New Developments of Information-Spectrum Theory

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The biggest significance of the information-spectrum method lies in its generality and simplicity. The aim of our research is to pursue this characteristic of the method and to extend its scope so as to give new lights to several information-theoretical problems for which construction of general theories had been considered to be difficult. Main results are as follows.(1)An extended and translated version of the book Information-Spectrum Methods in Information Theory has been published from Springer-Verlag, which has further developed mathematical foundations of the theory as well as mathematical tools for applications.(2)We have investigated asymptotic properties of the general hypothesis testing problem, which provides a basis of classical/quantum information theory, to clarify the quantum analogue of the information spectrum. This result has been applied to the channel coding problem to elucidate a close relation between universal coding and sufficient statistics.(3)The universal coding problem has been analyzed from an information-spectrum viewpoint, which has given a condition for a source to have a universal code and elucidated a close relation between universal coding and sufficient statistics.(4)We have investigated from an information-spectrum viewpoint the "folklore" of information theory that the output sequence seems to be almost completely random when a data sequence from an arbitrary source is losslessly compressed with the optimal rate, whereby the folklore has been given a clear mathematical expression and a condition for its validity.