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 thres holds of low density parity-check (LDPC) codes that employ the message pass ing decoding algorithm on the additive white Gaussian noise (AWGN) channel, In this paper, we apply the technique to the uncorrelated flat Rayleigh fa ding channel, Using a nonlinear code optimization technique, we optimize ir regular LDPC codes for such a channel. The thresholds of the optimized irre gular LDPC codes are very close to the Shannon limit for this channel, For example, at rate one-half, the optimized irregular LDPC code has a threshol d only 0.07 dB away from the capacity of the channel, Furthermore, we compa re simulated performance of the optimized irregular LDPC codes and turbo co des on a land mobile channel, and the results indicate that at a block size of 3072, irregular LDPC codes can outperform turbo codes over a wide range of mobile speeds.