Error floor analysis in LDGM codes

Abstract

Based on discrete density evolution (DDE), we develop closed form expressions to predict the error floor of LDGM codes. The first, rougher, approximation is obtained by assuming perfect message passing between systematic and parity bit nodes in DDE. The second, finer, expression leads to a more involved formulation. While the rougher approximation matches well to simulation results and DDE analysis for high signal to noise ratio (additive white Gaussian noise, AWGN, channel) or low crossover probability (binary symmetric channel, BSC), the finer approximation shows a good match for a wider range in the channel quality.