We present a light-extraction approach allowing for single-pass and omniangle outcoupling of light from light-emitting diodes (LED). By using transformation optics, we perceive a feasible graded-index structure that is a transition from the LED exit facet to a low refractive index region with expanded space that represents air. Apart from the material dispersion of the constituents, our approach is wavelength independent. The suggested extractor is geometrically compact with size parameters comparable to the width of an LED and therefore well adapted for pixelated LEDs. A beam-expanding functionality is possible while fully preserving the outcoupling efficiency by applying index and geometry truncation.