Performance analysis and code optimization of low density parity-check codes on Rayleigh fading channels

A numerical method has recently been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we extend this technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimized irregular LDPC codes for the uncorrelated Rayleigh fading channel. The thresholds of the optimized irregular LDPC codes are very close to the Shannon limit for this channel. For example, at rate 1/3, the optimized irregular LDPC code has a threshold only 0.08dB away from the channel capacity.