LDPC Decoding Dynamics from a PCA Viewpoint

Abstract

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.