2 research outputs found
First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture
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 epsilon, is called the
epsilon-optimum exponent. In this paper, we first give the second-order
epsilon-exponent in the case where the null hypothesis and the alternative
hypothesis are a mixed memoryless source and a stationary memoryless source,
respectively. We next generalize this setting to the case where the alternative
hypothesis is also a mixed memoryless source. We address the first-order
epsilon-optimum exponent in this setting. In addition, an extension of our
results to more general setting such as the hypothesis testing with mixed
general source and the relationship with the general compound hypothesis
testing problem are also discussed.Comment: 23 page
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects