On the performance and the optimization of LDPC Codes on Fading Channels with Imperfect CSI

In this article we investigate low-density parity-check (LDPC) codes for fast Rayleigh fading channels in the presence of channel estimation error. The analysis is carried out using the Density Evolution technique assuming a belief propagation (BP) decoder. After having derived the analytical framework for decoding analysis, we prove that there exists a simple approximated relationship, function of estimation error variance, between the signal-to-noise ratio thresholds in the two cases of perfect and imperfect channel state information (CSI). This approximation follows the exact computation tightly, when the variance of the estimation error is sufficiently smaller than the fading variance. As a result, optimized codes for perfect CSI are also approximately optimized for imperfect CSI.