Regular low-density parity-check (LDPC) code with normalized and UMP BP-based algorithms on fast rayleigh fading channel

In this paper, we analyze and evaluate the performance of the regular LDPC codes with the normalized and IMP BP-based algorithms on a fast Rayleigh fading channel. For the short regular LDPC codes, we derive the formula of the normalization factor theoretically by using the probability density function (pdf) of the initial likelihood information for the normalized BP-based algorithm on the fast Rayleigh fading channel. For the long regular LDPC codes, we derive the optimal normalization factor for the normalized BP-based algorithm on the fast Rayleigh fading channel by using density evolution (DE). We also analyze the performance of the long regular LDPC codes with the I IMP BP-based algorithm on the fast Rayleigh fading channel by using DE. From the numerical and simulation results, we show that the optimum normalization factor for the short regular LDPC codes on the fast Rayleigh fading channel is different from that on the AWGN channel. We also show that for the short regular LDPC codes, the normalized BP-based algorithm outperforms the IMP BP-based algorithm, and has the performance very close to those of the BP algorithm. Furthermore, for the long regular LDPC codes, we show that the normalized BP-based algorithm outperforms the BP algorithm and the UMP BP-based algorithm on the fast Rayleigh fading channel. Therefore, for the short and long regular LDPC codes, the normalized BP-based algorithm is shown to be suitable as the decoding algorithm on the fast Rayleigh fading channel.