Skip to main content

2020 | OriginalPaper | Buchkapitel

7. Forward Error Correction for Optical Transponders

verfasst von : Alexandre Graell i Amat, Laurent Schmalen

Erschienen in: Springer Handbook of Optical Networks

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Zusammenfassung

Forward error correction () is an essential technique required in almost all communication systems to guarantee reliable data transmission close to the theoretical limits. In this chapter, we discuss the state-of-the-art FEC schemes for fiber-optic communications. Following a historical overview of the evolution of FEC schemes, we first introduce the fundamental theoretical limits of common communication channel models and show how to compute them. These limits provide the reader with guidelines for comparing different FEC codes under various assumptions. We then provide a brief introduction to the general basic concepts of FEC, followed by an in-depth introduction to the main classes of codes for soft-decision decoding and hard-decision decoding. We include a wide range of performance curves, compare the different schemes, and give the reader guidelines on which FEC scheme to use. We also introduce the main techniques to combine coding and higher-order modulation (coded modulation), including constellation shaping. Finally, we include a guide on how to evaluate the performance of FEC schemes in transmission experiments. We conclude the chapter with an overview of the properties of some state-of-the-art FEC schemes used in optical communications, and an outlook.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat A.G. Dimakis, P.B. Godfrey, Y. Wu, M.J. Wainwright, K. Ramchandran: Network coding for distributed storage systems, IEEE Trans. Inf. Theory 56(9), 4539–4551 (2010)MATHCrossRef A.G. Dimakis, P.B. Godfrey, Y. Wu, M.J. Wainwright, K. Ramchandran: Network coding for distributed storage systems, IEEE Trans. Inf. Theory 56(9), 4539–4551 (2010)MATHCrossRef
Zurück zum Zitat G. Liva: Graph-based analysis and optimization of contention resolution diversity slotted ALOHA, IEEE Trans. Commun. 59(2), 477–487 (2011)CrossRef G. Liva: Graph-based analysis and optimization of contention resolution diversity slotted ALOHA, IEEE Trans. Commun. 59(2), 477–487 (2011)CrossRef
Zurück zum Zitat S. Li, M.A. Maddah-Ali, A.S. Avestimehr: A unified coding framework for distributed computing with straggling servers. In: Proc. IEEE Globecom Work. (GC Wkshps), Washington, DC, Dec (2016) S. Li, M.A. Maddah-Ali, A.S. Avestimehr: A unified coding framework for distributed computing with straggling servers. In: Proc. IEEE Globecom Work. (GC Wkshps), Washington, DC, Dec (2016)
Zurück zum Zitat S. Li, M.A. Maddah-Ali, A.S. Avestimehr: Coding for distributed fog computing, IEEE Commun. Mag. 55(4), 34–40 (2017)CrossRef S. Li, M.A. Maddah-Ali, A.S. Avestimehr: Coding for distributed fog computing, IEEE Commun. Mag. 55(4), 34–40 (2017)CrossRef
Zurück zum Zitat D. Pearson: High-speed QKD reconciliation using forward error correction. In: Proc. AIP Int. Conf. Quantum Commun., Measurement Comp, Vol. 734 (2004) pp. 299–302, Glasgow D. Pearson: High-speed QKD reconciliation using forward error correction. In: Proc. AIP Int. Conf. Quantum Commun., Measurement Comp, Vol. 734 (2004) pp. 299–302, Glasgow
Zurück zum Zitat R.J. McEliece: A public-key cryptosystem based on algebraic coding theory, Deep Space Netw. Prog. Rep. 44, 114–116 (1978) R.J. McEliece: A public-key cryptosystem based on algebraic coding theory, Deep Space Netw. Prog. Rep. 44, 114–116 (1978)
Zurück zum Zitat W. Grover: Error correction in dispersion-limited lightwave systems, J. Lightwave Technol. 6, 643–654 (1988)CrossRef W. Grover: Error correction in dispersion-limited lightwave systems, J. Lightwave Technol. 6, 643–654 (1988)CrossRef
Zurück zum Zitat D.J. Costello Jr., J. Hagenauer, H. Imai, S.B. Wicker: Applications of error-control coding, IEEE Trans. Inf. Theory 44(6), 2531–2560 (1998)MathSciNetMATHCrossRef D.J. Costello Jr., J. Hagenauer, H. Imai, S.B. Wicker: Applications of error-control coding, IEEE Trans. Inf. Theory 44(6), 2531–2560 (1998)MathSciNetMATHCrossRef
Zurück zum Zitat D.J. Costello Jr., G.D. Forney Jr.: Channel coding: the road to capacity, Proceedings IEEE 95(6), 1150–1177 (2007)CrossRef D.J. Costello Jr., G.D. Forney Jr.: Channel coding: the road to capacity, Proceedings IEEE 95(6), 1150–1177 (2007)CrossRef
Zurück zum Zitat M.J.E. Golay: Notes on digital coding, Proc. Inst. Radio Eng. 37(6), 657–657 (1949)MathSciNet M.J.E. Golay: Notes on digital coding, Proc. Inst. Radio Eng. 37(6), 657–657 (1949)MathSciNet
Zurück zum Zitat F. MacWilliams, N. Sloane: The Theory of Error-Correcting Codes, 2nd edn. (North-Holland, Amsterdam 1978)MATH F. MacWilliams, N. Sloane: The Theory of Error-Correcting Codes, 2nd edn. (North-Holland, Amsterdam 1978)MATH
Zurück zum Zitat D.E. Muller: Application of Boolean algebra to switching circuit design and to error detection, IRE Trans. Electron. Comput. 3, 6–12 (1954) D.E. Muller: Application of Boolean algebra to switching circuit design and to error detection, IRE Trans. Electron. Comput. 3, 6–12 (1954)
Zurück zum Zitat I. Reed: A class of multiple-error-correcting codes and the decoding scheme, IRE Trans. Inf. Theory 4(4), 38–49 (1954)MathSciNetCrossRef I. Reed: A class of multiple-error-correcting codes and the decoding scheme, IRE Trans. Inf. Theory 4(4), 38–49 (1954)MathSciNetCrossRef
Zurück zum Zitat R.D. Cideciyan, S. Furrer, M.A. Lantz: Product codes for data storage on magnetic tape, IEEE Trans. Magn. 53(2), 1–10 (2017)CrossRef R.D. Cideciyan, S. Furrer, M.A. Lantz: Product codes for data storage on magnetic tape, IEEE Trans. Magn. 53(2), 1–10 (2017)CrossRef
Zurück zum Zitat S. Emmadi, K.R. Narayanan, H.D. Pfister: Half-product codes for flash memory. In: Proc. Non-Volatile Memories Workshop (2015), San Diego S. Emmadi, K.R. Narayanan, H.D. Pfister: Half-product codes for flash memory. In: Proc. Non-Volatile Memories Workshop (2015), San Diego
Zurück zum Zitat M. Wang: WiMAX physical layer: Specifications overview and performance evaluation. In: Proc. Consumer Commun. Networking Conf. (CCNC) (2011) pp. 10–12 M. Wang: WiMAX physical layer: Specifications overview and performance evaluation. In: Proc. Consumer Commun. Networking Conf. (CCNC) (2011) pp. 10–12
Zurück zum Zitat J. Justesen, K.J. Larsen, L.A. Pedersen: Error correcting coding for OTN, IEEE Commun. Mag. 48(9), 70–75 (2010)CrossRef J. Justesen, K.J. Larsen, L.A. Pedersen: Error correcting coding for OTN, IEEE Commun. Mag. 48(9), 70–75 (2010)CrossRef
Zurück zum Zitat P. Elias: Coding for noisy channels. In: IRE Convention Record, Part IV (1955) pp. 37–46 P. Elias: Coding for noisy channels. In: IRE Convention Record, Part IV (1955) pp. 37–46
Zurück zum Zitat ETSI: Recommendation GSM 05.03 (ETSI, Sophia Antipolis 1994) ETSI: Recommendation GSM 05.03 (ETSI, Sophia Antipolis 1994)
Zurück zum Zitat IEEE: Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications amendment 5: Enhancements for higher throughput. In: IEEE Standard for Information technology–Telecommunications and information exchange between systems–Local and metropolitan area networks–Specific requirements (2005), Std 802.11-2005, Tech. Rep. IEEE: Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications amendment 5: Enhancements for higher throughput. In: IEEE Standard for Information technology–Telecommunications and information exchange between systems–Local and metropolitan area networks–Specific requirements (2005), Std 802.11-2005, Tech. Rep.
Zurück zum Zitat IEEE: Part 3: Carrier sense multiple access with collision detection (CSMA/CD): Access method and physical layer specifications. In: 802.3, Local and Metropolitan Area Networks-specific Requirements (2006) IEEE: Part 3: Carrier sense multiple access with collision detection (CSMA/CD): Access method and physical layer specifications. In: 802.3, Local and Metropolitan Area Networks-specific Requirements (2006)
Zurück zum Zitat A. Viterbi: Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Trans. Inf. Theory 13(2), 260–269 (1967)MATHCrossRef A. Viterbi: Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Trans. Inf. Theory 13(2), 260–269 (1967)MATHCrossRef
Zurück zum Zitat G.D. Forney Jr.: The Viterbi algorithm: A personal history. In: Proc. Viterbi Conf. (2005), University of Southern California, Los Angeles G.D. Forney Jr.: The Viterbi algorithm: A personal history. In: Proc. Viterbi Conf. (2005), University of Southern California, Los Angeles
Zurück zum Zitat T.T. Ha, R.L. Borchardt, E.-S. Hwang: Direct detection optical systems employing OOK modulation and error correction codes, J. Opt. Commun. 17(6), 212–215 (1996)CrossRef T.T. Ha, R.L. Borchardt, E.-S. Hwang: Direct detection optical systems employing OOK modulation and error correction codes, J. Opt. Commun. 17(6), 212–215 (1996)CrossRef
Zurück zum Zitat T. Wuth, E. Agrell, M. Karlsson, M. Sköld: Fiber communications using convolutional coding and bandwidth-efficient modulation, Opt. Express 14(2), 542–555 (2006)CrossRef T. Wuth, E. Agrell, M. Karlsson, M. Sköld: Fiber communications using convolutional coding and bandwidth-efficient modulation, Opt. Express 14(2), 542–555 (2006)CrossRef
Zurück zum Zitat A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, T. Kupfer: Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) pp. 1–3, Anaheim A. Bisplinghoff, N. Beck, M. Ene, M. Danninger, T. Kupfer: Phase slip tolerant, low power multi-level coding for 64QAM with 12.9 dB NCG. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) pp. 1–3, Anaheim
Zurück zum Zitat R. Blahut: Algebraic Codes for Data Transmission (Cambridge Univ. Press, New York 2003)MATHCrossRef R. Blahut: Algebraic Codes for Data Transmission (Cambridge Univ. Press, New York 2003)MATHCrossRef
Zurück zum Zitat S. Lin, D.J. Costello Jr.: Error Control Coding, 2nd edn. (Prentice Hall, Upper Saddle River 2004)MATH S. Lin, D.J. Costello Jr.: Error Control Coding, 2nd edn. (Prentice Hall, Upper Saddle River 2004)MATH
Zurück zum Zitat S. Quiroga, D. Torres, A. Veloz: In band FEC decoder for SONET/SDH at 2.5 Gbit/s and 10 Gbit/s. In: Proc. Int. Conf. Elec. Electron. Eng. (ICEEE) (2004) pp. 70–73 S. Quiroga, D. Torres, A. Veloz: In band FEC decoder for SONET/SDH at 2.5 Gbit/s and 10 Gbit/s. In: Proc. Int. Conf. Elec. Electron. Eng. (ICEEE) (2004) pp. 70–73
Zurück zum Zitat E. Berlekamp: Algebraic Coding Theory (McGraw-Hill, New York 1968)MATH E. Berlekamp: Algebraic Coding Theory (McGraw-Hill, New York 1968)MATH
Zurück zum Zitat S. Yamamoto, H. Takahira, E. Shibano, M. Tanaka, Y. Chen: BER performance improvement by forward error correcting code in 5 Gbit/s 9000 km EDFA transmission system, Electron. Lett. 30, 718–719 (1994)CrossRef S. Yamamoto, H. Takahira, E. Shibano, M. Tanaka, Y. Chen: BER performance improvement by forward error correcting code in 5 Gbit/s 9000 km EDFA transmission system, Electron. Lett. 30, 718–719 (1994)CrossRef
Zurück zum Zitat L. Schmalen, A. de Lind van Wijngaarden, S. ten Brink: Forward error correction in optical core and access networks, Bell Labs Tech. J. 18(3), 39–66 (2013)CrossRef L. Schmalen, A. de Lind van Wijngaarden, S. ten Brink: Forward error correction in optical core and access networks, Bell Labs Tech. J. 18(3), 39–66 (2013)CrossRef
Zurück zum Zitat ITU-T: Recommendation G.975: Forward error correction for submarine systems 1996) ITU-T: Recommendation G.975: Forward error correction for submarine systems 1996)
Zurück zum Zitat F. Chang, K. Onohara, T. Mizuochi: Forward error correction for 100 G transport networks, IEEE Commun. Mag. 48, S48–S55 (2010)CrossRef F. Chang, K. Onohara, T. Mizuochi: Forward error correction for 100 G transport networks, IEEE Commun. Mag. 48, S48–S55 (2010)CrossRef
Zurück zum Zitat G.D. Forney: Concatenated codes, Ph.D. dissertation (Massachusetts Institute of Technology (MIT), Cambridge 1965) G.D. Forney: Concatenated codes, Ph.D. dissertation (Massachusetts Institute of Technology (MIT), Cambridge 1965)
Zurück zum Zitat ETSI: DVB-S, ETSI standard EN 300 421 v.1.1.2 (ETSI, Sophia Antipolis 1997) ETSI: DVB-S, ETSI standard EN 300 421 v.1.1.2 (ETSI, Sophia Antipolis 1997)
Zurück zum Zitat ITU-T: Recommendation G.975.1: Forward error correction for high bit-rate DWDM submarine systems (ITU, Geneva 2004) ITU-T: Recommendation G.975.1: Forward error correction for high bit-rate DWDM submarine systems (ITU, Geneva 2004)
Zurück zum Zitat A. Afshar: Deployment of 100G in the metro network, applications and drivers, Cortina White Paper, Tech. Rep. 20. A. Afshar: Deployment of 100G in the metro network, applications and drivers, Cortina White Paper, Tech. Rep. 20.
