An approximate analytical model of the message passing decoder of LDPC codes

In this paper we introduce a novel one-dimensional model of the message passing decoding algorithm of low-density parity-check (LDPC) codes, based on Gaussian densities. The model consists of a closed-form 1-D map whose iterates directly represent the error probability. This map allows a qualitative analysis of the nonlinear dynamics of the decoding algorithm. Moreover, it is shown that our approach leads to the correct stability condition and that the corresponding threshold values are in good agreement with density evolution.