Ensemble weight enumerators for protographs: A proof of Abu Surra's conjecture and a continuous relaxation for a faster enumeration

Tarik Benaddi (1, 2, 3) , Charly Poulliat (1, 2, 4) , Marie-Laure Boucheret (1, 2, 4) , Benjamin Gadat (5) , Guy Lesthievent (3)

1 IRIT-SC - Signal et Communications
2 TéSA - Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics
3 CNES - Centre National d'Études Spatiales [Toulouse]
4 Toulouse INP - Institut National Polytechnique (Toulouse)
5 TAS - Thales Alenia Space [Toulouse]

In this paper, we provide a proof for the conjecture made by Abu Surra et al. [1] to simplify the computation of ensemble input output weight enumerators for protograph-based low density parity check (LDPC) codes. Furthermore, we propose a new method to compute more efficiently the ensemble weight enumerator. This approach can be applied particularly to lighten the computations for high rate codes, generalized LDPC codes or spatially coupled LDPC codes.

Mots clés: Nickel

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Tarik Benaddi, Charly Poulliat, Marie-Laure Boucheret, Benjamin Gadat, Guy Lesthievent. Ensemble weight enumerators for protographs: A proof of Abu Surra's conjecture and a continuous relaxation for a faster enumeration. IEEE International Symposium on Information Theory (ISIT 2015), Jun 2015, Hong Kong, Hong Kong SAR China. pp. 2889-2893. ⟨hal-01461712⟩