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Light-emitting diodes (LEDs) constitute a low-cost alternative for optical data transmission of up to ~ 1 Gb/s. What differentiates such applications from, e.g., backhaul optical networks, is the fact that apart from their data throughput, LEDs are generally not as well characterized by the manufacturer as, for example, optical fiber amplifiers. While for simple modulation formats, this lack of knowledge is not a severe impediment; in any other situation, one may face rather complex behaviors of commercial LEDs. In this paper, the main electro-optical characteristics of LEDs are discussed, and it is shown that some popular simple nonlinear models available in the literature are inadequate in describing their dynamics. As a way out of this malady, we present a reverse-engineering approach that is based on Volterra expansions of the electro-optical characteristic function of LEDs, enabling the introduction of a realistic empirical model for commercial devices.