Evidence of chaos in the Belief Propagation for LDPC codes

Jean-Christophe Sibel (1) , Sylvain Reynal (1) , David Declercq (1)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

In this paper, we investigate the behaviors of the Belief Propagation algorithm considered as a dynamic system. In the context of LDPC (Low Den- sity Parity-Check) codes, we use the noise power of the transmission channel as a potentiometer to evaluate the different motions that the BP can follow. The computations of dynamic quantifiers as the bifurcation diagram, the Lyapunov ex- ponent and the reconstructed trajectory enable to bring out four main behaviors. In addition, we propose a novel measure that is the hyperspheres method, which provides the knowledge of the time evolution of the attractor size. The information collected from these different quantifiers helps to better understand the BP evolu- tion and to focus on the noise power values for which the BP suffers from chaos.

Mots clés: LDPC; iterative map; chaos; Lyapunov exponent; bifurcation diagram.; bifurcation diagram

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]; Systèmes dynamiques [math.DS]

Jean-Christophe Sibel, Sylvain Reynal, David Declercq. Evidence of chaos in the Belief Propagation for LDPC codes. 5th Chaotic Modeling and Simulation International Conference, 12 - 15 June 2012, Athens Greece, Jun 2012, Athènes, Greece. pp.593. ⟨hal-00736202⟩