By KAKIHARA YUICHIRO
Information idea is studied from the next issues of view: (1) the speculation of entropy as quantity of data; (2) the mathematical constitution of data resources (probability measures); and (3) the idea of knowledge channels. Shannon entropy and Kolmogorov–Sinai entropy are outlined and their uncomplicated houses are tested, the place the latter entropy is prolonged to be a linear useful on a definite set of measures. Ergodic and combining houses of desk bound assets are studied in addition to AMS (asymptotically suggest desk bound) sources.
The major objective of this ebook is to provide details channels within the setting of sensible research and operator conception in addition to likelihood conception. Ergodic, blending, and AMS channels also are thought of intimately with a few illustrations. during this moment variation, channel operators are studied in lots of facets, which generalize traditional channels. additionally Gaussian channels are thought of intimately including Gaussian measures on a Hilbert area. The distinctive issues bankruptcy offers with positive aspects akin to generalized capability, channels with an intermediate noncommutative process, and von Neumann algebra procedure for channels. ultimately, quantum (noncommutative) details channels are tested in an self sustaining bankruptcy, that could be considered as an creation to quantum details thought. Von Neumann entropy is brought and its generalization to a C*-algebra atmosphere is given. simple effects on quantum channels and entropy transmission also are considered.
- Information Sources
- Information Channels
- Channel Operators
- Gaussian Channels
- Special Topics
- Quantum Channels
- Glossaries of Axioms
Readership: Graduate scholars and researchers from arithmetic and conversation Engineering.
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ABSTRACT METHODS IN INFORMATION THEORY (SECOND EDITION): 10 (SERIES ON MULTIVARIATE ANALYSIS) by KAKIHARA YUICHIRO