Zurück zum Zitat M. Scholten, T. Coe, J. Dillard: Continuously-interleaved BCH (CI-BCH) FEC delivers best in class NECG for 40G and 100G metro applications. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2010), San Diego M. Scholten, T. Coe, J. Dillard: Continuously-interleaved BCH (CI-BCH) FEC delivers best in class NECG for 40G and 100G metro applications. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2010), San Diego
Zurück zum Zitat B.P. Smith, A. Farhood, A. Hunt, F.R. Kschischang, J. Lodge: Staircase codes: FEC for 100 Gb/s OTN, J. Lightwave Technol. 30(1), 110–117 (2012)CrossRef B.P. Smith, A. Farhood, A. Hunt, F.R. Kschischang, J. Lodge: Staircase codes: FEC for 100 Gb/s OTN, J. Lightwave Technol. 30(1), 110–117 (2012)CrossRef
Zurück zum Zitat Y.-Y. Jian, H.D. Pfister, K.R. Narayanan, R. Rao, R. Mazahreh: Iterative hard-decision decoding of braided BCH codes for high-speed optical communication. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2013), Atlanta Y.-Y. Jian, H.D. Pfister, K.R. Narayanan, R. Rao, R. Mazahreh: Iterative hard-decision decoding of braided BCH codes for high-speed optical communication. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2013), Atlanta
Zurück zum Zitat D.C. MacKay, R. Neal: Near Shannon limit performance of low density parity check codes, Electron. Lett. 32, 1645–1646 (1996)CrossRef D.C. MacKay, R. Neal: Near Shannon limit performance of low density parity check codes, Electron. Lett. 32, 1645–1646 (1996)CrossRef
Zurück zum Zitat M. Luby, M. Mitzenmacher, A. Shokrollahi, D.A. Spielman, V. Stemann: Practical loss-resilient codes. In: Proc. ACM Symp. Theory Comput. (1997) pp. 150–159 M. Luby, M. Mitzenmacher, A. Shokrollahi, D.A. Spielman, V. Stemann: Practical loss-resilient codes. In: Proc. ACM Symp. Theory Comput. (1997) pp. 150–159
Zurück zum Zitat IEEE: 802.11, wireless LAN medium access control (MAC) and physical layer (PHY) specifications (IEEE, Piscataway Township 2012) IEEE: 802.11, wireless LAN medium access control (MAC) and physical layer (PHY) specifications (IEEE, Piscataway Township 2012)
Zurück zum Zitat ETSI: DVB-S2, ETSI standard EN 302 307 v.1.2.1 (ETSI, Sophia Antipolis 2009) ETSI: DVB-S2, ETSI standard EN 302 307 v.1.2.1 (ETSI, Sophia Antipolis 2009)
Zurück zum Zitat IEEE: 802.3an, local and metropolitan area networks-specific requirements Part 3: Carrier sense multiple access with collision detection (CSMA/CD): Access method and physical layer specifications (IEEE, Piscataway Township 2006) IEEE: 802.3an, local and metropolitan area networks-specific requirements Part 3: Carrier sense multiple access with collision detection (CSMA/CD): Access method and physical layer specifications (IEEE, Piscataway Township 2006)
Zurück zum Zitat R. Pyndiah: Near optimum decoding of product codes: Block turbo codes, IEEE Trans. Commun. 46(8), 1003–1010 (1998)MATHCrossRef R. Pyndiah: Near optimum decoding of product codes: Block turbo codes, IEEE Trans. Commun. 46(8), 1003–1010 (1998)MATHCrossRef
Zurück zum Zitat T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, 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. 10(2), 376–386 (2004)CrossRef T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, 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. 10(2), 376–386 (2004)CrossRef
Zurück zum Zitat B. Vasic, I.B. Djordjevic: Low-density parity check codes for long-haul optical communication systems, IEEE Photon. Technol. Lett. 14(8), 1208–1210 (2002)CrossRef B. Vasic, I.B. Djordjevic: Low-density parity check codes for long-haul optical communication systems, IEEE Photon. Technol. Lett. 14(8), 1208–1210 (2002)CrossRef
Zurück zum Zitat Y. Miyata, K. Kubo, H. Yoshida, T. Mizuochi: Proposal for frame structure of optical channel transport unit employing LDPC codes for 100 Gb/s FEC. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2009) Y. Miyata, K. Kubo, H. Yoshida, T. Mizuochi: Proposal for frame structure of optical channel transport unit employing LDPC codes for 100 Gb/s FEC. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2009)
Zurück zum Zitat I.B. Djordjevic, B. Vasic: Nonbinary LDPC codes for optical communication systems, IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005)CrossRef I.B. Djordjevic, B. Vasic: Nonbinary LDPC codes for optical communication systems, IEEE Photon. Technol. Lett. 17(10), 2224–2226 (2005)CrossRef
Zurück zum Zitat T. Richardson: Error floors of LDPC codes. In: Proc. Allerton Annu. Conf. Commun. Control Comp. (2003) T. Richardson: Error floors of LDPC codes. In: Proc. Allerton Annu. Conf. Commun. Control Comp. (2003)
Zurück zum Zitat D.A. Morero, M.A. Castrillon, F.A. Ramos, T.A. Goette, O.E. Agazzi, M.R. Hueda: Non-concatenated FEC codes for ultra-high speed optical transport networks. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2011) pp. 1–5 D.A. Morero, M.A. Castrillon, F.A. Ramos, T.A. Goette, O.E. Agazzi, M.R. Hueda: Non-concatenated FEC codes for ultra-high speed optical transport networks. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2011) pp. 1–5
Zurück zum Zitat E. Arıkan: Channel polarization: A method for constructing capacity-achieving codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2008) pp. 1173–1177 E. Arıkan: Channel polarization: A method for constructing capacity-achieving codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2008) pp. 1173–1177
Zurück zum Zitat E. Arıkan: Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels, IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009)MathSciNetMATHCrossRef E. Arıkan: Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels, IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009)MathSciNetMATHCrossRef
Zurück zum Zitat ETSI: 3GPP TR 38.802 V14.2.0, Technical Specification Group Radio Access Network: Study on new radio access technology physical layer aspects (release 14), 3GPP (ETSI, Sophia Antipolis 2017), Tech. Rep. ETSI: 3GPP TR 38.802 V14.2.0, Technical Specification Group Radio Access Network: Study on new radio access technology physical layer aspects (release 14), 3GPP (ETSI, Sophia Antipolis 2017), Tech. Rep.
Zurück zum Zitat G. Sarkis, P. Giard, A. Vardy, C. Thibeault, W.J. Gross: Fast list decoders for polar codes, IEEE J. Sel. Areas Commun. 34(2), 318–328 (2016)CrossRef G. Sarkis, P. Giard, A. Vardy, C. Thibeault, W.J. Gross: Fast list decoders for polar codes, IEEE J. Sel. Areas Commun. 34(2), 318–328 (2016)CrossRef
Zurück zum Zitat P. Giard, C. Thibeault, W.J. Gross: High-Speed Decoders for Polar Codes (Springer, Berlin, Heidelberg 2016) P. Giard, C. Thibeault, W.J. Gross: High-Speed Decoders for Polar Codes (Springer, Berlin, Heidelberg 2016)
Zurück zum Zitat A.J. Felström, K.S. Zigangirov: Time-varying periodic convolutional codes with low-density parity-check matrix, IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999)MathSciNetMATHCrossRef A.J. Felström, K.S. Zigangirov: Time-varying periodic convolutional codes with low-density parity-check matrix, IEEE Trans. Inf. Theory 45(6), 2181–2191 (1999)MathSciNetMATHCrossRef
Zurück zum Zitat M. Lentmaier, G. Fettweis, K. Zigangirov, D. Costello: Approaching capacity with asymptotically regular LDPC codes. In: Proc. Inform. Theory Appl. Workshop (ITA) (2009) M. Lentmaier, G. Fettweis, K. Zigangirov, D. Costello: Approaching capacity with asymptotically regular LDPC codes. In: Proc. Inform. Theory Appl. Workshop (ITA) (2009)
Zurück zum Zitat M. Lentmaier, A. Sridharan, D.J. Costello, K. Zigangirov: Iterative decoding threshold analysis for LDPC convolutional codes, IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010)MathSciNetMATHCrossRef M. Lentmaier, A. Sridharan, D.J. Costello, K. Zigangirov: Iterative decoding threshold analysis for LDPC convolutional codes, IEEE Trans. Inf. Theory 56(10), 5274–5289 (2010)MathSciNetMATHCrossRef
Zurück zum Zitat M. Lentmaier, D. Mitchell, G. Fettweis, D. Costello: Asymptotically good LDPC convolutional codes with AWGN channel thresholds close to the shannon limit. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2010), Brest M. Lentmaier, D. Mitchell, G. Fettweis, D. Costello: Asymptotically good LDPC convolutional codes with AWGN channel thresholds close to the shannon limit. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2010), Brest
Zurück zum Zitat S. Kudekar, T. Richardson, R. Urbanke: Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC, IEEE Trans. Inf. Theory 57(2), 803–834 (2011)MathSciNetMATHCrossRef S. Kudekar, T. Richardson, R. Urbanke: Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC, IEEE Trans. Inf. Theory 57(2), 803–834 (2011)MathSciNetMATHCrossRef
Zurück zum Zitat S. Kudekar, T. Richardson, R. Urbanke: Spatially coupled ensembles universally achieve capacity under belief propagation, IEEE Trans. Inf. Theory 59(12), 7761–7813 (2013)MathSciNetMATHCrossRef S. Kudekar, T. Richardson, R. Urbanke: Spatially coupled ensembles universally achieve capacity under belief propagation, IEEE Trans. Inf. Theory 59(12), 7761–7813 (2013)MathSciNetMATHCrossRef
Zurück zum Zitat A. Iyengar, M. Papaleo, P. Siegel, J. Wolf, A. Vanelli-Coralli, G. Corazza: Windowed decoding of protograph-based LDPC convolutional codes over erasure channels, IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012)MathSciNetMATHCrossRef A. Iyengar, M. Papaleo, P. Siegel, J. Wolf, A. Vanelli-Coralli, G. Corazza: Windowed decoding of protograph-based LDPC convolutional codes over erasure channels, IEEE Trans. Inf. Theory 58(4), 2303–2320 (2012)MathSciNetMATHCrossRef
Zurück zum Zitat S. Moloudi, M. Lentmaier, A. Graell i Amat: Spatially coupled turbo-like codes, IEEE Trans. Inf. Theory 63(10), 6199–6215 (2017)MathSciNetMATHCrossRef S. Moloudi, M. Lentmaier, A. Graell i Amat: Spatially coupled turbo-like codes, IEEE Trans. Inf. Theory 63(10), 6199–6215 (2017)MathSciNetMATHCrossRef
Zurück zum Zitat V. Aref, N. Macris, R. Urbanke, M. Vuffray: Lossy source coding via spatially coupled LDGM ensembles. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2012) pp. 373–377, Cambridge V. Aref, N. Macris, R. Urbanke, M. Vuffray: Lossy source coding via spatially coupled LDGM ensembles. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2012) pp. 373–377, Cambridge
Zurück zum Zitat K. Takeuchi, T. Tanaka, T. Kawabata: Improvement of BP-based CDMA multiuser detection by spatial coupling. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2011) pp. 1489–1493, St. Petersburg K. Takeuchi, T. Tanaka, T. Kawabata: Improvement of BP-based CDMA multiuser detection by spatial coupling. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2011) pp. 1489–1493, St. Petersburg
Zurück zum Zitat D.L. Donoho, A. Javanmard, A. Montanari: Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing, IEEE Trans. Inf. Theory 59(11), 7434–7464 (2013)MathSciNetMATHCrossRef D.L. Donoho, A. Javanmard, A. Montanari: Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing, IEEE Trans. Inf. Theory 59(11), 7434–7464 (2013)MathSciNetMATHCrossRef
Zurück zum Zitat Z. Wu, J.K. Fischer, B. Lankl: Experimental investigation of polar code performance for coherent UDWDM PONs. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015) Z. Wu, J.K. Fischer, B. Lankl: Experimental investigation of polar code performance for coherent UDWDM PONs. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015)
Zurück zum Zitat L. Schmalen, D. Suikat, D. Rösener, V. Aref, A. Leven, S. ten Brink: Spatially coupled codes and optical fiber communications: An ideal match? In: Proc. IEEE Workshop Signal Process. Adv. Wirel. Commun. (SPAWC) (2015) pp. 460–464 L. Schmalen, D. Suikat, D. Rösener, V. Aref, A. Leven, S. ten Brink: Spatially coupled codes and optical fiber communications: An ideal match? In: Proc. IEEE Workshop Signal Process. Adv. Wirel. Commun. (SPAWC) (2015) pp. 460–464
Zurück zum Zitat D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F.N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, Q. Xiong: LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2012) p. OW1H.4CrossRef D. Chang, F. Yu, Z. Xiao, N. Stojanovic, F.N. Hauske, Y. Cai, C. Xie, L. Li, X. Xu, Q. Xiong: LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2012) p. OW1H.4CrossRef
Zurück zum Zitat I.B. Djordjevic, W. Ryan, B. Vasic: Coding for Optical Channels (Springer, Cham 2010)CrossRef I.B. Djordjevic, W. Ryan, B. Vasic: Coding for Optical Channels (Springer, Cham 2010)CrossRef
Zurück zum Zitat A. Leven, L. Schmalen: Status and recent advances on forward error correction technologies for lightwave systems, J. Lightw. Technol. 32(16), 2735–2750 (2014)CrossRef A. Leven, L. Schmalen: Status and recent advances on forward error correction technologies for lightwave systems, J. Lightw. Technol. 32(16), 2735–2750 (2014)CrossRef
Zurück zum Zitat N. Merhav, G. Kaplan, A. Lapidoth, S. Shamai Shitz: On information rates for mismatched decoders, IEEE Trans. Inf. Theory 40(6), 1953–1967 (1994)MATHCrossRef N. Merhav, G. Kaplan, A. Lapidoth, S. Shamai Shitz: On information rates for mismatched decoders, IEEE Trans. Inf. Theory 40(6), 1953–1967 (1994)MATHCrossRef
Zurück zum Zitat A. Ganti, A. Lapidoth, I.E. Telatar: Mismatched decoding revisited: general alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory 46(7), 2315–2328 (2000)MathSciNetMATHCrossRef A. Ganti, A. Lapidoth, I.E. Telatar: Mismatched decoding revisited: general alphabets, channels with memory, and the wide-band limit, IEEE Trans. Inf. Theory 46(7), 2315–2328 (2000)MathSciNetMATHCrossRef
Zurück zum Zitat T. Fehenberger, A. Alvarado, P. Bayvel, N. Hanik: On achievable rates for long-haul fiber-optic communications, Opt. Express 23(7), 9183–9191 (2015)CrossRef T. Fehenberger, A. Alvarado, P. Bayvel, N. Hanik: On achievable rates for long-haul fiber-optic communications, Opt. Express 23(7), 9183–9191 (2015)CrossRef
Zurück zum Zitat A. Sheikh, A. Graell i Amat, G. Liva: Achievable information rates for coded modulation with hard decision decoding for coherent fiber-optic systems, J. Lightwave Technol. 35(23), 5069–5078 (2017)CrossRef A. Sheikh, A. Graell i Amat, G. Liva: Achievable information rates for coded modulation with hard decision decoding for coherent fiber-optic systems, J. Lightwave Technol. 35(23), 5069–5078 (2017)CrossRef
Zurück zum Zitat I.B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov: Achievable information rates for high-speed long-haul optical transmission, J. Lightwave Technol. 23(11), 3755–3763 (2005)CrossRef I.B. Djordjevic, B. Vasic, M. Ivkovic, I. Gabitov: Achievable information rates for high-speed long-haul optical transmission, J. Lightwave Technol. 23(11), 3755–3763 (2005)CrossRef
Zurück zum Zitat E. Agrell, A. Alvarado, G. Durisi, M. Karlsson: Capacity of a nonlinear optical channel with finite memory, J. Lightwave Technol. 32(16), 2862–2876 (2014)CrossRef E. Agrell, A. Alvarado, G. Durisi, M. Karlsson: Capacity of a nonlinear optical channel with finite memory, J. Lightwave Technol. 32(16), 2862–2876 (2014)CrossRef
Zurück zum Zitat R.J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, B. Goebel: Capacity limits of optical fiber networks, J. Lightwave Technol. 28(4), 662–701 (2010)CrossRef R.J. Essiambre, G. Kramer, P.J. Winzer, G.J. Foschini, B. Goebel: Capacity limits of optical fiber networks, J. Lightwave Technol. 28(4), 662–701 (2010)CrossRef
Zurück zum Zitat M. Secondini, E. Forestieri, G. Prati: Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps, J. Lightwave Technol. 31(23), 3839–3852 (2013)CrossRef M. Secondini, E. Forestieri, G. Prati: Achievable information rate in nonlinear WDM fiber-optic systems with arbitrary modulation formats and dispersion maps, J. Lightwave Technol. 31(23), 3839–3852 (2013)CrossRef
Zurück zum Zitat A. Martinez, A. Guillén i Fàbregas, G. Caire, F.M.J. Willems: Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory 55(6), 2756–2765 (2009)MathSciNetMATHCrossRef A. Martinez, A. Guillén i Fàbregas, G. Caire, F.M.J. Willems: Bit-interleaved coded modulation revisited: A mismatched decoding perspective, IEEE Trans. Inf. Theory 55(6), 2756–2765 (2009)MathSciNetMATHCrossRef
Zurück zum Zitat G. Kaplan, S. Shamai Shitz: Information rates and error exponents of compound channels with application to antipodal signaling in a fading environment, AEÜ 47(4), 228–230 (1993) G. Kaplan, S. Shamai Shitz: Information rates and error exponents of compound channels with application to antipodal signaling in a fading environment, AEÜ 47(4), 228–230 (1993)
Zurück zum Zitat P. Poggiolini: The GN model of non-linear propagation in uncompensated coherent optical systems, J. Lightwave Technol. 30(24), 3857–3879 (2012)CrossRef P. Poggiolini: The GN model of non-linear propagation in uncompensated coherent optical systems, J. Lightwave Technol. 30(24), 3857–3879 (2012)CrossRef
Zurück zum Zitat P. Johannisson, E. Agrell: Modeling of nonlinear signal distortion in fiber-optic networks, J. Lightwave Technol. 32(23), 3942–3950 (2014)CrossRef P. Johannisson, E. Agrell: Modeling of nonlinear signal distortion in fiber-optic networks, J. Lightwave Technol. 32(23), 3942–3950 (2014)CrossRef
Zurück zum Zitat W.E. Ryan, S. Lin: Channel Codes. Classical and Modern (Cambridge Univ. Press, Cambridge 2009)MATHCrossRef W.E. Ryan, S. Lin: Channel Codes. Classical and Modern (Cambridge Univ. Press, Cambridge 2009)MATHCrossRef
Zurück zum Zitat R.L. Dobrushin: Asymptotic optimality of group and systematic codes for some channels, Theory Probab. Appl. 8(1), 47–60 (1963)MATHCrossRef R.L. Dobrushin: Asymptotic optimality of group and systematic codes for some channels, Theory Probab. Appl. 8(1), 47–60 (1963)MATHCrossRef
Zurück zum Zitat A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, F. Forghieri: EGN model of non-linear fiber propagation, Opt. Express 22(13), 16335–16362 (2014)CrossRef A. Carena, G. Bosco, V. Curri, Y. Jiang, P. Poggiolini, F. Forghieri: EGN model of non-linear fiber propagation, Opt. Express 22(13), 16335–16362 (2014)CrossRef
Zurück zum Zitat N.A. Shevchenko, J.E. Prilepsky, S.A. Derevyanko, A. Alvarado, P. Bayvel, S.K. Turitsyn: A lower bound on the per soliton capacity of the nonlinear optical fibre channel. In: Proc. IEEE Inform. Theory Workshop (ITW) (2015) pp. 104–108 N.A. Shevchenko, J.E. Prilepsky, S.A. Derevyanko, A. Alvarado, P. Bayvel, S.K. Turitsyn: A lower bound on the per soliton capacity of the nonlinear optical fibre channel. In: Proc. IEEE Inform. Theory Workshop (ITW) (2015) pp. 104–108
Zurück zum Zitat A. Alvarado, L. Szczecinski, R. Feick: On the distribution of extrinsic L-values in gray-mapped 16-QAM. In: Proc. Int. Conf. Wirel. Commun. Mobile Comp. (IWCMC) (2007) pp. 329–336 A. Alvarado, L. Szczecinski, R. Feick: On the distribution of extrinsic L-values in gray-mapped 16-QAM. In: Proc. Int. Conf. Wirel. Commun. Mobile Comp. (IWCMC) (2007) pp. 329–336
Zurück zum Zitat S. Dolinar, D. Divsalar, F. Pollara: Code performance as a function of block size (Jet Propulsion Laboratory, Pasadena 1998) pp. 42–133, TMO Prog. Rep. S. Dolinar, D. Divsalar, F. Pollara: Code performance as a function of block size (Jet Propulsion Laboratory, Pasadena 1998) pp. 42–133, TMO Prog. Rep.
Zurück zum Zitat Y. Polyanskiy, H. Poor, S. Verdu: Channel coding rate in the finite blocklength regime, IEEE Trans. Inf. Theory 56(5), 2307–2359 (2010)MathSciNetMATHCrossRef Y. Polyanskiy, H. Poor, S. Verdu: Channel coding rate in the finite blocklength regime, IEEE Trans. Inf. Theory 56(5), 2307–2359 (2010)MathSciNetMATHCrossRef
Zurück zum Zitat C.E. Shannon: Probability of error for optimal codes in a gaussian channel, Bell Syst. Tech. J. 38, 611–656 (1959)MathSciNetCrossRef C.E. Shannon: Probability of error for optimal codes in a gaussian channel, Bell Syst. Tech. J. 38, 611–656 (1959)MathSciNetCrossRef
Zurück zum Zitat T. Erseghe: Coding in the finite-blocklength regime: Bounds based on Laplace integrals and their asymptotic approximations, IEEE Trans. Inf. Theory 62(12), 6854–6883 (2016)MathSciNetMATHCrossRef T. Erseghe: Coding in the finite-blocklength regime: Bounds based on Laplace integrals and their asymptotic approximations, IEEE Trans. Inf. Theory 62(12), 6854–6883 (2016)MathSciNetMATHCrossRef
Zurück zum Zitat T. Richardson, R. Urbanke: Modern Coding Theory (Cambridge Univ. Press, Cambridge 2008)MATHCrossRef T. Richardson, R. Urbanke: Modern Coding Theory (Cambridge Univ. Press, Cambridge 2008)MATHCrossRef
Zurück zum Zitat T.J. Richardson, M.A. Shokrollahi, R.L. Urbanke: Design of capacity-approaching irregular low-density parity-check codes, IEEE Trans. Inf. Theory 47(2), 619–637 (2001)MathSciNetMATHCrossRef T.J. Richardson, M.A. Shokrollahi, R.L. Urbanke: Design of capacity-approaching irregular low-density parity-check codes, IEEE Trans. Inf. Theory 47(2), 619–637 (2001)MathSciNetMATHCrossRef
Zurück zum Zitat D. Divsalar, C. Jones, S. Dolinar, J. Thorpe: Protograph based LDPC codes with minimum distance linearly growing with block size. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Vol. 3 (2005) p. 5 D. Divsalar, C. Jones, S. Dolinar, J. Thorpe: Protograph based LDPC codes with minimum distance linearly growing with block size. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Vol. 3 (2005) p. 5
Zurück zum Zitat Consultative Committee for Space Data Systems (CCSDS): TM synchronization and channel coding, recommended standard, CCSDS 131.0-B-2, blue book (CCSDS, Washington 2011), Tech. Rep. Consultative Committee for Space Data Systems (CCSDS): TM synchronization and channel coding, recommended standard, CCSDS 131.0-B-2, blue book (CCSDS, Washington 2011), Tech. Rep.
