- Early work (1998, during my sabbatical stay in University of Toronto): definition of a code construction hardware friendly.
- PhD of Frederic Guilloud (2001-2004): sub-optimal check node processing, generic architecture of decoder
- PhD of Cedric Marchand (2007-2010): Optimisation of DVB-S2 decoder (precision, scheduling, solution to solve problem of double diagonals of the parity check matrix).
- Sabbatical stay in Lab-STICC of Chris Winstead (2013-2014): Low complexity LDPC decoder (one bit per message).
- New construction of QC-LDPC matrices with high girth (2018-19).
- Noise Against Noise LDPC decoder (2016-19): go to the ANR NAND Project WEB site.
- General articles on LDPC architecture.

With the sabbatical stay of Chris Winstead in my lab in 2013/2014, I also start to work on bit-flipping algorithm. On this topic, you can see the presentation of Chris Winstead and the papers related to this topic.

- Emmanuel Boutillon, Jeff Castura, Frank R. Kschischang, "Decoder-First Code Design", Proceedings of the 2nd International Symposium on Turbo Codes and Related Topics, pp 459-462, Brest, France, Sept. 2000.

Related publications

- F. Guilloud, E. Boutillon, J. Tousch, J.L. Danger, "Generic description and synthesis of LDPC decoder", IEEE Transactions On Communications, IEEE Transactions on Communications, Vol. 55, n°11, pp 2084 - 2091, nov. 2007.
- Fédéric Guilloud, Emmanuel Boutillon, Jacky Tousch, "Description et synthèse générique des décodeurs de codes LDPC", Journées Francophones sur l’Adéquation Algorithme Architecture, Dijon, Janv. 2005.
- Frédéric Guilloud, "Generic Architecture for LDPC Codes Decoding", PHD Thesis, ENST Paris, July the 2nd, 2004. (slides of the presentation: slides)
- Jacky Tousch, Emmnuel Boutillon, David Gnaedig, "appareil de décodage de code LDPC", French Patent pending, june 19, 2004.
- E. Boutillon, J. Tousch, F. Guilloud, "LDPC decoder, corresponding method, system and computer programm", United States Patent n°7174495, Feb. 6, 2007 (deposal n°10/742,643, dec. 19, 2003).
- Frédéric Guilloud, Emmanuel Boutillon, Jean-Luc Danger, ""lambda-Min Decoding Algorithm of Regular and Irregular LDPC Codes"", 3nd International Symposium on Turbo Codes and Related Topics, Brest, France, pp 451-454, Sept. 2003, (Poster of the paper).
- F. Guilloud, E. Boutillon, J.-L. Danger, "Décodage des codes LDPC par l'algorithme lambda-Min", GRETSI 2003, Paris, Sept. 2003, (Poster of the paper).

Miscellaneous

- Organization of a one day workwhop on LDPC (Paris, december 19, 2002): Journée LDPC GDR-ISIS (in french).
- Slides of the talk given at University of Massachusset, University of Toronto, University of Minneapolis, University of Alberta (feb-march 2003): slides.
- "Architecture de décodeur LDPC", SCEE seminar, SUPELEC, Rennes, april 7th, 2005 : slides (in french).
- Slides of the talk given by Frederic Guilloud at 2005 IEEE Communication Theory Workshop (Utah, june 2005) : slides.
- "Proposition d'une méthodologie d'adéquation algorithme architecture", E. Boutillon, GDR-ISIS meeting (Paris, 27/06/2005): slides (pdf) and slides (powerpoint).
- "Architecture générique de décodage de code LDPC", E. Boutillon, CNES meeting (Toulouse, 29/06/2006): slides (pdf)
- "Generic model of LDPC code decoders", E. Boutillon, NewCom meeting (Pisa, 6/10/2006): slides (pdf)

