Performance of affine geometry low-density parity-check codes in long-haul optical communications

In this paper, we investigate the performance of low-density parity-check (LDPC) codes in long-haul optical communication systems for different modulation formats (nonreturn to zero (NRZ), return to zero (RZ), chirped return to zero (CRZ)). We are particularly concerned with high-rate codes based on affine geometries. These codes have large minimum distance and simple iterative decoding algorithms, which make them good candidates for high-speed applications such as optical communications. We consider both bit-flipping iterative decoding and iterative decoding based on min-sum algorithms. We demonstrate a significant performance improvement with respect to the state-of-the-art error control schemes employed in long-haul systems. Contrary to the common practice of considering the performance of error controlling schemes using the AWGN channel assumption, we consider the performance of the proposed LDPC schemes taking into account, in a natural way, all major impairments in long-haul optical transmission such as ASE noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol-interference (ISI), etc.