LEDs can be modulated to support wireless optical data communication. However, particularly LEDs optimized for illumination act as a non-linear low-pass communication channel. In this paper, we translate the non-linear differential equations for the hole-electron recombination and photon emissions, into a discrete-time model with delay taps and non-linear coefficients. This LED model can be inverted, to actively eliminate or mitigate the non-linear dynamic LED distortion. We propose a further simplification of the compensation circuit that allows us to use a relatively simple structure with only a couple of parameters. We experimentally characterize and measure signals communicated via commercially available illumination LEDs that are also used for LiFi communication. In an Intensity Modulation Direct Detection (IM/DD) system employing Pulse Amplitude Modulation (PAM), we show that the proposed equalizer can effectively widen the measured eye diagram, thereby reduce the error rate or can allow a larger constellation. For Orthogonal Frequency Division Multiplexing (OFDM), the reduction in distortion allows at least a 50% increase in bit rate, even on measured noisy channels. This confirms the suitability of the LED model on which our non-linear equalizer is based. We show how non-linear time-constants can be estimated from electrical measurements on the LED signal. With the proposed parameter estimation, the equalizer converges to appropriate compensation settings, in Minimum Mean Square Error (MMSE) sense.