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By KAKIHARA YUICHIRO

Information conception 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 speculation of knowledge channels. Shannon entropy and Kolmogorov–Sinai entropy are outlined and their easy homes are tested, the place the latter entropy is prolonged to be a linear practical on a undeniable set of measures. Ergodic and combining houses of desk bound resources are studied in addition to AMS (asymptotically suggest desk bound) sources.

The major objective of this publication is to offer info channels within the surroundings of useful research and operator idea in addition to chance 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 usual channels. additionally Gaussian channels are thought of intimately including Gaussian measures on a Hilbert house. The targeted issues bankruptcy bargains with positive factors comparable to generalized means, channels with an intermediate noncommutative approach, and von Neumann algebra approach for channels. ultimately, quantum (noncommutative) info channels are tested in an self reliant 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. simple effects on quantum channels and entropy transmission also are considered.

Contents:

  • Entropy
  • Information Sources
  • Information Channels
  • Channel Operators
  • Gaussian Channels
  • Special Topics
  • Quantum Channels
  • References
  • Glossaries of Axioms
  • Indices

Readership: Graduate scholars and researchers from arithmetic and verbal exchange Engineering.

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