Related Publications

- C. Marchand; Laura Conde-Canencia; Emmanuel Boutillon High-speed conflict-free layered LDPC decoder for the DVB-S2, -T2 AND -C2 standards 2013 IEEE Workshop on Signal Processing Systems (SISP'2013), Tapei, pp. 1-6, Oct 2013.
- C. Marchand, L. Conde-Canencia, E. Boutillon, " Architecture and finite precision optimization for layered LDPC Decoders ", Journal of Signal Processing Systems, Springer, pp. 185-197, vol. 65, n°2, Nov. 2011.
- C. Marchand, L. Conde-Canencia, E. Boutillon, "Architecture and finite precision optimization for layered LDPC decoders", Processing Systems (SIPS’2010), San Franscisco, Oct 2010.
- C. Marchand, J.-B. Doré, L. Conde-Canencia, E. Boutillon, "Conflict Resolution by Matrix Reordering for DVB-T2 LDPC Decoders", Globecom 2009, Haiwai, Dec. 2009.
- C. Marchand, J.-B. Doré, L. Conde-Canencia, E. Boutillon,"Conflict resolution for pipelined layered LDPC decoders", SIPS 2009, Tampere, Oct. 2009.

Related publications

- Yangyang Tang (january 2013), "Computation on Unreliable Architecture"(PhD report (6.5 Mo))
- C. Winstead, Y. Tang,, E. Boutillon, C. Jego, Christophe and M. Jézéquel, A Space-Time Redundancy Technique for Embedded Stochastic Error Correction, 7th International Symposium on Turbo Codes & Iterative Information Processing, Gothenburg, Sweden, august 2012.
- Y. Tang, C. Winstead, E. Boutillon, C. Jego, Christophe and M. Jézéquel, An LDPC decoding method for fault-tolerant digital logic, IEEE International Symposium on Circuits and Systems (ISCAS), pp: 3025-3028, Seoul, may 2012.

Related Publications

- C. Winstead, E. Boutillon, "Decoding LDPC Codes with Locally Maximum-Likelihood Binary Messages", IEEE Communications Letters, Accepted for publications, available on line., pp.4
- G. Sundararajan, C. Winstead, E. Boutillon, Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes, IEEE Transactions on Communications, 62 (10), pp.16 Octobre. 2014.
- C. Winstead; G. Sundararajan; E. Boutillon, "A Case Study in Noise Enhanced Computing: Noisy Gradient Descent Bit Flip Decoding., Designing with Uncertainty - Opportunities & Challenges workshop, Mar 2014, United Kingdom.

- Slides of the presentation given by Chris Winstead in Telecom Bretagne the 22nd of April 2014: Recent results on Bit Flipping LDPC decoders
- Slides of the presentation given by Emmanuel Boutillon the 4th November 2014 (GDR SoCSiP-ISIS) day on Error Control Code architecture A Survey On Binary Message LDPC Decoder
- WEB site of Chris Winstead'Lab: Low-Energy / Fault-Tolerant systems laboratory

[1]Alban Derrien, Emmanuel Boutillon, Audrey Cerqueus. Additive, Structural and Multiplicative Transformations for the Construction of Quasi-Cyclic LDPC matrices. IEEE Transactions on Communications, doi: 10.1109/TCOMM.2018.2890251, in press, 2019 ( available online).

[2]M. Battaglioni, A. Tasdighi, M. Baldi, M. H. Tadayon and F. Chiaraluce, "Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications," 2018 IEEE 29th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Bologna, 2018, pp. 1-5.

[3] M. Karimi and A.H. Banihashemi. "On the girth of quasi-cyclic protograph LDPC codes". IEEE Trans. Inf Theory, vo1.S9, no.7, pp.4542-45S2, July 2013.

