  The nonlinear Shannon capacity limit has been identified as the fundamental
barrier to the maximum rate of transmitted information in optical
communications. In long-haul high-bandwidth optical networks, this limit is
mainly attributed to deterministic Kerr-induced fiber nonlinearities and from
the interaction of amplified spontaneous emission noise from cascaded optical
amplifiers with fiber nonlinearity: the stochastic parametric noise
amplification. Unlike earlier impractical approaches that compensate solely
deterministic nonlinearities, here we demonstrate a novel electronic-based deep
neural network with multiple-inputs and outputs (MIMO) that tackles the
interplay of deterministic and stochastic nonlinearity manifestation in
coherent optical signals. Our demonstration shows that MIMO deep learning can
compensate nonlinear inter-carrier crosstalk effects even in the presence of
frequency stochastic variations, which has hitherto been considered impossible.
Our solution significantly outperforms conventional machine learning and
gold-standard nonlinear equalizers without sacrificing computational
complexity, leading to record-breaking transmission performance for up to 40
Gbit/sec high-spectral-efficient optical signals.
