Light-emitting diodes (LEDs), which will be increasingly used in lighting technology, will also allow for distribution of broadband optical wireless signals. Visible-light communication (VLC) using white LEDs offers several advantages over the RF-based wireless systems, i.e., license-free spectrum, low power consumption, and higher privacy. Mostly, optical wireless can provide much higher data rates. In this paper, we demonstrate a VLC system based on a white LED for indoor broadband wireless access. After investigating the nonlinear effects of the LED and the power amplifier, a data rate of 1 Gb/s has been achieved at the standard illuminance level, by using an optimized discrete multitone modulation technique and adaptive bit- and power-loading algorithms. The bit-error ratio of the received data was 1.5\cdot 10^{-3} , which is within the limit of common forward error correction (FEC) coding. These results twice the highest capacity that had been previously obtained.