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The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, fixed-length source coding is 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 is quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In particular, for i.i.d. sources, the second-order achievable rates have earlier been determined simply by using the asymptotic normality.
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