Zurück zum Zitat L. Dolecek, P. Lee, Z. Zhang, V. Anantharam, B. Nikolic, M. Wainwright: Predicting error floors of structured LDPC codes: Deterministic bounds and estimates, IEEE J. Sel. Areas Commun. 27(6), 908–917 (2009)CrossRef L. Dolecek, P. Lee, Z. Zhang, V. Anantharam, B. Nikolic, M. Wainwright: Predicting error floors of structured LDPC codes: Deterministic bounds and estimates, IEEE J. Sel. Areas Commun. 27(6), 908–917 (2009)CrossRef
Zurück zum Zitat T. Richardson, R. Urbanke: The capacity of low-density parity-check codes under belief propagation decoding, IEEE Trans. Inf. Theory 47(2), 599–618 (2001)MATHCrossRef T. Richardson, R. Urbanke: The capacity of low-density parity-check codes under belief propagation decoding, IEEE Trans. Inf. Theory 47(2), 599–618 (2001)MATHCrossRef
Zurück zum Zitat S. Jayasooriya, M. Shirvanimoghaddam, L. Ong, G. Lechner, S.J. Johnson: A new density evolution approximation for LDPC and multi-edge type LDPC codes, IEEE Trans. Commun. 64(10), 4044–4056 (2016) S. Jayasooriya, M. Shirvanimoghaddam, L. Ong, G. Lechner, S.J. Johnson: A new density evolution approximation for LDPC and multi-edge type LDPC codes, IEEE Trans. Commun. 64(10), 4044–4056 (2016)
Zurück zum Zitat S.-Y. Chung, G.D. Forney Jr., T. Richardson, R. Urbanke: On the design of low-density parity-check codes within 0.0045 db of the Shannon limit, IEEE Commun. Lett. 5(2), 58–60 (2001)CrossRef S.-Y. Chung, G.D. Forney Jr., T. Richardson, R. Urbanke: On the design of low-density parity-check codes within 0.0045 db of the Shannon limit, IEEE Commun. Lett. 5(2), 58–60 (2001)CrossRef
Zurück zum Zitat S. ten Brink, G. Kramer, A. Ashikhmin: Design of low-density parity-check codes for modulation and detection, IEEE Trans. Commun. 52(4), 670–678 (2004)CrossRef S. ten Brink, G. Kramer, A. Ashikhmin: Design of low-density parity-check codes for modulation and detection, IEEE Trans. Commun. 52(4), 670–678 (2004)CrossRef
Zurück zum Zitat L. Schmalen, S. ten Brink, A. Leven: Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs. In: Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, ed. by X. Zhou, C. Xie (Wiley, Hoboken 2016), Chap. 3 L. Schmalen, S. ten Brink, A. Leven: Advances in detection and error correction for coherent optical communications: Regular, irregular, and spatially coupled LDPC code designs. In: Enabling Technologies for High Spectral-Efficiency Coherent Optical Communication Networks, ed. by X. Zhou, C. Xie (Wiley, Hoboken 2016), Chap. 3
Zurück zum Zitat B. Vasic, I.B. Djordjevic, R.K. Kostuk: Low-density parity check codes and iterative decoding for long-haul optical communication systems, J. Lightwave Technol. 21(2), 438 (2003)CrossRef B. Vasic, I.B. Djordjevic, R.K. Kostuk: Low-density parity check codes and iterative decoding for long-haul optical communication systems, J. Lightwave Technol. 21(2), 438 (2003)CrossRef
Zurück zum Zitat G. Liva, S. Song, L. Lan, Y. Zhang, S. Lin, W. Ryan: Design of LDPC codes: A survey and new results, J. Commun. Software Syst. 2(3), 191–211 (2006)CrossRef G. Liva, S. Song, L. Lan, Y. Zhang, S. Lin, W. Ryan: Design of LDPC codes: A survey and new results, J. Commun. Software Syst. 2(3), 191–211 (2006)CrossRef
Zurück zum Zitat N. Bonello, S. Chen, L. Hanzo: Design of low-density parity-check codes, IEEE Veh. Technol. Mag. 6(4), 1574–1606 (2011)CrossRef N. Bonello, S. Chen, L. Hanzo: Design of low-density parity-check codes, IEEE Veh. Technol. Mag. 6(4), 1574–1606 (2011)CrossRef
Zurück zum Zitat X.-Y. Hu, E. Eleftheriou, D.M. Arnold: Regular and irregular progressive edge-growth Tanner graphs, IEEE Trans. Inf. Theory 51(1), 386–398 (2005)MathSciNetMATHCrossRef X.-Y. Hu, E. Eleftheriou, D.M. Arnold: Regular and irregular progressive edge-growth Tanner graphs, IEEE Trans. Inf. Theory 51(1), 386–398 (2005)MathSciNetMATHCrossRef
Zurück zum Zitat T. Tian, C. Jones, J.D. Villasenor, R.D. Wesel: Construction of irregular LDPC codes with low error floors. In: Proc. IEEE Int. Conf. Commun. (ICC) (2003) pp. 3125–3129 T. Tian, C. Jones, J.D. Villasenor, R.D. Wesel: Construction of irregular LDPC codes with low error floors. In: Proc. IEEE Int. Conf. Commun. (ICC) (2003) pp. 3125–3129
Zurück zum Zitat H. Xiao, A.H. Banihashemi: Improved progressive-edge-growth (PEG) construction of irregular LDPC codes, IEEE Commun. Lett. 8(12), 715–717 (2004)CrossRef H. Xiao, A.H. Banihashemi: Improved progressive-edge-growth (PEG) construction of irregular LDPC codes, IEEE Commun. Lett. 8(12), 715–717 (2004)CrossRef
Zurück zum Zitat T. Tian, C.R. Jones, J.D. Villasenor, R.D. Wesel: Selective avoidance of cycles in irregular LDPC code construction, IEEE Trans. Commun. 52(8), 1242–1247 (2004)CrossRef T. Tian, C.R. Jones, J.D. Villasenor, R.D. Wesel: Selective avoidance of cycles in irregular LDPC code construction, IEEE Trans. Commun. 52(8), 1242–1247 (2004)CrossRef
Zurück zum Zitat T. Richardson, R. Urbanke: Multi-edge type LDPC codes. In: Workshop honoring Prof. Bob McEliece on his 60th birthday (California Institute of Technology, Pasadena 2002) pp. 24–25 T. Richardson, R. Urbanke: Multi-edge type LDPC codes. In: Workshop honoring Prof. Bob McEliece on his 60th birthday (California Institute of Technology, Pasadena 2002) pp. 24–25
Zurück zum Zitat J. Thorpe: Low-density parity-check (LDPC) codes constructed from protographs (NASA JPL, Pasadena 2003), IPN Progress Report 42-154 J. Thorpe: Low-density parity-check (LDPC) codes constructed from protographs (NASA JPL, Pasadena 2003), IPN Progress Report 42-154
Zurück zum Zitat J. Li, S. Lin, K. Abdel-Ghaffar, W.E. Ryan, D.J. Costello Jr.: LDPC Code Designs, Constructions, and Unification (Cambridge Univ. Press, Cambridge 2016)MATH J. Li, S. Lin, K. Abdel-Ghaffar, W.E. Ryan, D.J. Costello Jr.: LDPC Code Designs, Constructions, and Unification (Cambridge Univ. Press, Cambridge 2016)MATH
Zurück zum Zitat M.P.C. Fossorier: Quasi-cyclic low-density parity-check codes from circulant permutation matrices, IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004)MathSciNetMATHCrossRef M.P.C. Fossorier: Quasi-cyclic low-density parity-check codes from circulant permutation matrices, IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004)MathSciNetMATHCrossRef
Zurück zum Zitat R. Smarandache, P.O. Vontobel: Quasi-cyclic LDPC codes: Influence of proto-and Tanner-graph structure on minimum Hamming distance upper bounds, IEEE Trans. Inf. Theory 58(2), 585–607 (2012)MathSciNetMATHCrossRef R. Smarandache, P.O. Vontobel: Quasi-cyclic LDPC codes: Influence of proto-and Tanner-graph structure on minimum Hamming distance upper bounds, IEEE Trans. Inf. Theory 58(2), 585–607 (2012)MathSciNetMATHCrossRef
Zurück zum Zitat X. Jiang, M.H. Lee: Large girth quasi-cyclic LDPC codes based on the Chinese remainder theorem, IEEE Commun. Lett. 13(5), 342–344 (2009)CrossRef X. Jiang, M.H. Lee: Large girth quasi-cyclic LDPC codes based on the Chinese remainder theorem, IEEE Commun. Lett. 13(5), 342–344 (2009)CrossRef
Zurück zum Zitat T. Richardson, R. Urbanke: Efficient encoding of low-density parity-check codes, IEEE Trans. Inf. Theory 47(2), 638–656 (2001)MathSciNetMATHCrossRef T. Richardson, R. Urbanke: Efficient encoding of low-density parity-check codes, IEEE Trans. Inf. Theory 47(2), 638–656 (2001)MathSciNetMATHCrossRef
Zurück zum Zitat D.J.C. MacKay: Information Theory, Inference and Learning Algorithms (Cambridge Univ. Press, Cambridge 2003)MATH D.J.C. MacKay: Information Theory, Inference and Learning Algorithms (Cambridge Univ. Press, Cambridge 2003)MATH
Zurück zum Zitat J. Pearl: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, New York 1988)MATH J. Pearl: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, New York 1988)MATH
Zurück zum Zitat G. Lechner, T. Pedersen, G. Kramer: Analysis and design of binary message passing decoders, IEEE Trans. Commun. 60(3), 601–607 (2012)CrossRef G. Lechner, T. Pedersen, G. Kramer: Analysis and design of binary message passing decoders, IEEE Trans. Commun. 60(3), 601–607 (2012)CrossRef
Zurück zum Zitat J. Hagenauer, E. Offer, L. Papke: Iterative decoding of binary block and convolutional codes, IEEE Trans. Inf. Theory 42(2), 429–445 (1996)MATHCrossRef J. Hagenauer, E. Offer, L. Papke: Iterative decoding of binary block and convolutional codes, IEEE Trans. Inf. Theory 42(2), 429–445 (1996)MATHCrossRef
Zurück zum Zitat D.R. Pauluzzi, N.C. Beaulieu: A comparison of SNR estimation techniques for the AWGN channel, IEEE Trans. Commun. 48(10), 1681–1691 (2000)CrossRef D.R. Pauluzzi, N.C. Beaulieu: A comparison of SNR estimation techniques for the AWGN channel, IEEE Trans. Commun. 48(10), 1681–1691 (2000)CrossRef
Zurück zum Zitat C.F. Mecklenbräuker, S. Paul: On estimating the signal to noise ratio from BPSK signals. In: Proc. Int. Conf. Acoust. Speech Signal Process. (ICASSP), Vol. 4 (2005) C.F. Mecklenbräuker, S. Paul: On estimating the signal to noise ratio from BPSK signals. In: Proc. Int. Conf. Acoust. Speech Signal Process. (ICASSP), Vol. 4 (2005)
Zurück zum Zitat T.K. Moon: Error Correction Coding - Mathematical Methods and Algorithms (Wiley, Hoboken 2005)MATHCrossRef T.K. Moon: Error Correction Coding - Mathematical Methods and Algorithms (Wiley, Hoboken 2005)MATHCrossRef
Zurück zum Zitat J. Chen, M.P.C. Fossorier: Near optimum universal belief propagation based decoding of low-density parity check codes, IEEE Trans. Commun. 50(3), 406–414 (2002)CrossRef J. Chen, M.P.C. Fossorier: Near optimum universal belief propagation based decoding of low-density parity check codes, IEEE Trans. Commun. 50(3), 406–414 (2002)CrossRef
Zurück zum Zitat M. Ardakani, F.R. Kschischang: Gear-shift decoding, IEEE Trans. Commun. 54(7), 1235–1242 (2006)CrossRef M. Ardakani, F.R. Kschischang: Gear-shift decoding, IEEE Trans. Commun. 54(7), 1235–1242 (2006)CrossRef
Zurück zum Zitat J. Zhao, F. Zarkeshvari, A.H. Banihashemi: On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes, IEEE Trans. Commun. 53(4), 549–554 (2005)CrossRef J. Zhao, F. Zarkeshvari, A.H. Banihashemi: On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes, IEEE Trans. Commun. 53(4), 549–554 (2005)CrossRef
Zurück zum Zitat D. Hocevar: A reduced complexity decoder architecture via layered decoding of LDPC codes. In: Proc. IEEE Workshop Signal Process. Syst. (SiPS) (2004) D. Hocevar: A reduced complexity decoder architecture via layered decoding of LDPC codes. In: Proc. IEEE Workshop Signal Process. Syst. (SiPS) (2004)
Zurück zum Zitat A. Leven, L. Schmalen: Implementation aspects of coherent transmit and receive functions in application-specific integrated circuits. In: Optical Fiber Telecommunications VI-A, ed. by I.P. Kaminow, T. Li, A.E. Willner (Academic, New York 2013), Chap. 15 A. Leven, L. Schmalen: Implementation aspects of coherent transmit and receive functions in application-specific integrated circuits. In: Optical Fiber Telecommunications VI-A, ed. by I.P. Kaminow, T. Li, A.E. Willner (Academic, New York 2013), Chap. 15
Zurück zum Zitat A. Yedla, Y.-Y. Jian, P.S. Nguyen, H.D. Pfister: A simple proof of Maxwell saturation for coupled scalar recursions, IEEE Trans. Inf. Theory 60(11), 6943–6965 (2014)MathSciNetMATHCrossRef A. Yedla, Y.-Y. Jian, P.S. Nguyen, H.D. Pfister: A simple proof of Maxwell saturation for coupled scalar recursions, IEEE Trans. Inf. Theory 60(11), 6943–6965 (2014)MathSciNetMATHCrossRef
Zurück zum Zitat A. Yedla, Y.-Y. Jian, P. Nguyen, H. Pfister: A simple proof of threshold saturation for coupled vector recursions. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 25–29, Lausanne A. Yedla, Y.-Y. Jian, P. Nguyen, H. Pfister: A simple proof of threshold saturation for coupled vector recursions. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 25–29, Lausanne
Zurück zum Zitat A. Piemontese, A. Graell i Amat, G. Colavolpe: Nonbinary spatially-coupled LDPC codes on the binary erasure channel. In: Proc. IEEE Int. Conf. Commun. (ICC) (2013) pp. 3270–3274, Budapest A. Piemontese, A. Graell i Amat, G. Colavolpe: Nonbinary spatially-coupled LDPC codes on the binary erasure channel. In: Proc. IEEE Int. Conf. Commun. (ICC) (2013) pp. 3270–3274, Budapest
Zurück zum Zitat I. Andriyanova, A. Graell i Amat: Threshold saturation for nonbinary SC-LDPC codes on the binary erasure channel, IEEE Trans. Inf. Theory 62(5), 2622–2638 (2016)MathSciNetMATHCrossRef I. Andriyanova, A. Graell i Amat: Threshold saturation for nonbinary SC-LDPC codes on the binary erasure channel, IEEE Trans. Inf. Theory 62(5), 2622–2638 (2016)MathSciNetMATHCrossRef
Zurück zum Zitat ITU-T: Recommendation G.709: Interfaces for the optical transport network (ITU-T, Genf 2016) ITU-T: Recommendation G.709: Interfaces for the optical transport network (ITU-T, Genf 2016)
Zurück zum Zitat W. Lautenschlaeger, N. Benzaoui, F. Buchali, L. Dembeck, R. Dischler, B. Franz, U. Gebhard, J. Milbrandt, Y. Pointurier, D. Roesener, L. Schmalen, A. Leven: Optical ethernet – flexible optical metro networks, J. Lightwave Technol. 35(12), 2346–2357 (2017)CrossRef W. Lautenschlaeger, N. Benzaoui, F. Buchali, L. Dembeck, R. Dischler, B. Franz, U. Gebhard, J. Milbrandt, Y. Pointurier, D. Roesener, L. Schmalen, A. Leven: Optical ethernet – flexible optical metro networks, J. Lightwave Technol. 35(12), 2346–2357 (2017)CrossRef
Zurück zum Zitat S. Kudekar, C. Méasson, T. Richardsony, R. Urbanke: Threshold saturation on BMS channels via spatial coupling. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2010) pp. 309–313 S. Kudekar, C. Méasson, T. Richardsony, R. Urbanke: Threshold saturation on BMS channels via spatial coupling. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2010) pp. 309–313
Zurück zum Zitat C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, E. Agrell: Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels. In: Proc. IEEE Int. Conf. Commun. (ICC) (2014) pp. 2064–2069, Sydney C. Häger, A. Graell i Amat, A. Alvarado, F. Brännström, E. Agrell: Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels. In: Proc. IEEE Int. Conf. Commun. (ICC) (2014) pp. 2064–2069, Sydney
Zurück zum Zitat S. Cammerer, V. Aref, L. Schmalen, S. ten Brink: Triggering wave-like convergence of tail-biting spatially coupled LDPC codes. In: Conf. Inform. Sci. Syst. (CISS) (2016) pp. 93–98 S. Cammerer, V. Aref, L. Schmalen, S. ten Brink: Triggering wave-like convergence of tail-biting spatially coupled LDPC codes. In: Conf. Inform. Sci. Syst. (CISS) (2016) pp. 93–98
Zurück zum Zitat L. Schmalen, V. Aref, F. Jardel: Non-uniformly coupled LDPC codes: Better thresholds, smaller rate-loss, and less complexity. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017), Aachen L. Schmalen, V. Aref, F. Jardel: Non-uniformly coupled LDPC codes: Better thresholds, smaller rate-loss, and less complexity. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017), Aachen
Zurück zum Zitat S. Kudekar, T. Richardson, R. Urbanke: Wave-like solutions of general one-dimensional spatially coupled systems, IEEE Trans. Inf. Theory 61(8), 4117–4157 (2015)MATHCrossRef S. Kudekar, T. Richardson, R. Urbanke: Wave-like solutions of general one-dimensional spatially coupled systems, IEEE Trans. Inf. Theory 61(8), 4117–4157 (2015)MATHCrossRef
Zurück zum Zitat M. Tavares: On low-density parity-check convolutional codes: Constructions, analysis and VLSI implementations, Ph.D. dissertation (TU Dresden, Dresden 2010) M. Tavares: On low-density parity-check convolutional codes: Constructions, analysis and VLSI implementations, Ph.D. dissertation (TU Dresden, Dresden 2010)
Zurück zum Zitat A.E. Pusane, A.J. Feltström, A. Sridharan, M. Lentmaier, K.S. Zigangirov, D.J. Costello Jr.: Implementation aspects of LDPC convolutional codes, IEEE Trans. Commun. 56(7), 1060–1069 (2008)CrossRef A.E. Pusane, A.J. Feltström, A. Sridharan, M. Lentmaier, K.S. Zigangirov, D.J. Costello Jr.: Implementation aspects of LDPC convolutional codes, IEEE Trans. Commun. 56(7), 1060–1069 (2008)CrossRef
Zurück zum Zitat V. Aref, L. Schmalen, S. ten Brink: On the convergence speed of spatially coupled LDPC ensembles. In: Proc. Allerton Annu. Conf. Commun. Control Comp. (2013) p. 2013, arXiv: 1307.3780 V. Aref, L. Schmalen, S. ten Brink: On the convergence speed of spatially coupled LDPC ensembles. In: Proc. Allerton Annu. Conf. Commun. Control Comp. (2013) p. 2013, arXiv: 1307.3780
Zurück zum Zitat R. El-Khatib, N. Macris: The velocity of the decoding wave for spatially coupled codes on BMS channels. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2119–2123 R. El-Khatib, N. Macris: The velocity of the decoding wave for spatially coupled codes on BMS channels. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2119–2123
Zurück zum Zitat R. El-Khatib, N. Macris: The velocity of the propagating wave for spatially coupled systems with applications to LDPC codes, IEEE Trans. Inf. Theory 64(11), 7113–7131 (2018)MathSciNetMATHCrossRef R. El-Khatib, N. Macris: The velocity of the propagating wave for spatially coupled systems with applications to LDPC codes, IEEE Trans. Inf. Theory 64(11), 7113–7131 (2018)MathSciNetMATHCrossRef
Zurück zum Zitat L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, A. Leven: Spatially coupled soft-decision error correction for future lightwave systems, J. Lightwave Technol. 33(5), 1109–1116 (2015)CrossRef L. Schmalen, V. Aref, J. Cho, D. Suikat, D. Rösener, A. Leven: Spatially coupled soft-decision error correction for future lightwave systems, J. Lightwave Technol. 33(5), 1109–1116 (2015)CrossRef
Zurück zum Zitat P.M. Olmos, R. Urbanke: A scaling law to predict the finite-length performance of spatially-coupled LDPC codes, IEEE Trans. Inf. Theory 61(6), 3164–3184 (2015)MathSciNetMATHCrossRef P.M. Olmos, R. Urbanke: A scaling law to predict the finite-length performance of spatially-coupled LDPC codes, IEEE Trans. Inf. Theory 61(6), 3164–3184 (2015)MathSciNetMATHCrossRef
Zurück zum Zitat M. Stinner, P.M. Olmos: Analyzing finite-length protograph-based spatially coupled LDPC codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2014) pp. 891–895 M. Stinner, P.M. Olmos: Analyzing finite-length protograph-based spatially coupled LDPC codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2014) pp. 891–895
Zurück zum Zitat J. Cho, L. Schmalen: Construction of protographs for large-girth structured LDPC convolutional codes. In: Proc. IEEE Int. Conf. Commun. (ICC) (2015) pp. 4412–4417 J. Cho, L. Schmalen: Construction of protographs for large-girth structured LDPC convolutional codes. In: Proc. IEEE Int. Conf. Commun. (ICC) (2015) pp. 4412–4417
Zurück zum Zitat M. Battaglioni, A. Tasdighi, G. Cancellieri, F. Chiaraluce, M. Baldi: Design and analysis of time-invariant SC-LDPC codes with small constraint length, IEEE Trans. Commun. 66(3), 918–931 (2018)CrossRef M. Battaglioni, A. Tasdighi, G. Cancellieri, F. Chiaraluce, M. Baldi: Design and analysis of time-invariant SC-LDPC codes with small constraint length, IEEE Trans. Commun. 66(3), 918–931 (2018)CrossRef
Zurück zum Zitat D. Achlioptas, H. Hassani, W. Liu, R. Urbanke: Time-invariant LDPC convolutional codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017), Aachen D. Achlioptas, H. Hassani, W. Liu, R. Urbanke: Time-invariant LDPC convolutional codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017), Aachen
Zurück zum Zitat L. Schmalen, D. Suikat, D. Rösener, A. Leven: Evaluation of left-terminated spatially coupled LDPC codes for optical communications. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014) L. Schmalen, D. Suikat, D. Rösener, A. Leven: Evaluation of left-terminated spatially coupled LDPC codes for optical communications. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014)
Zurück zum Zitat K. Tazoe, K. Kasai, K. Sakaniwa: Efficient termination of spatially-coupled codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) K. Tazoe, K. Kasai, K. Sakaniwa: Efficient termination of spatially-coupled codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012)
Zurück zum Zitat M.R. Sanatkar, H.D. Pfister: Increasing the rate of spatially-coupled codes via optimized irregular termination. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2016) M.R. Sanatkar, H.D. Pfister: Increasing the rate of spatially-coupled codes via optimized irregular termination. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2016)
Zurück zum Zitat H. Kwak, J. Kim, Jong-Seon: Rate-loss reduction of SC-LDPC codes by optimizing reliable variable nodes via expected graph evolution. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017) pp. 2930–2934 H. Kwak, J. Kim, Jong-Seon: Rate-loss reduction of SC-LDPC codes by optimizing reliable variable nodes via expected graph evolution. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2017) pp. 2930–2934
Zurück zum Zitat T. Jerkovits, G. Liva, A. Graell i Amat: Improving the decoding threshold of tailbiting spatially coupled LDPC codes by energy shaping, IEEE Commun. Lett. 22(4), 660–663 (2018)CrossRef T. Jerkovits, G. Liva, A. Graell i Amat: Improving the decoding threshold of tailbiting spatially coupled LDPC codes by energy shaping, IEEE Commun. Lett. 22(4), 660–663 (2018)CrossRef
Zurück zum Zitat C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Comparison of terminated and tailbiting spatially coupled LDPC codes with optimized bit mapping for PM-64-QAM. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014) C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Comparison of terminated and tailbiting spatially coupled LDPC codes with optimized bit mapping for PM-64-QAM. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014)
Zurück zum Zitat C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Improving soft FEC performance for higher-order modulations via optimized bit channel mappings, Opt. Express 22(12), 14544–14558 (2014)CrossRef C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Improving soft FEC performance for higher-order modulations via optimized bit channel mappings, Opt. Express 22(12), 14544–14558 (2014)CrossRef
Zurück zum Zitat C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Terminated and tailbiting spatially coupled codes with optimized bit mappings for spectrally efficient fiber-optical systems, J. Lightwave Technol. 33(7), 1275–1285 (2015)CrossRef C. Häger, A. Graell i Amat, F. Brännström, A. Alvarado, E. Agrell: Terminated and tailbiting spatially coupled codes with optimized bit mappings for spectrally efficient fiber-optical systems, J. Lightwave Technol. 33(7), 1275–1285 (2015)CrossRef
Zurück zum Zitat S. Cammerer, L. Schmalen, V. Aref, S. ten Brink: Wave-like decoding of tail-biting spatially coupled LDPC codes through iterative demapping. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2016) pp. 121–125 S. Cammerer, L. Schmalen, V. Aref, S. ten Brink: Wave-like decoding of tail-biting spatially coupled LDPC codes through iterative demapping. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2016) pp. 121–125
Zurück zum Zitat L. Schmalen, D. Suikat, V. Aref, D. Rösener: On the design of capacity-approaching unit-memory spatially coupled LDPC codes for optical communications. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2016) pp. 1–3 L. Schmalen, D. Suikat, V. Aref, D. Rösener: On the design of capacity-approaching unit-memory spatially coupled LDPC codes for optical communications. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2016) pp. 1–3
