Read e-book online ABSTRACT METHODS IN INFORMATION THEORY (SECOND EDITION): 10 PDF

Discrete Mathematics

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 easy homes are tested, the place the latter entropy is prolonged to be a linear useful on a definite set of measures. Ergodic and combining homes of desk bound resources are studied in addition to AMS (asymptotically suggest desk bound) sources.

The major function of this ebook is to offer details channels within the surroundings of sensible research and operator idea in addition to chance thought. 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 points, which generalize usual channels. additionally Gaussian channels are thought of intimately including Gaussian measures on a Hilbert house. The unique issues bankruptcy offers with beneficial properties reminiscent of generalized potential, channels with an intermediate noncommutative process, and von Neumann algebra process for channels. eventually, quantum (noncommutative) details channels are tested in an self sufficient bankruptcy, that could be considered as an advent to quantum details idea. 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.

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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ABSTRACT METHODS IN INFORMATION THEORY (SECOND EDITION): 10 (SERIES ON MULTIVARIATE ANALYSIS) by KAKIHARA YUICHIRO


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