Non-Binary Low-Density Parity-Check (NB-LDPC) codes are an extension of binary LDPC codes constructed over GF(q) (q>2). NB-LDPC codes are known to have better error-correcting performance than their binary counterpart, especially for short to medium-length frames [1]. Morever, when the GF(q) symbols are directly mapped into a q-ary modulation, there is no loss of information during the demapping process. In contrast, binary codes mapped on q-ary modulation suffers from binary marginalization [8]. NB-LDPC codes are standardized in [9]. To be an option for future standards, efficient hardware architectures for NB-LDPC decoders is a must.

This diagram is a mind map of a Non-Binary LDPC decoder conception. It helps to visualize design space and constraint associated to the design of an efficient LDPC decoder.

• [1]: M. Davey and D. MacKay, "Low-density parity check codes over GF(q)," Communications Letters, IEEE, vol. 2, no. 6, pp. 165-167, June 1998.
• [2]: D. MacKay and M. Davey, "Evaluation of Gallager codes for short block length and high rate applications," in In Codes, Systems and Graphical Models. Springer-Verlag, 1999, pp. 113-190.
• [3]: D. Declercq and M. Fossorier, "Decoding algorithms for nonbinary LDPC codes over GF(q)," IEEE Trans. on Commun., vol. 55, pp. 633-643, April 2007.
• [4]: ErbaoLi, D.Declercq and K.Gunnam. Trellis-BasedExtendedMin-SumAlgorithm for Non-Binary LDPC Codes and its Hardware Structure. Communications, IEEE Transactions on, 61(7) :2600-2611, July 2013.
• [5] : A. Voicila, D. Declercq, F. Verdier, M. Fossorier and P. Urard, "Low-complexity decoding for non-binary LDPC codes in high order fields," in IEEE Transactions on Communications, vol. 58, no. 5, pp. 1365-1375, May 2010.
• [6]: P. Schlafer, N. When, T. Lehnigk-Emden, E. Boutillon, "Syndrome Based Check Node Processing of High Order NB-LDPC Decoders", International Conference on Telecommunication, Apr 2015, Sydney, Australia.
• [7]: Zhang Z, Anantharam V, Wainwright M, Nikolic B (2010) An efficient 10GBASE-T ethernet LDPC decoder design with low error floors. IEEE J Solid State Circuits 45(4):843. DOI 10. 1109/JSSC.2010.2042255 49.
• [8]: G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Transactions on Information Theory, vol. 44, no. 3, pp.927–946, 1998.
• [9]: BeiDou Navigation Satellite System, Signal In Space, Interface Control Document, Open Service Signals B1C, China Satellite Navigation Office, 2017

The Lab-STICC started to work on Non-Binary Low Density Parity Check (NB-LDPC) codes in 2007, in the framework of the FP7 DaVinci project .

The laboratory continued research on NB-LDPC through:

• Oussama Abassi's PhD Thesis "Etude des décodeurs LDPC non-binaires" 2010 - 2014, supervised by Prof. E. Boutillon and Dr. L. Conde-Canencia)
• Ali Haroun's PhD Thesis "Récepteur itératif pour des systémes MIMO basés sur l'algorithme de la propagation de croyance" from October 2010 to November 2014, supervised by Prof. C. Jego
• Ahmed Abdmouleh's PhD Thesis "Non-binary LDPC codes associated to high-order modulations" 2013-2017, supervised by Prof. E. Boutillon, Dr. L. Conde-Canencia, Prof. C. Douillard and Dr. C. Abdel Nour
• Nhat-Quang Nhan's PhD Thesis "Association et optimisation conjointe de codes LDPC non binaires aux sytèmes MIMO à diversité d'émission utilisés dans le standard LTE", started in October 2014, supevised by Dr. K. Amis Cavalec et Dr. P. Rostaing.
• Hassan Harb's PhD Thesis " High rate NB-LDPC decoder" started in 2016, supervised by Prof E. Boutillon, Dr. L Conde-Canencia and Dr. Ali Al Ghouwayel
• Cedric Marchand, research engineer, from 2014.
• Quasy Cyclic Small Packet (QCSP) project, October 2019 - October 2022 QCSP
• Joseph Jabour's PhD Thesis " High speed hardware implementation of non binary decoders" 2020-2023
• Abdallah Abdallah PhD Thesis " Simplified Non-Binary Decoder" started in December 2023

In this webpage we aim at presenting most of the knowledge generated on NB-LDPC from our team, including simulation results, performance curves, C code and VHDL code.

In order to advance more on these topics, academic and industrial partnerships are welcome. Would you have any questions, interests, please contact Professor Emmanuel Boutillon ..

Picture taken near "Plage de Kerpape" in 2016. From left to right: Master Student, Emmanuel Boutillon, Hassan Harb, Cedric Marchand, Titouan Gendron, Laura Conde-Canencia.

Lab-STICC can offer funding for:

• Short visit of professor (one month minimum)
• Post-doc student
• PhD student