Zurück zum Zitat T. Koike-Akino, S.C. Draper, Y. Wang, K. Sugihara, W. Matsumoto, D.S. Millar, K. Parsons, V. Arlunno, K. Kojima: Optimal layered scheduling for hardware-efficient windowed decoding of LDPC convolutional codes. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2016) pp. 1–3 T. Koike-Akino, S.C. Draper, Y. Wang, K. Sugihara, W. Matsumoto, D.S. Millar, K. Parsons, V. Arlunno, K. Kojima: Optimal layered scheduling for hardware-efficient windowed decoding of LDPC convolutional codes. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2016) pp. 1–3
Zurück zum Zitat K. Klaiber, S. Cammerer, L. Schmalen, S. ten Brink: Avoiding burst-like error patterns in windowed decoding of spatially coupled LDPC codes. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2018), Hong Kong K. Klaiber, S. Cammerer, L. Schmalen, S. ten Brink: Avoiding burst-like error patterns in windowed decoding of spatially coupled LDPC codes. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2018), Hong Kong
Zurück zum Zitat D.J. Costello Jr., L. Dolecek, T. Fuja, J. Kliewer, D. Mitchell, R. Smarandache: Spatially coupled sparse codes on graphs: Theory and practice, IEEE Commun. Mag. 52(7), 168–176 (2014)CrossRef D.J. Costello Jr., L. Dolecek, T. Fuja, J. Kliewer, D. Mitchell, R. Smarandache: Spatially coupled sparse codes on graphs: Theory and practice, IEEE Commun. Mag. 52(7), 168–176 (2014)CrossRef
Zurück zum Zitat E. Şaşoğlu, I. Telatar, E. Arıkan: Polarization for arbitrary discrete memoryless channels. In: Proc. IEEE Inform. Theory Workshop (ITW) (2009) pp. 144–148 E. Şaşoğlu, I. Telatar, E. Arıkan: Polarization for arbitrary discrete memoryless channels. In: Proc. IEEE Inform. Theory Workshop (ITW) (2009) pp. 144–148
Zurück zum Zitat D. Sutter, J.M. Renes, F. Dupuis, R. Renner: Achieving the capacity of any DMC using only polar codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 114–118 D. Sutter, J.M. Renes, F. Dupuis, R. Renner: Achieving the capacity of any DMC using only polar codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 114–118
Zurück zum Zitat N. Stolte: Rekursive Codes mit der Plotkin-Konstruktion und ihre Decodierung, Ph.D. dissertation (Technische Universität Darmstadt, Darmstadt 2002) N. Stolte: Rekursive Codes mit der Plotkin-Konstruktion und ihre Decodierung, Ph.D. dissertation (Technische Universität Darmstadt, Darmstadt 2002)
Zurück zum Zitat E. Arıkan: Systematic polar coding, IEEE Commun. Lett. 15(8), 860–862 (2011)CrossRef E. Arıkan: Systematic polar coding, IEEE Commun. Lett. 15(8), 860–862 (2011)CrossRef
Zurück zum Zitat T. Ahmad: Polar codes for optical communications, Ph.D. dissertation (Bilkent University, Ankara 2016) T. Ahmad: Polar codes for optical communications, Ph.D. dissertation (Bilkent University, Ankara 2016)
Zurück zum Zitat G. Sarkis, P. Giard, A. Vardy, C. Thibeault, W.J. Gross: Fast polar decoders: Algorithm and implementation, IEEE J. Sel. Areas Commun. 32(5), 946–957 (2014)CrossRef G. Sarkis, P. Giard, A. Vardy, C. Thibeault, W.J. Gross: Fast polar decoders: Algorithm and implementation, IEEE J. Sel. Areas Commun. 32(5), 946–957 (2014)CrossRef
Zurück zum Zitat S. Cammerer, M. Ebada, A. Elkelesh, S. ten Brink: Sparse graphs for belief propagation decoding of polar codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2018) pp. 1465–1469, Vail S. Cammerer, M. Ebada, A. Elkelesh, S. ten Brink: Sparse graphs for belief propagation decoding of polar codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2018) pp. 1465–1469, Vail
Zurück zum Zitat C. Berrou, A. Glavieux: Near optimum error correcting coding and decoding: Turbo-codes, IEEE Trans. Commun. 44(10), 1261–1271 (1996)CrossRef C. Berrou, A. Glavieux: Near optimum error correcting coding and decoding: Turbo-codes, IEEE Trans. Commun. 44(10), 1261–1271 (1996)CrossRef
Zurück zum Zitat J. Zhang, Y. Wang, M.P.C. Fossorier, J.S. Yedidia: Iterative decoding with replicas, IEEE Trans. Inf. Theory 53(5), 1644–1663 (2007)MathSciNetMATHCrossRef J. Zhang, Y. Wang, M.P.C. Fossorier, J.S. Yedidia: Iterative decoding with replicas, IEEE Trans. Inf. Theory 53(5), 1644–1663 (2007)MathSciNetMATHCrossRef
Zurück zum Zitat M. Mondelli, S.H. Hassani, R.L. Urbanke: Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors, IEEE Trans. Inf. Theory 62(12), 6698–6712 (2016)MathSciNetMATHCrossRef M. Mondelli, S.H. Hassani, R.L. Urbanke: Unified scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error floors, IEEE Trans. Inf. Theory 62(12), 6698–6712 (2016)MathSciNetMATHCrossRef
Zurück zum Zitat Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, M. Wainwright: Investigation of error floors of structured low-density parity-check codes by hardware emulation. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2006) Z. Zhang, L. Dolecek, B. Nikolic, V. Anantharam, M. Wainwright: Investigation of error floors of structured low-density parity-check codes by hardware emulation. In: Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (2006)
Zurück zum Zitat M. Arabaci, I.B. Djordjevic: An alternative FPGA implementation of decoders for quasi-cyclic LDPC codes. In: Proc. Telecommun. Forum (TELFOR) (2008) M. Arabaci, I.B. Djordjevic: An alternative FPGA implementation of decoders for quasi-cyclic LDPC codes. In: Proc. Telecommun. Forum (TELFOR) (2008)
Zurück zum Zitat D.-U. Lee, J.D. Villasenor, W. Luk, P.H.W. Leong: A hardware Gaussian noise generator using the Box-Muller method and its error analysis, IEEE Trans. Comput. 55(6), 659–671 (2006)CrossRef D.-U. Lee, J.D. Villasenor, W. Luk, P.H.W. Leong: A hardware Gaussian noise generator using the Box-Muller method and its error analysis, IEEE Trans. Comput. 55(6), 659–671 (2006)CrossRef
Zurück zum Zitat F. Yu, M. Li, N. Stojanovic, C. Xie, Z. Xiao, L. Li: FPGA demonstration of stretched continuously interleaved BCH code with low error floor for short-range optical transmission. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2017), Los Angeles F. Yu, M. Li, N. Stojanovic, C. Xie, Z. Xiao, L. Li: FPGA demonstration of stretched continuously interleaved BCH code with low error floor for short-range optical transmission. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2017), Los Angeles
Zurück zum Zitat A.J. Feltström, D. Truhachev, M. Lentmaier, K.S. Zigangirov: Braided block codes, IEEE Trans. Inf. Theory 55(6), 2640–2658 (2009)MathSciNetMATHCrossRef A.J. Feltström, D. Truhachev, M. Lentmaier, K.S. Zigangirov: Braided block codes, IEEE Trans. Inf. Theory 55(6), 2640–2658 (2009)MathSciNetMATHCrossRef
Zurück zum Zitat S. Benedetto, E. Biglieri: Principles of Digital Transmission: With Wireless Applications (Kluwer Academic, Norwell 1999)MATH S. Benedetto, E. Biglieri: Principles of Digital Transmission: With Wireless Applications (Kluwer Academic, Norwell 1999)MATH
Zurück zum Zitat European Telecommunications Standards Institute: Digital video broadcasting (DVB); upper layer FEC for DVB systems, ETSI TR 102 993, 2007 (ETSI, Sophia Antipolis 2011), Tech. Rep. European Telecommunications Standards Institute: Digital video broadcasting (DVB); upper layer FEC for DVB systems, ETSI TR 102 993, 2007 (ETSI, Sophia Antipolis 2011), Tech. Rep.
Zurück zum Zitat Consultative Committee for Space Data Systems: CCSDS 131.0-B-2, CCSDS recommended standard for TM synchronization and channel coding (CCSDS, Washington 2011), Tech. Rep. Consultative Committee for Space Data Systems: CCSDS 131.0-B-2, CCSDS recommended standard for TM synchronization and channel coding (CCSDS, Washington 2011), Tech. Rep.
Zurück zum Zitat J.S. Plank: A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems, Softw. Pract. Exp. 27(9), 995–1012 (1997)MathSciNetCrossRef J.S. Plank: A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems, Softw. Pract. Exp. 27(9), 995–1012 (1997)MathSciNetCrossRef
Zurück zum Zitat M. Alipour, O. Etesami, G. Maatouk, A. Shokrollahi: Irregular product codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 197–201, Lausanne M. Alipour, O. Etesami, G. Maatouk, A. Shokrollahi: Irregular product codes. In: Proc. IEEE Inform. Theory Workshop (ITW) (2012) pp. 197–201, Lausanne
Zurück zum Zitat L.M. Zhang, F.R. Kschischang: Staircase codes with 6% to 33% overhead, J. Lightwave Technol. 32(10), 1999–2002 (2014)CrossRef L.M. Zhang, F.R. Kschischang: Staircase codes with 6% to 33% overhead, J. Lightwave Technol. 32(10), 1999–2002 (2014)CrossRef
Zurück zum Zitat C. Häger, A. Graell i Amat, H.D. Pfister, A. Alvarado, F. Brännström, E. Agrell: On parameter optimization for staircase codes. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015) C. Häger, A. Graell i Amat, H.D. Pfister, A. Alvarado, F. Brännström, E. Agrell: On parameter optimization for staircase codes. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015)
Zurück zum Zitat A. Sheikh, A. Graell i Amat, M. Karlsson: Nonbinary staircase codes for spectrally and energy efficient fiber-optic systems. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2017) p. W1J.1, Los AngelesCrossRef A. Sheikh, A. Graell i Amat, M. Karlsson: Nonbinary staircase codes for spectrally and energy efficient fiber-optic systems. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2017) p. W1J.1, Los AngelesCrossRef
Zurück zum Zitat M. Schwartz, P.H. Siegel, A. Vardy: On the asymptotic performance of iterative decoders for product codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2005) pp. 1758–1762, Adelaide M. Schwartz, P.H. Siegel, A. Vardy: On the asymptotic performance of iterative decoders for product codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2005) pp. 1758–1762, Adelaide
Zurück zum Zitat H.D. Pfister, S.K. Emmadi, K. Narayanan: Symmetric product codes. In: Proc. Inform. Theory Appl. Workshop (ITA) (2015) pp. 282–290, San Diego H.D. Pfister, S.K. Emmadi, K. Narayanan: Symmetric product codes. In: Proc. Inform. Theory Appl. Workshop (ITA) (2015) pp. 282–290, San Diego
Zurück zum Zitat C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Density evolution and error floor analysis for staircase and braided codes. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) pp. 1–3, Los Angeles C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Density evolution and error floor analysis for staircase and braided codes. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) pp. 1–3, Los Angeles
Zurück zum Zitat C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Deterministic and ensemble-based spatially-coupled product codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2114–2118, Barcelona C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Deterministic and ensemble-based spatially-coupled product codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2114–2118, Barcelona
Zurück zum Zitat C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Density evolution for deterministic generalized product codes on the binary erasure channel at high rates, IEEE Trans. Inf. Theory 63(7), 4357–4378 (2017)MathSciNetMATHCrossRef C. Häger, H.D. Pfister, A. Graell i Amat, F. Brännström: Density evolution for deterministic generalized product codes on the binary erasure channel at high rates, IEEE Trans. Inf. Theory 63(7), 4357–4378 (2017)MathSciNetMATHCrossRef
Zurück zum Zitat D. Chase: Class of algorithms for decoding block codes with channel measurement information, IEEE Trans. Inf. Theory 18(1), 170–182 (1972)MathSciNetMATHCrossRef D. Chase: Class of algorithms for decoding block codes with channel measurement information, IEEE Trans. Inf. Theory 18(1), 170–182 (1972)MathSciNetMATHCrossRef
Zurück zum Zitat C. Häger, H.D. Pfister: Approaching miscorrection-free performance of product codes with anchor decoding, IEEE Trans. Commun. 66(7), 2797–2808 (2018)CrossRef C. Häger, H.D. Pfister: Approaching miscorrection-free performance of product codes with anchor decoding, IEEE Trans. Commun. 66(7), 2797–2808 (2018)CrossRef
