Proving threshold saturation for nonbinary SC-LDPC codes on the binary erasure channel

Alexandre Graell I Amat (1) , Iryna Andriyanova (2) , Amina Piemontese (3)

1 Chalmers University of Technology [Göteborg]
2 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
3 UNIPR - Università degli studi di Parma = University of Parma

We analyze nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group for transmission over the binary erasure channel. We prove threshold saturation of the belief propagation decoding to the potential threshold, by generalizing the proof technique based on potential functions recently introduced by Yedla et al. The existence of the potential function is also discussed for a vector sparse system in the general case, and some existence conditions are developed. We finally give density evolution and simulation results for several nonbinary SC-LDPC code ensembles.

Domaines: Théorie de l'information [cs.IT]

Alexandre Graell I Amat, Iryna Andriyanova, Amina Piemontese. Proving threshold saturation for nonbinary SC-LDPC codes on the binary erasure channel. 2014 XXXIth URSI General Assembly and Scientific Symposium (URSI GASS), Aug 2014, Beijing, China. ⟨10.1109/URSIGASS.2014.6929239⟩. ⟨hal-01262858⟩