A novel region graph construction based on trapping sets for the Generalized Belief Propagation

The Belief Propagation (BP) is an inference algorithm used to estimate marginal probability distributions for any Markov Random Field (MRF). In the realm of Low-Density Parity-Check (LDPC) codes that can be represented by MRF called Tanner graphs, the BP is used as a decoding algorithm to estimate the states of bits sent through a noisy channel. Known to be optimal when the Tanner graph is a tree, the BP suffers from suboptimality when the Tanner graph has a loop-like topology. Furthermore, combinations of loops, namely the trapping sets, are particularly harmful for the decoding. To circumvent this problem were proposed other algorithms, like the Generalized Belief Propagation (GBP) that comes from statistical physics. This algorithm allows to absorb topological structures inside new nodes called regions. An advantage is that the resulting graph, the region graph, is not unique then according to its construction this region graph is a media for the GBP that can provide more accurate estimates than the BP. In this paper, we propose novel constructions of the region graph for the famous Tanner code of length N = 155 by making use of the trapping sets as basis for the regions.