaving, which enables us to use codes with lower overhead.

JEL Classification: 94A05; 94B15

Funding statement: Funding: This work was supported in part by Vetenskapsrådet under grant no. 0379801 and in part by FP7-PEOPLE-2012-IAPP under project GRIFFON 324391.


1. Chang F, Onohara K, Mizuochi T. Forward error correction for 100 G transport networks. IEEE Commun Mag 2010 Mar;48(3):S48–55.10.1109/MCOM.2010.5434378Search in Google Scholar

2. Leven A, Schmalen L. Status and recent advances on forward error correction technologies for lightwave systems. In: Proc. ECOC; 2013. We.2.C.1. in Google Scholar

3. Lin S, Costello DJ. Error control coding, 2nd ed. New Jersey, USA: Prentice Hall, 2004.Search in Google Scholar

4. Pfau T. Carrier recovery algorithms and real-time DSP implementation for coherent receivers. In: Proc. OFC; 2014. W4K.1. in Google Scholar

5. Taylor MG. Phase estimation methods for optical coherent detection using digital signal processing. J Lightwave Technol 2009 Apr;27(7):901–14.10.1109/JLT.2008.927778Search in Google Scholar

6. Schmalen L. A low-complexity LDPC coding scheme for channels with phase slips. J Lightwave Technol 2015 Apr;33(7):1319–25.10.1109/JLT.2014.2377493Search in Google Scholar

7. Koike-Akino T, Kojima K, Millar D, et al. Cycle slip-mitigating turbo demodulation in LDPC-coded coherent optical communications. In: Proc. OFC; 2014. M3A.3. in Google Scholar

8. Yu F, Stojanovic N, Hauske FN, et al. Soft-decision LDPC turbo decoding for DQPSK modulation in coherent optical receivers. In: Proc. ECOC; 2011. We.10.P1.70. in Google Scholar

9. Leong MY, Larsen KJ, Jacobsen G, Popov S, Zibar D, Sergeyev S. Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips. J Lightwave Technol 2014 Nov;32(21):4048–52.10.1109/JLT.2014.2345768Search in Google Scholar

10. Leong MY, Larsen KJ, Jacobsen G, Popov S, Zibar D, Sergeyev S. Interleavers and BCH codes for coherent DQPSK systems with laser phase noise. IEEE Photon Technol Lett 2015 Apr;27(7):685–8.10.1109/LPT.2014.2385731Search in Google Scholar

11. Beppu S, Kasai K, Yoshida M, Nakazawa M. 2048 QAM (66 Gbit/s) single-carrier coherent optical transmission over 150 km with a potential SE of 15.3 bit/s/Hz. Opt Express 2015 Feb;23(4):4960–9.10.1364/OFC.2014.W1A.6Search in Google Scholar

12. Sano A, Kobayashi T, Yamanaka S, et al. 102.3-Tb/s (224 × 548-Gb/s) C- and extended L-band all-Raman transmission over 240 km using PDM-64QAM single carrier FDM with digital pilot tone. In: Proc. optical fiber communication and the national fiber optic engineers conference (OFC/NFOEC); 2012. PDP5C.3.10.1364/NFOEC.2012.PDP5C.3Search in Google Scholar

13. Qian D, Huang MF, Ip E, et al. 101.7-Tb/s (370 × 294-Gb/s) PDM-128QAM-OFDM transmission over 3 × 55-km SSMF using pilot-based phase noise mitigation. In: Proc. optical fiber communication and the national fiber optic engineers conference (OFC/NFOEC); 2011. Th.3.C.1.10.1364/OFC.2011.PDPB5Search in Google Scholar

14. Zafra SO, Pang X, Jacobsen G, Popov S, Sergeyev S. Phase noise tolerance study in coherent optical circular QAM transmissions with Viterbi-Viterbi carrier phase estimation. Opt Express 2014 Dec;22(25):30579–85.10.1364/OE.22.030579Search in Google Scholar PubMed

15. Webb WT, Hanzo L, Steele R. Bandwidth efficient QAM schemes for Rayleigh fading channels. IEEE Proc Commun Speech Vision, 1991 Jun;138(3):169–75.10.1049/ip-i-2.1991.0023Search in Google Scholar

