  The problem of phase-noise compensation for correlated phase noise in coded
multichannel optical transmission is investigated. To that end, a simple
multichannel phase-noise model is considered and the maximum a posteriori
detector for this model is approximated using two frameworks, namely factor
graphs (FGs) combined with the sum-product algorithm (SPA), and a variational
Bayesian (VB) inference method. The resulting pilot-aided algorithms perform
iterative phase-noise compensation in cooperation with a decoder, using
extended Kalman smoothing to estimate the a posteriori phase-noise distribution
jointly for all channels. The system model and the proposed algorithms are
verified using experimental data obtained from space-division multiplexed
multicore-fiber transmission. Through Monte Carlo simulations, the algorithms
are further evaluated in terms of phase-noise tolerance for coded transmission.
It is observed that they significantly outperform the conventional approach to
phase-noise compensation in the optical literature. Moreover, the FG/SPA
framework performs similarly or better than the VB framework in terms of
phase-noise tolerance of the resulting algorithms, for a slightly higher
computational complexity.
