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The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to ε, is called the ε-optimum exponent. In this paper, we first give the second-order ε-exponent in the case where the null hypothesis and...
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding variable-length uniform random numbers, and the asymptotically minimum average length rate of the uniform random numbers, called the (variable-length) resolvability, is investigated. We first analyze the variable-length resolvability with the variational distance...
This paper studies the first- and second-order maximum achievable rates of codes with/without cost constraints for general mixed channels whose channel law is characterized by a mixture of uncountably many stationary and memoryless discrete channels. These channels are referred to as general mixed memoryless channels and include mixed memoryless channels of finitely or countably many memoryless channels...
The second-order achievable rate region in Slepian-Wolf source coding systems is investigated. The concept of second-order achievable rates, which enables us to make a finer evaluation of achievable rates, has already been introduced and analyzed for general sources in the single-user source coding problem. Accordingly, in this paper, we first define the second-order achievable rate region for the...
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...
Basic logics underlying typical theorems in informtion theory are scrutinized from the viewpoint of information-spectra. Very general sources, which may be neither stationary nor ergodic, are introduced to establish conceptually simple formulars holding for the generalized AEP theorem, the optimal source coding theorem along with the reliability function, the fundamental limits of random number generation,...
The problem of network coding for multicasting a single source to multiple sinks has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they have established the celebrated max-flow mini-cut theorem on non-physical information flow over a network of independent channels. On the other hand, in 1980, Han has studied the case with correlated multiple sources and a single sink from the...
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