By KAKIHARA YUICHIRO
Information thought is studied from the subsequent issues of view: (1) the idea of entropy as volume of knowledge; (2) the mathematical constitution of knowledge assets (probability measures); and (3) the speculation of knowledge channels. Shannon entropy and Kolmogorov–Sinai entropy are outlined and their uncomplicated homes are tested, the place the latter entropy is prolonged to be a linear sensible on a definite set of measures. Ergodic and combining houses of desk bound resources are studied in addition to AMS (asymptotically suggest desk bound) sources.
The major function of this publication is to give info channels within the atmosphere of practical research and operator conception in addition to likelihood idea. Ergodic, blending, and AMS channels also are thought of intimately with a few illustrations. during this moment version, channel operators are studied in lots of elements, which generalize usual channels. additionally Gaussian channels are thought of intimately including Gaussian measures on a Hilbert area. The exact subject matters bankruptcy bargains with beneficial properties resembling generalized means, channels with an intermediate noncommutative method, and von Neumann algebra approach for channels. eventually, quantum (noncommutative) info channels are tested in an self sustaining bankruptcy, that may be considered as an advent to quantum info conception. Von Neumann entropy is brought and its generalization to a C*-algebra environment is given. easy 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 communique Engineering.
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ABSTRACT METHODS IN INFORMATION THEORY (SECOND EDITION): 10 (SERIES ON MULTIVARIATE ANALYSIS) by KAKIHARA YUICHIRO