The purpose of this research is twofold. One is to analyze the noise threshold of the regular LDPC codes with a BPSK system on an LEO satellite channel. For this, we derive the initial message probability density function required in the density evolution under the LEO satellite channel and determine the noise threshold for ensemble of regular LDPC codes having different code rates and degree parameters. The other is to analyze the effect of fading parameters of the Loo\\`s model for an LEO channel on the performance of regular LDPC codes with a BPSK system. For this, we investigate the probability density function of a fading factor depending on the parameter values of the Loo\\`s model and analyze the performance of regular LDPC codes. Numerical analysis results and simulation results are shown in this thesis with discussions.