Code-aided Expectation-maximization and Probabilistic Constellation Shaping for Fiber-optic Communication Systems

Book excerpt: This thesis provides signal-processing and constellation shaping algorithms to combat equalizer-enhanced phase-noise and nonlinearity-induced interference in long-haul fiber-optic communication systems. In the first part of this work, an iterative phase-estimation algorithm is designed that combines expectation-maximization (EM) with a soft-input soft-output error control decoder. At 280 Gbit/s, this system doubles the optical system reach, and generally enhances phase-noise tolerance. Among three different 16-point constellations, the 4-4-4-4 ring constellation was found to have the best performance. The laser linewidth tolerance gain is improved further by reducing the code rate. In the second part of this work, this code-aided (CA) EM approach is applied to long-haul systems dominated by nonlinearity-induced interference. Based on laboratory measurements, a second-order autoregressive phase-noise model is proposed, and used to modify the EM regularizer term. Simulation and experimental results show that in a dual-polarization wavelength-division-multiplexed 16 QAM system, launch-power tolerance can be increased by 1.5 dB, and the optical signal-to-noise ratio requirement can be relaxed by 0.3 dB to achieve the same error ratio. The complexity of the CAEM algorithm was found to be about 1/4 of the complexity of digital back-propagation. In the third part of this work, a low complexity probabilistic constellation shaping scheme is proposed to increase the system tolerance to nonlinearity impairments. A theoretical analysis predicts that, with 16 and 64-point constellations, reach improvements of 7% and 10% respectively can be achieved at a mutual information of 3.2 bit/symbol/polarization. Such probabilistic constellation shaping requires minimal added complexity.