Value of L | Value of P [1] | Value of P [2] | New found P | Low bound [3] | (m,n) matrix size | (k,n) LDPC code | code rate |
---|---|---|---|---|---|---|---|

L = 4 | 37 | 37 | 37 | 37 | (111, 148) | (37, 148) | 0.250 |

L = 5 | 61 | 61 | 61 | 61 | (183, 305) | (122, 305) | 0.400 |

L = 6 | 91 | 91 | 91 | 91 | (273, 546) | (273, 546) | 0.500 |

L = 7 | 139 | 137 | 129 | 127 | (387, 903) | (516, 903) | 0.571 |

L = 8 | 201 | 181 | 181 | 169 | (543, 1448) | (905, 1448) | 0.625 |

L = 9 | 280 | 241 | 219 | 217 | (657, 1971) | (1314, 1971) | 0.667 |

L = 10 | 383 | 313 | 273 | 271 | (819, 2730) | (1911, 2730) | 0.700 |

L = 11 | 507 | 397 | 373 | 331 | (1119, 4103) | (2984, 4103) | 0.727 |

L = 12 | - | 523 | 463 | 397 | (1389, 5556) | (4167, 5556) | 0.750 |

L = 13 | - | - | 571 | 469 | (1713, 7423) | (5710, 7423) | 0.769 |

L = 14 | - | - | 687 | 547 | (2061, 9618) | (7557, 9618) | 0.786 |

L = 15 | - | - | 823 | 631 | (2469, 12345) | (9876, 12345) | 0.800 |

L = 16 | - | - | 1009 | 721 | (3027, 16144) | (13117, 16144) | 0.813 |

L = 17 | - | - | 1191 | 817 | (3573, 20247) | (16674, 20247) | 0.824 |

L = 18 | - | - | 1399 | 919 | (4197, 25182) | (20985, 25182) | 0.833 |

L = 19 | - | - | 1657 | 1027 | (4971, 31483) | (26512, 31483) | 0.842 |

L = 20 | - | - | 1929 | 1141 | (5787, 38580) | (32793, 38580) | 0.850 |

L = 21 | - | - | 2203 | 1261 | (6609, 46263) | (39654, 46263) | 0.857 |

L = 22 | - | - | 2473 | 1387 | (7419, 54406) | (46987, 54406) | 0.864 |

L = 23 | - | - | 2797 | 1519 | (8391, 64331) | (55940, 64331) | 0.870 |

L = 24 | - | - | 3181 | 1657 | (9543, 76344) | (66801, 76344) | 0.875 |

L = 25 | - | - | 3583 | 1801 | (10749, 89575) | (78826, 89575) | 0.880 |

L = 26 | - | - | 3919 | 1951 | (11757, 101894) | (90137, 101894) | 0.885 |

L = 27 | - | - | 4483 | 2107 | (13449, 121041) | (107592, 121041) | 0.889 |

L = 28 | - | - | 5119 | 2269 | (15357, 143332) | (127975, 143332) | 0.893 |

L = 29 | - | - | 5179 | 2437 | (15537, 150191) | (134654, 150191) | 0.897 |

L = 30 | - | - | 6037 | 2611 | (18111, 181110) | (162999, 181110) | 0.900 |

This figure shows the evolution of P as a function of L for L= 4 to 15

If you are interested to know the new matrices, please send a mail to "emmanuel.boutillon@univ-ubs.fr" with the subjet: "request for QC-LDPC matrices". In the core of the mail, you should indicate the sizes of matrices that you need. If you know other papers or better matrices with smaller expension factors, please, fell free to send an email to inform me.

Alireza Tasdighi, Emmanuel Boutillon, "Integer Ring Sieve for Constructing Compact QC-LDPC Codes with Girths 8, 10, and 12.", Submitted to IEEE Trans. on Information Theory, Feb. 2021.

- E. Boutillon, C. Douillard, G. Montorsi, " Iterative Decoding of Concatenated Convolutional Codes: Implementation Issues", Proceedings of the IEEE, vol. 95, n°6, june 2007.
- "Codes et Turbocodes", Collection IRIS, C. Berrou (Réd.), Springer, Paris, 2007, 397 p. (Iris), ISBN 978-2-287-32739-1
- COCA Project ; Channel coding: State of the art and perspectives", Internal Report, Groupe des Ecoles de Telecommunications (GET).
- WEB site of the TU Kaiserslautern that gives some ML decoding performance of several codes: Maximum Likelihood (ML) Simulation Results

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