Suppression of intrachannel nonlinear effects in high-speed WDM systems

High-speed optical transmission systems operating at 40 Gb/s or higher are severely limited by intrachannel nonlinearities such as intrachannel four-wave mixing (IFWM) and intrachannel cross-phase modulation (IXPM). Approaches to deal with intrachannel nonlinearities may be classified into three broad categories: modulation formats, constrained (or line) coding, and equalization techniques. The IFWM is a phase-sensitive effect, and the aim of the first approach is to remove the phase short-term coherence of the pulses emitted in a given neighborhood. The role of constrained coding is to avoid those waveforms in the transmitted signal that are most likely to be received incorrectly. In this paper we describe two alternative techniques for suppression of intrachannel nolinearities: (i) constrained coding techniques, and (ii) combined nonlinear ISI cancellation and error control. Three different constrained coding techniques will be presented: (a) the use of constrained encoding itself, (b) combined constrained and error control coding and (c) deliberate error insertion. The nonlinear ISI cancellation scheme employs the maximum a posteriori probability (MAP) symbol decoding based on Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, while the forward error correction is based on low-density parity-check (LDPC) codes. The nonlinear ISI channel is modeled by a finite state machine (FSM) whose transition and output functions describe the dependency of the channel statistics and the ISI on transmitted patterns. The BCJR algorithm operates on a trellis of the corresponding FSM, and creates the soft information (detected bit likelihoods) used in the iterative decoder. To improve the BER performance of nonlinear BCJR equalizer further, a noise-predictive BCJR equalizer is introduced. The main feature of these schemes is that they can operate in the regime of very strong intrachannel nonlinearities where FEC schemes such as turbo or LDPC codes are not designed to operate.