In this paper, we propose a coded orbital angular momentum (OAM)-based heterogeneous transparent optical networking scenario. The OAM is associated with the azimuthal phase dependence of the complex electric field. Because OAM eigenstates are orthogonal, they can be used as basis functions for multidimensional signal constellations. From Shannon's theory, we know that information capacity is a linear function of a number of dimensions and a logarithmic function of signal-to-noise ratio (SNR). Therefore, through multidimensional signal constellations, we can dramatically improve the overall aggregate data rate per single wavelength. The ability to generate the OAM modes, such as Bessel and Laguerre-Gaussian (LG) modes, in both multimode fibers (MMFs) and free-space optical (FSO) links will allow the realization of heterogeneous transparent FSO-fiber-optics communication networks, composed of MMF and FSO links, with ultrahigh bits-per-photon efficiencies. We perform Monte Carlo simulations to demonstrate the feasibility of the proposed heterogeneous optical networking scenario. We demonstrate the high potential of the proposed network to solve high-bandwidth demands and interoperability problems simultaneously. Finally, we prove that a dramatic improvement in spectral efficiency is possible by employing this OAM-based multidimensional signaling scheme.