Soft Decision LDPC Decoding Over Chi-Square Based Optical Channels

In this paper, we consider low density parity check (LDPC) codes as a solution to enhance the optical transmission performance. The decoding algorithm based on message passing algorithm uses the probability density function of the received signal. Its efficiency thus depends on the right evaluation of the signal distribution. We do not make here the classical additive white Gaussian noise (AWGN) assumption, but we investigate a chi-square based channel model which is more accurate for the description of optical impairments. As opposed to previous chi-square based models, no assumption on the signal power of 0 and 1 data is done. The calculation of the logarithmic likelihood ratio (LLR) needed to implement soft LDPC decoder is thus developed for a chi-square channel in a general manner. Computer simulations validate the efficiency of the soft decoder for this type of channel. The results also confirm that the adaptation of LDPC decoder to the specific chi-square channel statistic is necessary to obtain the optimal performance.