Matrices and simulation results from UBS 
NB-LDPC matrix alist format
How to use the GF64 and GF256 tables
The matrices here presented have been generated following the methods in [1, 2, 3].
Each box in the table is refers to a given information length in bits (i.e., K/log2(q) GF(q) symbols) and a constant check node degree dc. All the considered code have a constant variable degree value dv = 2 and the code rate can then be calculated as R = 1 - 2/dc.
As an example, column dc = 10 corresponds to a code rate R = 1 - 2/10 = 4/5.
An orange box means that there is no code for the given value of K and dc.
A grey box means that, so far, no code is proposed.
A yellow box contains the number of existing codes for the corresponding values of K and dc.
Click on a yellow box to check the simulation curves of the proposed codes. Click on a simulation curve to access a directory that contains all the information related to the code: its a-list format, its topological properties, its performance, and the author and date of the matrix.
Note that most of the proposed matrices have been generated by an automatic process. In some case, hand made optimization can further improve the decoding performance.
Click on the 'DC' link below each column to check the required Eb/No to get a frame error rate of 10-2, for a given value of K.
Black circles represents hand made matrices, and points represents the automatically constructed ones.
The color code is as follows :
Blue for the matrices expanded from the N=dc full of '1' protomatrices
Red for the N=dc2 girth 8 protomatrices
Green for the (3, dc)Cage protomatrices (girth 6).
Simulation results are obtained using the Extended Min-Sum (EMS) algorithm. The Check Nodes (CN) are implemented using Forward-backward algorithm where Elementary Check Nodes (ECN)are computed as in [4].
The decoder stop after a maximum of 10 iterations. The ECN is set with nm=20 and nop=25 for GF(64) and is set to nm=60 and nop=70 for GF(256).
If you use these results in your publication, please cite our website as:
Cedric Marchand, Hassan Harb, Titouan Gendron, Bertrand Orvoine and Emmanuel Boutillon. free NB-LDPC code database of the Lab-STICC laboratory. http://www-labsticc.univ-ubs.fr/nb_ldpc/, 2018.
- [1] C. Poulliat and M. Fossorier and D. DeclercqDesign of regular (2,dc)-{LDPC} codes over {GF}(q) using their binary images, IEEE Transactions on Communications, vol. 56, pp = 1626-1635, Oct. 2008.
- [2] E. Boutillon, "Optimization of Non Binary Parity Check Coefficients", IEEE Transactions on Information theory, 2019.
- [3] Alban Derrien, Emmanuel Boutillon, Audrey Cerqueus, "Additive, structural and multiplicative transformations for the Construction of Quasi Cyclic LDPC matrices". IEEE Transactions on Communications, 2019.
- [4] Oussama Abassi, Laura Conde-Canencia, Ali Al Ghouwayel, Emmanuel Boutillon. A Novel Architecture For Elementary Check Node Processing In Non-Binary LDPC Decoders. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017.
If you have a special request for a particular code construction, please, send a mail to nb-ldpc@univ-ubs.fr