A Semi Linear State Space Model for Error Floor Estimation of LDPC codes over the AWGN Channel

Abstract

In this paper, we propose a novel state-space model to represent the behavior of sum-product algorithm (SPA) in the vicinity of a trapping set (TS) of a low-density parity-check (LDPC) code over the additive white Gaussian noise (AWGN) channel in the error floor region. The proposed model takes into account the non-linear behavior of SPA and dynamically adjusts the operating point of the model in accordance to the statistical properties of TS messages. This is in contrast to the existing linear state-space models which linearly approximate such behavior at around the operating point of zero. Simulation results are provided to demonstrate the higher accuracy of the proposed model in estimating the error floor of LDPC codes compared to the linear state-space model.