Zurück zum Zitat J. Hagenauer: The turbo principle: Tutorial introduction and state of the art. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (1997), Brest J. Hagenauer: The turbo principle: Tutorial introduction and state of the art. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (1997), Brest
Zurück zum Zitat Y.Y. Jian, H.D. Pfister, K.R. Narayanan: Approaching capacity at high rates with iterative hard-decision decoding. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2012) pp. 2696–2700, Cambridge Y.Y. Jian, H.D. Pfister, K.R. Narayanan: Approaching capacity at high rates with iterative hard-decision decoding. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2012) pp. 2696–2700, Cambridge
Zurück zum Zitat D. Truhachev, A. Karami, L. Zhang, F. Kschischang: Decoding analysis accounting for mis-corrections for spatially-coupled split-component codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2124–2128, Barcelona D. Truhachev, A. Karami, L. Zhang, F. Kschischang: Decoding analysis accounting for mis-corrections for spatially-coupled split-component codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2016) pp. 2124–2128, Barcelona
Zurück zum Zitat L.M. Zhang, F.R. Kschischang: Low-complexity soft-decision concatenated LDGM-staircase FEC for high-bit-rate fiber-optic communication, J. Lightwave Technol. 35(18), 3991–3999 (2017)CrossRef L.M. Zhang, F.R. Kschischang: Low-complexity soft-decision concatenated LDGM-staircase FEC for high-bit-rate fiber-optic communication, J. Lightwave Technol. 35(18), 3991–3999 (2017)CrossRef
Zurück zum Zitat M. Barakatain, F.R. Kschischang: Low-complexity concatenated LDPC-staircase codes, J. Lightwave Technol. 36(12), 2443–2449 (2018)CrossRef M. Barakatain, F.R. Kschischang: Low-complexity concatenated LDPC-staircase codes, J. Lightwave Technol. 36(12), 2443–2449 (2018)CrossRef
Zurück zum Zitat A. Sheikh, A. Graell i Amat, G. Liva: Iterative bounded distance decoding of product codes with scaled reliability. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2018), Rome A. Sheikh, A. Graell i Amat, G. Liva: Iterative bounded distance decoding of product codes with scaled reliability. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2018), Rome
Zurück zum Zitat A. Sheikh, A. Graell i Amat, G. Liva: On low-complexity decoding of product codes for high-throughput fiber-optic systems. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2018), Hong Kong A. Sheikh, A. Graell i Amat, G. Liva: On low-complexity decoding of product codes for high-throughput fiber-optic systems. In: Proc. Int. Symp. Turbo Codes Iterative Inform. Process. (ISTC) (2018), Hong Kong
Zurück zum Zitat G. Ungerboeck, I. Csajka: On improving data-link performance by increasing channel alphabet and introducing sequence decoding. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (1976), Ronneby G. Ungerboeck, I. Csajka: On improving data-link performance by increasing channel alphabet and introducing sequence decoding. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (1976), Ronneby
Zurück zum Zitat E. Biglieri, D. Divsalar, P.J. McLane, M.K. Simon: Introduction to Trellis-Coded Modulation with Applications, 2nd edn. (Prentice Hall, Englewood Cliffs 1992)MATH E. Biglieri, D. Divsalar, P.J. McLane, M.K. Simon: Introduction to Trellis-Coded Modulation with Applications, 2nd edn. (Prentice Hall, Englewood Cliffs 1992)MATH
Zurück zum Zitat P. Robertson, T. Worz: Bandwidth-efficient turbo trellis-coded modulation using punctured component codes, IEEE J. Sel. Areas Commun. 16(2), 206–218 (1998)CrossRef P. Robertson, T. Worz: Bandwidth-efficient turbo trellis-coded modulation using punctured component codes, IEEE J. Sel. Areas Commun. 16(2), 206–218 (1998)CrossRef
Zurück zum Zitat L.-F. Wei: Trellis-coded modulation with multidimensional constellations, IEEE Trans. Inf. Theory 33(4), 483–501 (1987)MathSciNetCrossRef L.-F. Wei: Trellis-coded modulation with multidimensional constellations, IEEE Trans. Inf. Theory 33(4), 483–501 (1987)MathSciNetCrossRef
Zurück zum Zitat S. Benedetto, G. Olmo, P. Poggiolini: Trellis coded polarization shift keying modulation for digital optical communications, IEEE Trans. Commun. 43(234), 1591–1602 (1995)CrossRef S. Benedetto, G. Olmo, P. Poggiolini: Trellis coded polarization shift keying modulation for digital optical communications, IEEE Trans. Commun. 43(234), 1591–1602 (1995)CrossRef
Zurück zum Zitat M. Magarini, R.J. Essiambre, B.E. Basch, A. Ashikhmin, G. Kramer, A.J. de Lind van Wijngaarden: Concatenated coded modulation for optical communications systems, IEEE Photon. Technol. Lett. 22(16), 1244–1246 (2010)CrossRef M. Magarini, R.J. Essiambre, B.E. Basch, A. Ashikhmin, G. Kramer, A.J. de Lind van Wijngaarden: Concatenated coded modulation for optical communications systems, IEEE Photon. Technol. Lett. 22(16), 1244–1246 (2010)CrossRef
Zurück zum Zitat H. Imai, S. Hirakawa: A new multilevel coding method using error-correcting codes, IEEE Trans. Inf. Theory 23(3), 371–377 (1977)MATHCrossRef H. Imai, S. Hirakawa: A new multilevel coding method using error-correcting codes, IEEE Trans. Inf. Theory 23(3), 371–377 (1977)MATHCrossRef
Zurück zum Zitat U. Wachsmann, R.F.H. Fischer, J.B. Huber: Multilevel codes: theoretical concepts and practical design rules, IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999)MathSciNetMATHCrossRef U. Wachsmann, R.F.H. Fischer, J.B. Huber: Multilevel codes: theoretical concepts and practical design rules, IEEE Trans. Inf. Theory 45(5), 1361–1391 (1999)MathSciNetMATHCrossRef
Zurück zum Zitat E. Zehavi: 8-PSK trellis codes for a Rayleigh channel, IEEE Trans. Commun. 40(5), 873–884 (1992)MATHCrossRef E. Zehavi: 8-PSK trellis codes for a Rayleigh channel, IEEE Trans. Commun. 40(5), 873–884 (1992)MATHCrossRef
Zurück zum Zitat X. Li, J.A. Ritcey: Bit-interleaved coded modulation with iterative decoding, IEEE Commun. Lett. 1(6), 169–171 (1997)CrossRef X. Li, J.A. Ritcey: Bit-interleaved coded modulation with iterative decoding, IEEE Commun. Lett. 1(6), 169–171 (1997)CrossRef
Zurück zum Zitat X. Li, J.A. Ritcey: Trellis-coded modulation with bit interleaving and iterative decoding, IEEE J. Sel. Areas Commun. 17(4), 715–724 (1999)CrossRef X. Li, J.A. Ritcey: Trellis-coded modulation with bit interleaving and iterative decoding, IEEE J. Sel. Areas Commun. 17(4), 715–724 (1999)CrossRef
Zurück zum Zitat S. ten Brink, J. Speidel, R.H. Han: Iterative demapping for QPSK modulation, Electron. Lett. 34(15), 1459–1460 (1998)CrossRef S. ten Brink, J. Speidel, R.H. Han: Iterative demapping for QPSK modulation, Electron. Lett. 34(15), 1459–1460 (1998)CrossRef
Zurück zum Zitat A. Bennatan, D. Burshtein: Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels, IEEE Trans. Inf. Theory 52(2), 549–583 (2006)MathSciNetMATHCrossRef A. Bennatan, D. Burshtein: Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels, IEEE Trans. Inf. Theory 52(2), 549–583 (2006)MathSciNetMATHCrossRef
Zurück zum Zitat G.D. Forney, F. Ungerboeck: Modulation and coding for linear Gaussian channels, IEEE Trans. Inf. Theory 44(6), 2384–2415 (1998)MathSciNetMATHCrossRef G.D. Forney, F. Ungerboeck: Modulation and coding for linear Gaussian channels, IEEE Trans. Inf. Theory 44(6), 2384–2415 (1998)MathSciNetMATHCrossRef
Zurück zum Zitat A.R. Calderbank, L.H. Ozarow: Nonequiprobable signaling on the Gaussian channel, IEEE Trans. Inf. Theory 36(4), 726–740 (1990)MathSciNetCrossRef A.R. Calderbank, L.H. Ozarow: Nonequiprobable signaling on the Gaussian channel, IEEE Trans. Inf. Theory 36(4), 726–740 (1990)MathSciNetCrossRef
Zurück zum Zitat F. Steiner, G. Böcherer: Comparison of geometric and probabilistic shaping with application to ATSC 3.0. In: Proc. Int. ITG Conf. Source Channel Coding (SCC) (2017), Hamburg F. Steiner, G. Böcherer: Comparison of geometric and probabilistic shaping with application to ATSC 3.0. In: Proc. Int. ITG Conf. Source Channel Coding (SCC) (2017), Hamburg
Zurück zum Zitat B.P. Smith, F.R. Kschischang: A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications, J. Lightwave Technol. 30(13), 2047–2053 (2012)CrossRef B.P. Smith, F.R. Kschischang: A pragmatic coded modulation scheme for high-spectral-efficiency fiber-optic communications, J. Lightwave Technol. 30(13), 2047–2053 (2012)CrossRef
Zurück zum Zitat L. Beygi, E. Agrell, J.M. Kahn, M. Karlsson: Rate-adaptive coded modulation for fiber-optic communications, J. Lightwave Technol. 32(2), 333–343 (2014)CrossRef L. Beygi, E. Agrell, J.M. Kahn, M. Karlsson: Rate-adaptive coded modulation for fiber-optic communications, J. Lightwave Technol. 32(2), 333–343 (2014)CrossRef
Zurück zum Zitat F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, W. Idler: Rate adaptation and reach increase by probabilistically shaped 64-QAM: An experimental demonstration, J. Lightw. Technol. 34(7), 1599–1609 (2016)CrossRef F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, W. Idler: Rate adaptation and reach increase by probabilistically shaped 64-QAM: An experimental demonstration, J. Lightw. Technol. 34(7), 1599–1609 (2016)CrossRef
Zurück zum Zitat M.P. Yankov, F.D. Ros, E.P. da Silva, S. Forchhammer, K.J. Larsen, L.K. Oxenløwe, M. Galili, D. Zibar: Constellation shaping for WDM systems using 256QAM/1024QAM with probabilistic optimization, J. Lightwave Technol. 34(22), 5146–5156 (2016)CrossRef M.P. Yankov, F.D. Ros, E.P. da Silva, S. Forchhammer, K.J. Larsen, L.K. Oxenløwe, M. Galili, D. Zibar: Constellation shaping for WDM systems using 256QAM/1024QAM with probabilistic optimization, J. Lightwave Technol. 34(22), 5146–5156 (2016)CrossRef
Zurück zum Zitat A. Ghazisaeidi, I. Fernandez de Jauregui Ruiz, R. Rios-Müller, L. Schmalen, P. Tran, P. Brindel, A.C. Meseguer, Q. Hu, F. Buchali, G. Charlet, J. Renaudier: Advanced C+L-band transoceanic transmission systems based on probabilistically shaped PDM-64QAM, J. Lightwave Technol. 35(7), 1291–1299 (2017)CrossRef A. Ghazisaeidi, I. Fernandez de Jauregui Ruiz, R. Rios-Müller, L. Schmalen, P. Tran, P. Brindel, A.C. Meseguer, Q. Hu, F. Buchali, G. Charlet, J. Renaudier: Advanced C+L-band transoceanic transmission systems based on probabilistically shaped PDM-64QAM, J. Lightwave Technol. 35(7), 1291–1299 (2017)CrossRef
Zurück zum Zitat A. Sheikh, A. Graell i Amat, G. Liva: Probabilistically-shaped coded modulation with hard decision decoding for coherent optical systems. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017), Gothenburg A. Sheikh, A. Graell i Amat, G. Liva: Probabilistically-shaped coded modulation with hard decision decoding for coherent optical systems. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017), Gothenburg
Zurück zum Zitat A. Sheikh, A. Graell i Amat, G. Liva, F. Steiner: Probabilistic amplitude shaping with hard decision decoding and staircase codes, J. Lightwave Technol. 36(9), 1689–1697 (2018)CrossRef A. Sheikh, A. Graell i Amat, G. Liva, F. Steiner: Probabilistic amplitude shaping with hard decision decoding and staircase codes, J. Lightwave Technol. 36(9), 1689–1697 (2018)CrossRef
Zurück zum Zitat G. Böcherer, F. Steiner, P. Schulte: Bandwidth efficient and rate-matched low-density parity-check coded modulation, IEEE Trans. Commun. 63(12), 4651–4665 (2015)CrossRef G. Böcherer, F. Steiner, P. Schulte: Bandwidth efficient and rate-matched low-density parity-check coded modulation, IEEE Trans. Commun. 63(12), 4651–4665 (2015)CrossRef
Zurück zum Zitat Alcatel-Lucent: The 400G photonic service engine – leaping toward a future of faster speeds and higher capacity, Alcatel-Lucent Strategic White Paper, Tech. Rep. (2012) Alcatel-Lucent: The 400G photonic service engine – leaping toward a future of faster speeds and higher capacity, Alcatel-Lucent Strategic White Paper, Tech. Rep. (2012)
