Projective geometry LDPC codes for ultralong-haul WDM high-speed transmission

In this letter, we investigate the performance of low-density parity-check (LDPC) codes in long-haul optical communication systems for carrier-suppressed return-to-zero signal format at 40 Gb/s per channel in a wavelength-division-multiplexing environment. We are particularly concerned with high-rate codes based on projective geometries. These codes have large minimum distance and simple iterative decoding algorithms, which makes them good candidates for such high-speed application. We consider iterative decoding based on min-sum algorithm since it requires only simple addition and minimum operations and, as such, is suitable for highspeed optical transmission. Contrary to the common practice of considering the performance of error controlling schemes using the additive white Gaussian noise 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 amplifier spontaneous emission noise, pulse distortion due to fiber nonlinearities, chromatic dispersion or polarization dispersion, crosstalk effects, intersymbol interference, etc.