Low-density parity-check (LDPC) code has recently become of great interest. The statistical mechanics approach has been used to reveal some characteristics of LDPC in the thermodynamic limit. In this paper, we analyze this system for finite size rather than within the thermodynamic limit through a principal component analysis (PCA) approach. Specifically, both the decoding dynamics of belief propagation (BP) and the phases of the system are visualized and discussed. The result implies that the decoding dynamics roughly corresponds to the system temperature we introduced, and this system has several phases such as ferromagnetic, paramagnetic, and 1RSB spin-glass phases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.