Abstract: An apparatus includes an optical communications receiver receiving a turbulence-distorted, optical signal. The turbulence-distorted, optical signal includes a plurality of fundamental modes encoded via a combinatorial multiplexings dictionary. The received optical signal includes a plurality of two-dimensional images. Each two-dimensional image of the plurality of two-dimensional images respectively represents received fundamental modes of the plurality of fundamental modes. The receiver includes a neural network trained to assign to each two-dimensional image of the plurality of two-dimensional images at least one respective active fundamental mode of the plurality of fundamental modes and a corresponding accuracy probability based on the dictionary.

Abstract: A method, wherein a first plurality of numerical support sub-regions is provided. A manufacturing constraint and a response objective are provided. A first plurality of shapes for the first plurality of numerical support sub-regions is generated. Each shape of the first plurality of shapes corresponds to a respective numerical support sub-region. Each shape corresponds to a respective function of numerical support within the respective numerical support sub-region. Each respective function of numerical support uses: a first respective center number corresponding to each numerical support sub-region, the first respective center number depending on the at least one manufacturing constraint, a first respective Beta distribution, a first respective alpha Beta distribution shape parameter constrained by the at least one manufacturing constraint, and a first respective beta Beta distribution shape parameter constrained by the at least one manufacturing constraint.

Abstract: An apparatus includes an optical communications receiver receiving a turbulence-distorted, optical signal. The turbulence-distorted, optical signal includes a plurality of fundamental modes encoded via a combinatorial multiplexings dictionary. The received optical signal includes a plurality of two-dimensional images. Each two-dimensional image of the plurality of two-dimensional images respectively represents received fundamental modes of the plurality of fundamental modes. The receiver includes a neural network trained to assign to each two-dimensional image of the plurality of two-dimensional images at least one respective active fundamental mode of the plurality of fundamental modes and a corresponding accuracy probability based on the dictionary.