Because the density of the outer core of the Earth from seismic data is about 10% lower than that of pure hcp iron at core pressures and temperatures, the outer core should consist of iron alloy with a small amount of light elements. Although there are several candidates of light elements, no consensus has been made on which of light elements (or their mixture) are actually present in the outer core of the Earth. To identify light elements alloyed with liquid iron in the outer core, it is crucial to know densities of liquid iron alloys at outer-core conditions. Experimentally, densities of liquid iron alloys are measured by using sink/float method or X-ray absorption method. However, these measurements have been limited to low pressure so far. Here, I will show a series of first-principles molecular dynamics on liquid iron-sulfur alloy to determine its density and other thermodynamical quantities; sulfur is one of the most probable candidates of light element. We will discuss if sulfur can explain density deficiency in the outer core and if other elements must be considered.