Temporal Probabilistic Shaping for Mitigation of Nonlinearities in Optical Fiber Systems

In this paper, finite state machine sources (FSMSs) are used to shape quadrature amplitude modulation (QAM) for nonlinear transmission in optical fiber communication systems. The previous optimization algorithm for FSMSs is extended to cover an average power constraint, thus enabling temporal optimization with multiamplitude constellations output, such as QAM. The optimized source results in increased received SNR and, thereby, increased achievable information rates (AIR)s under memoryless assumption. The AIR is increased even further when taking the channel and transmitter memory into account via trellis processing at the receiver. Significant gains are reported in the highly nonlinear region of transmission for an FSMS of up to second order and 16QAM and particularly for unrepeated transmission. At the optimal launch power of WDM transmission, the FSMS order needs to be increased further in order to notably outperform previous probabilistic shaping schemes.