Second-order achievable rates in random number generation for mixed sources

The second-order achievable rates in typical random number generation problems are considered. In these problems, several researchers have derived the first-order and the second-order achievability rates for general sources using the information spectrum methods. Although these formulas are general, their computation are quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In this paper, we consider mixed sources of two i.i.d. sources and compute the second-order achievable rates explicitly.