16. Webb WT. QAM: the modulation scheme for future mobile radio communications? Electron Commun Eng J 1992 Aug;4(4):167–76.10.1049/ecej:19920032Search in Google Scholar

17. Adachi F, Sawahashi M. Performance analysis of various 16 level modulation schemes under Rayleigh fading. Electron Lett 1992 Aug;28(17):1579–81.10.1049/el:19921005Search in Google Scholar

18. Dong X, Beaulieu NC, Wittke PH. Error probabilities of two-dimensional M-ary signaling in fading. IEEE Trans Commun 1999 Mar;47(3):352–5.10.1109/26.752813Search in Google Scholar

19. Ishibashi K, Shin WY, Ochiai H, Tarokh VA. Peak power efficient cooperative diversity using star-QAM with coherent/noncoherent detection. IEEE Trans Wireless Commun 2013 May;12(5):2137–47.10.1109/TWC.2013.032013.120507Search in Google Scholar

20. Seimetz M. Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation. In: Proc. optical fiber communication conference and exposition and the national fiber optic engineers conference (OFC/NFOEC); 2008. OTuM2.10.1109/OFC.2008.4528637Search in Google Scholar

21. Digital Video Broadcasting (DVB). Second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications; Part 2: DVB-S2 extensions (DVB-S2X); 2014. Draft ETSI EN 302 307–2v1.1.1.Search in Google Scholar

22. Viterbi A, Viterbi A. Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission. IEEE Trans Inf Theory 1983 Jul;IT–29(4):543–51.10.1142/9789814287517_0003Search in Google Scholar

23. Weber WJIII. Differential encoding for multiple amplitude and phase shift keying systems. IEEE Trans Commun 1978 Mar;26(3):385–91.10.1109/TCOM.1978.1094074Search in Google Scholar

24. Dolinar S, Divsalar D. Weight distributions for turbo codes using random and nonrandom permutations. TDA progress report 42–122, 1995 Aug.Search in Google Scholar

25. Takeshita OY. Permutation polynomial interleavers: an algebraic-geometric perspective. IEEE Trans Inf Theory 2007 Jun;53(6):2116–32.10.1109/TIT.2007.896870Search in Google Scholar

26. 2015. Available at: in Google Scholar

27. Leong MY, Larsen KJ, Jacobsen G, Popov S, Zibar D, Sergeyev S. Novel BCH code design for mitigation of phase noise induced cycle slips in DQPSK systems. In: Proc. CLEO; 2014. STu3J.6.10.1364/CLEO_SI.2014.STu3J.6Search in Google Scholar

28. Proakis JG. Digital communications, 4th ed. New York, USA: McGraw-Hill, 2000.Search in Google Scholar

29. Craig JW. A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations. In: Military communications conference (MILCOM), IEEE. vol. 2; 1991: p. 571–575.Search in Google Scholar

30. Pfau T, Liu X, Chandrasekhar S. Optimization of 16-ary Quadrature Amplitude Modulation constellations for phase noise impaired channels. In: Optical Communication (ECOC), 2011 37th European Conference and Exhibition on; 2011. p. 1–3.10.1364/ECOC.2011.Tu.3.A.6Search in Google Scholar

31. Krishnan R, Graell i Amat A, Eriksson T, Colavolpe G. Constellation optimization in the presence of strong phase noise. IEEE Trans Commun 2013 Dec;61(12):5056–66.10.1109/TCOMM.2013.102313.130131Search in Google Scholar

32. Gordon JP, Mollenauer LF. Phase noise in photonic communications systems using linear amplifiers. Opt Lett 1990 Dec;15(23):1351–3.10.1364/OL.15.001351Search in Google Scholar

33. Xu T, Jacobsen G, Popov S, Li J, Friberg AT, Zhang Y. Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization. Opt Express 2011 Apr;19(8):7756–68.10.1364/OE.19.007756Search in Google Scholar PubMed

34. Jacobsen G, Xu T, Popov S, Li J, Friberg AT, Zhang Y. Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems. Opt Express 2011 Jul;19(15):14487–94.10.1364/OE.19.014487Search in Google Scholar PubMed

Received: 2016-1-10
Accepted: 2016-2-26
Published Online: 2016-3-25
Published in Print: 2017-6-27

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