Read e-book online A Mathematical Theory of Communication PDF

By Claude E. Shannon

Scientific wisdom grows at an exquisite pace--but few books have had as lasting an influence or performed as very important a job in our sleek global as The Mathematical idea of Communication, released initially as a paper on communique conception within the Bell method Technical Journal greater than fifty years in the past. Republished in publication shape presently thereafter, it has given that undergone 4 hardcover and 16 paperback printings. it's a innovative paintings, wonderful in its foresight and contemporaneity. The collage of Illinois Press is happy and commemorated to factor this commemorative reprinting of a classic.

Show description

Read Online or Download A Mathematical Theory of Communication PDF

Best number theory books

Download PDF by Jürgen Neukirch: Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass)

Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, sleek und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

Download e-book for iPad: Selected Chapters of Geomety, Analysis and Number Theory by Sandor J.

The purpose of this ebook is to give brief notes or articles, in addition to stories on a few subject matters of Geometry, research, and quantity idea. the cloth is split into ten chapters: * Geometry and geometric inequalities; * Sequences and sequence of actual numbers; * designated numbers and sequences of integers; * Algebraic and analytic inequalities; * Euler gamma functionality; * skill and suggest price theorems; * useful equations and inequalities; * Diophantine equations; * mathematics services; * Miscellaneous issues.

Extra resources for A Mathematical Theory of Communication

Example text

When a message x is originated it will (with probability approaching 1 as T ! ∞) lie within at least one of the fans. The corresponding binary number is transmitted (or one of them chosen arbitrarily if there are several) over the channel by suitable coding means to give a small probability of error. Since R1  C this is possible. At the receiving point the corresponding y is reconstructed and used as the recovered message. The evaluation v01 for this system can be made arbitrarily close to v1 by taking T sufficiently large.

Some examples are: 1. The set of functions: : f t  = sint + Each particular value of determines a particular function in the set. 2. The set of all functions of time containing no frequencies over W cycles per second. 3. The set of all functions limited in band to W and in amplitude to A. 4. The set of all English speech signals as functions of time. 1 For example with the set, f t  = sint + ; we may give a probability distribution for , P . The set then becomes an ensemble. Some further examples of ensembles of functions are: ; ;:::; n) with the probability of fk being pk .

The entropy for a continuous stochastic process has many properties analogous to that for discrete processes. In the discrete case the entropy was related to the logarithm of the probability of long sequences, and to the number of reasonably probable sequences of long length. In the continuous case it is related in a similar fashion to the logarithm of the probability density for a long series of samples, and the volume of reasonably high probability in the function space. More precisely, if we assume px1 xn  continuous in all the xi for all n, then for sufficiently large n ;:::; log p , H0 n 38 ;:::; for all choices of x1 xn  apart from a set whose total probability is less than , with and arbitrarily small.

Download PDF sample

A Mathematical Theory of Communication by Claude E. Shannon

by Richard

Rated 4.17 of 5 – based on 34 votes