Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous) have been recently discussed as promising transmission methods to combat fiber nonlinearity impairments. In this paper, for the first time, we demonstrate the generation, detection, and transmission performance over transoceanic distances of 10 Gbd nonlinear inverse synthesis-based signal (4 Gb/s line rate), in which the transmitted information is encoded directly onto the continuous part of the signal nonlinear spectrum. By applying effective digital signal processing techniques, a reach of 7344 km was achieved with a bit error rate (2.1 × 10^−2) below the 20% FEC threshold. This represents an improvement by a factor of ∼12 in data capacity × distance product compared with other previously demonstrated NFT-based systems, showing a significant advance in the active research area of NFT-based communication systems.