Zurück zum Zitat A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, W. Idler: Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett. 20(23), 1547–1549 (2011)CrossRef A. Leven, F. Vacondio, L. Schmalen, S. ten Brink, W. Idler: Estimation of soft FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett. 20(23), 1547–1549 (2011)CrossRef
Zurück zum Zitat W. Idler, F. Buchali: Higher-order modulation formats – concepts and enabling devices. In: Fibre Optic Communication, Springer Ser. Opt. Sci., Vol. 161, ed. by H. Venghaus, N. Grote (Springer, Heidelberg, Berlin, New York 2017) pp. 291–357CrossRef W. Idler, F. Buchali: Higher-order modulation formats – concepts and enabling devices. In: Fibre Optic Communication, Springer Ser. Opt. Sci., Vol. 161, ed. by H. Venghaus, N. Grote (Springer, Heidelberg, Berlin, New York 2017) pp. 291–357CrossRef
Zurück zum Zitat F. Buchali, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, 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, F. Steiner, G. Böcherer, L. Schmalen, P. Schulte, W. Idler: Rate adaptation and reach increase by probabilistically shaped 64-QAM: An experimental demonstration, J. Lightwave Technol. 34(7), 1599–1609 (2016)CrossRef
Zurück zum Zitat A. Alvarado, E. Agrell, D. Lavery, R. Maher, P. Bayvel: Replacing the soft-decision FEC limit paradigm in the design of optical communication systems, J. Lightwave Technol. 33(20), 4338–4352 (2015)CrossRef A. Alvarado, E. Agrell, D. Lavery, R. Maher, P. Bayvel: Replacing the soft-decision FEC limit paradigm in the design of optical communication systems, J. Lightwave Technol. 33(20), 4338–4352 (2015)CrossRef
Zurück zum Zitat A. Alvarado, E. Agrell, D. Lavery, R. Maher, P. Bayvel: Corrections to ‘replacing the soft-decision FEC limit paradigm in the design of optical communication systems', J. Lightwave Technol. 34(2), 722 (2016)CrossRef A. Alvarado, E. Agrell, D. Lavery, R. Maher, P. Bayvel: Corrections to ‘replacing the soft-decision FEC limit paradigm in the design of optical communication systems', J. Lightwave Technol. 34(2), 722 (2016)CrossRef
Zurück zum Zitat L. Schmalen, A. Alvarado, R. Rios-Müller: Predicting the performance of nonbinary forward error correction in optical transmission experiments. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) p. M2A.2CrossRef L. Schmalen, A. Alvarado, R. Rios-Müller: Predicting the performance of nonbinary forward error correction in optical transmission experiments. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2016) p. M2A.2CrossRef
Zurück zum Zitat L. Schmalen, A. Alvarado, R. Rios-Müller: Performance prediction of nonbinary forward error correction in optical transmission experiments, J. Lightwave Technol. 35(4), 1015–1027 (2017)CrossRef L. Schmalen, A. Alvarado, R. Rios-Müller: Performance prediction of nonbinary forward error correction in optical transmission experiments, J. Lightwave Technol. 35(4), 1015–1027 (2017)CrossRef
Zurück zum Zitat L. Schmalen: Performance metrics for communication systems with forward error correction. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2018), Rome L. Schmalen: Performance metrics for communication systems with forward error correction. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2018), Rome
Zurück zum Zitat M. Franceschini, G. Ferrari, R. Raheli: Does the performance of LDPC codes depend on the channel?, IEEE Trans. Commun. 54(12), 2129–2132 (2006)CrossRef M. Franceschini, G. Ferrari, R. Raheli: Does the performance of LDPC codes depend on the channel?, IEEE Trans. Commun. 54(12), 2129–2132 (2006)CrossRef
Zurück zum Zitat I. Sason, B. Shuval: On universal LDPC code ensembles over memoryless symmetric channels, IEEE Trans. Inf. Theory 57(8), 5182–5202 (2011)MathSciNetMATHCrossRef I. Sason, B. Shuval: On universal LDPC code ensembles over memoryless symmetric channels, IEEE Trans. Inf. Theory 57(8), 5182–5202 (2011)MathSciNetMATHCrossRef
Zurück zum Zitat A. Sanaei, M. Ramezani, M. Ardakani: On the design of universal LDPC codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2008) pp. 802–806, Toronto A. Sanaei, M. Ramezani, M. Ardakani: On the design of universal LDPC codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2008) pp. 802–806, Toronto
Zurück zum Zitat S.H. Hassani, R. Urbanke: Universal polar codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2014) pp. 1451–1455, Honolulu S.H. Hassani, R. Urbanke: Universal polar codes. In: Proc. IEEE Int. Symp. Inform. Theory (ISIT) (2014) pp. 1451–1455, Honolulu
Zurück zum Zitat T.A. Eriksson, T. Fehenberger, P.A. Andrekson, M. Karlsson, N. Hanik, E. Agrell: Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments, J. Lightwave Technol. 34(9), 2256–2266 (2016)CrossRef T.A. Eriksson, T. Fehenberger, P.A. Andrekson, M. Karlsson, N. Hanik, E. Agrell: Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments, J. Lightwave Technol. 34(9), 2256–2266 (2016)CrossRef
Zurück zum Zitat A. Alvarado, T. Fehenberger, B. Chen, F.M.J. Willems: Achievable information rates for fiber optics: applications and computations, J. Lightwave Technol. 36(2), 424–439 (2018)CrossRef A. Alvarado, T. Fehenberger, B. Chen, F.M.J. Willems: Achievable information rates for fiber optics: applications and computations, J. Lightwave Technol. 36(2), 424–439 (2018)CrossRef
Zurück zum Zitat J. Cho, L. Schmalen, P. Winzer: Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017) J. Cho, L. Schmalen, P. Winzer: Normalized generalized mutual information as a forward error correction threshold for probabilistically shaped QAM. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017)
Zurück zum Zitat W. Idler, F. Buchali, L. Schmalen, E. Lach, R.-P. Braun, G. Böcherer, P. Schulte, F. Steiner: Field trial of a 1 Tb/s super-channel network using probabilistically shaped constellations, J. Lightwave Technol. 35(8), 1399–1406 (2017)CrossRef W. Idler, F. Buchali, L. Schmalen, E. Lach, R.-P. Braun, G. Böcherer, P. Schulte, F. Steiner: Field trial of a 1 Tb/s super-channel network using probabilistically shaped constellations, J. Lightwave Technol. 35(8), 1399–1406 (2017)CrossRef
Zurück zum Zitat L. Schmalen, F. Buchali, A. Leven, S. ten Brink: A generic tool for assessing the soft-FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett. 24(1), 40–42 (2012) L. Schmalen, F. Buchali, A. Leven, S. ten Brink: A generic tool for assessing the soft-FEC performance in optical transmission experiments, IEEE Photon. Technol. Lett. 24(1), 40–42 (2012)
Zurück zum Zitat N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, F. Yu: Reusing common uncoded experimental data in performance estimation of different FEC codes, IEEE Photon. Technol. Lett. 25(24), 2494–2497 (2013)CrossRef N. Stojanovic, Y. Zhao, D. Chang, Z. Xiao, F. Yu: Reusing common uncoded experimental data in performance estimation of different FEC codes, IEEE Photon. Technol. Lett. 25(24), 2494–2497 (2013)CrossRef
Zurück zum Zitat J. Hou, P.H. Siegel, L.B. Milstein, H.D. Pfister: Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes, IEEE Trans. Inf. Theory 49(9), 2141–2155 (2003)MathSciNetMATHCrossRef J. Hou, P.H. Siegel, L.B. Milstein, H.D. Pfister: Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes, IEEE Trans. Inf. Theory 49(9), 2141–2155 (2003)MathSciNetMATHCrossRef
Zurück zum Zitat R. Rios-Müller, J. Renaudier, L. Schmalen, G. Charlet: Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015) p. W3K.4CrossRef R. Rios-Müller, J. Renaudier, L. Schmalen, G. Charlet: Joint coding rate and modulation format optimization for 8QAM constellations using BICM mutual information. In: Proc. Opt. Fiber Commun. Conf. (OFC) (2015) p. W3K.4CrossRef
Zurück zum Zitat R. Rios-Müller, J. Renaudier, P. Tran, G. Charlet: Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-haul transmission link. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014) p. P.5.1, Cannes R. Rios-Müller, J. Renaudier, P. Tran, G. Charlet: Experimental comparison of two 8-QAM constellations at 200 Gb/s over ultra long-haul transmission link. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2014) p. P.5.1, Cannes
Zurück zum Zitat Z. Wang: Super-FEC codes for 40/100 Gbps networking, IEEE Commun. Lett. 16(12), 2056–2059 (2012)CrossRef Z. Wang: Super-FEC codes for 40/100 Gbps networking, IEEE Commun. Lett. 16(12), 2056–2059 (2012)CrossRef
Zurück zum Zitat G. Tzimpragos, C. Kachris, I.B. Djordjevic, M. Cvijetic, D. Soudris, I. Tomkos: A survey on FEC codes for 100 G and beyond optical networks, IEEE Commun. Surv. Tutor. 18(1), 209–221 (2016)CrossRef G. Tzimpragos, C. Kachris, I.B. Djordjevic, M. Cvijetic, D. Soudris, I. Tomkos: A survey on FEC codes for 100 G and beyond optical networks, IEEE Commun. Surv. Tutor. 18(1), 209–221 (2016)CrossRef
Zurück zum Zitat K. Lee, H.-G. Kang, J.-I. Park, H. Lee: 100GB/S two-iteration concatenated BCH decoder architecture for optical communications. In: Proc. IEEE Workshop Signal Process. Syst. (SiPS) (2010) pp. 404–409 K. Lee, H.-G. Kang, J.-I. Park, H. Lee: 100GB/S two-iteration concatenated BCH decoder architecture for optical communications. In: Proc. IEEE Workshop Signal Process. Syst. (SiPS) (2010) pp. 404–409
Zurück zum Zitat M. Scholten, T. Coe, J. Dillard, F. Chang: Enhanced FEC for 40G / 100G. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2009), Vienna, presentation in Workshop WS-1 M. Scholten, T. Coe, J. Dillard, F. Chang: Enhanced FEC for 40G / 100G. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2009), Vienna, presentation in Workshop WS-1
Zurück zum Zitat J. Li, K. Liu, S. Lin, K. Abdel-Ghaffar: Algebraic quasi-cyclic LDPC codes: Construction, low error-floor, large girth and a reduced-complexity decoding scheme, IEEE Trans. Commun. 62(8), 2626–2637 (2014)CrossRef J. Li, K. Liu, S. Lin, K. Abdel-Ghaffar: Algebraic quasi-cyclic LDPC codes: Construction, low error-floor, large girth and a reduced-complexity decoding scheme, IEEE Trans. Commun. 62(8), 2626–2637 (2014)CrossRef
Zurück zum Zitat B. Smith, I. Lyobomirsky, S. Bhoja: Leveraging 400G ZR FEC technology. In: IEEE 802.3 Beyond 10km Optical PHYs Study Group (2017), Orlando B. Smith, I. Lyobomirsky, S. Bhoja: Leveraging 400G ZR FEC technology. In: IEEE 802.3 Beyond 10km Optical PHYs Study Group (2017), Orlando
Zurück zum Zitat K. Cushon, P. Larsson-Edefors, P. Andrekson: Low-power 400-Gbps soft-decision LDPC FEC for optical transport networks, J. Lightwave Technol. 34(18), 4304–4311 (2016)CrossRef K. Cushon, P. Larsson-Edefors, P. Andrekson: Low-power 400-Gbps soft-decision LDPC FEC for optical transport networks, J. Lightwave Technol. 34(18), 4304–4311 (2016)CrossRef
Zurück zum Zitat K. Cushon, P. Larsson-Edefors, P. Andrekson: Improved low-power LDPC FEC for coherent optical systems. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017) pp. 1–3, Gothenburg K. Cushon, P. Larsson-Edefors, P. Andrekson: Improved low-power LDPC FEC for coherent optical systems. In: Proc. Eur. Conf. Opt. Commun. (ECOC) (2017) pp. 1–3, Gothenburg
Zurück zum Zitat K. Onohara, Y. Miyata, K. Sugihara, T. Sugihara, K. Kubo, H. Yoshida, K. Koguchi, T. Mizuochi: Implementation of soft-decision forward error correction for 100G digital coherent system. In: Proc. Opto-Electron. Commun. Conf. (OECC) (2011) pp. 423–424 K. Onohara, Y. Miyata, K. Sugihara, T. Sugihara, K. Kubo, H. Yoshida, K. Koguchi, T. Mizuochi: Implementation of soft-decision forward error correction for 100G digital coherent system. In: Proc. Opto-Electron. Commun. Conf. (OECC) (2011) pp. 423–424
Metadaten
Titel
Forward Error Correction for Optical Transponders
verfasst von
Alexandre Graell i Amat
Laurent Schmalen
Copyright-Jahr
2020
Verlag
Springer International Publishing
DOI
https://doi.org/10.1007/978-3-030-16250-4_7

Neuer Inhalt