Nonlinear impairments induced by the opto-electronic components are one of the fundamental performance-limiting factors in high-speed optical short-reach communications, significantly hindering capacity improvement. This paper proposes to employ a kernel mapping function to map the signals in a Hilbert space to its inner product in a reproducing kernel Hilbert space, which has been successfully demonstrated to mitigate nonlinear impairments in optical short-reach communication systems. The operation principle is derived. An intensity modulation/direct detection system with 1.5-µm vertical cavity surface emitting laser and 10-km 7-core fiber achieving 540.68-Gbps (net-rate 505.31-Gbps) has been carried out. The experimental results reveal that the kernel mapping based schemes are able to realize comparable transmission performance as the Volterra filtering scheme even with a high order.