Generalized Belief Propagation to break trapping sets in LDPC codes

Abstract : In this paper, we focus on the Generalized Belief Propagation (GBP) algorithm to solve trapping sets in Low-Density Parity-Check (LDPC) codes. Trapping sets are topological structures in Tanner graphs of LDPC codes that are not correctly decoded by Belief Propagation (BP), leading to exhibit an error-floor in the bit-error rate. Stemming from statistical physics of spin glasses, GBP consists in passing messages between groups of Tanner graph nodes. Provided a well-suited grouping, this algorithm proves to be a powerful decoder as it may lower harmful topological effects of the Tanner graph. We then propose to use GBP to break trapping sets and create a new decoder to outperform BP and to defeat error-floor.
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Jean-Christophe Sibel, Sylvain Reynal, David Declercq. Generalized Belief Propagation to break trapping sets in LDPC codes. 2014 Australian Communications Theory Workshop (AusCTW), Feb 2014, Sydney, Australia. pp.132. ⟨hal-00968251⟩

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