Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel

Iryna Andriyanova (1) , Alexandre Graell I Amat (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 Chalmers University of Technology [Göteborg]

We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) code ensembles defined over the general linear group on the binary erasure channel. In particular, we prove threshold saturation of the belief propagation decoding to the so called potential threshold, using the proof technique based on potential functions recently introduced by Yedla et al.. We rewrite the density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion form which is suited for the use of the potential function. We then discuss the existence of the potential function for the general case of vector recursions defined by multivariate polynomials, and give a method to construct the potential function. We define a potential function in a slightly more general form than one by Yedla et al., in order to make the technique based on potential functions applicable to the case of nonbinary LDPC codes.

Mots clés: SC-LDPC codes; threshold saturation; BEC

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

Iryna Andriyanova, Alexandre Graell I Amat. Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel. 2016. ⟨hal-01262833⟩