A Mathematical Theory of Communication by Claude E. Shannon PDF

Posted by

By Claude E. Shannon

Scientific wisdom grows at an exquisite pace--but few books have had as lasting an impression or performed as very important a task in our sleek global as The Mathematical concept of Communication, released initially as a paper on verbal exchange thought within the Bell process Technical Journal greater than fifty years in the past. Republished in ebook shape presently thereafter, it has on the grounds that undergone 4 hardcover and 16 paperback printings. it's a innovative paintings, dazzling in its foresight and contemporaneity. The college of Illinois Press is happy and commemorated to factor this commemorative reprinting of a classic.

Show description

Read or Download A Mathematical Theory of Communication PDF

Best number theory books

Read e-book online Number Theory and Its Applications PDF

"Addresses modern advancements in quantity conception and coding conception, initially awarded as lectures at summer season college held at Bilkent collage, Ankara, Turkey. comprises many ends up in publication shape for the 1st time. "

Download PDF by Machiel van Frankenhuijsen: The Riemann Hypothesis for Function Fields: Frobenius Flow

This publication presents a lucid exposition of the connections among non-commutative geometry and the well-known Riemann speculation, concentrating on the speculation of one-dimensional forms over a finite box. The reader will stumble upon many very important facets of the idea, reminiscent of Bombieri's facts of the Riemann speculation for functionality fields, in addition to a proof of the connections with Nevanlinna thought and non-commutative geometry.

Additional resources for A Mathematical Theory of Communication

Example text

If we think of the different frequency components as the original coordinate system, the new frequency components are merely the old ones multiplied by factors. The coordinate transformation matrix is thus essentially diagonalized in terms of these coordinates. The Jacobian of the transformation is (for n sine and n cosine components) n J = ∏ jY  fi j2 i=1 where the fi are equally spaced through the band W . This becomes in the limit exp 1 W Z W log jY  f j2 d f : Since J is constant its average value is the same quantity and applying the theorem on the change of entropy with a change of coordinates, the result follows.

The region ofp high probability is a sphere of radius nN. As n ! ∞ the probability of being outside a sphere of radius nN +  approaches zero and 1n times the logarithm of the p volume of the sphere approaches log 2 eN. In the continuous case it is convenient to work not with the entropy H of an ensemble but with a derived quantity which we will call the entropy power. This is defined as the power in a white noise limited to the same band as the original ensemble and having the same entropy. In other words if H 0 is the entropy of an ensemble its entropy power is 1 N1 = exp2H 0 2 e In the geometrical picture this amounts to measuring the high probability volume by the squared radius of a sphere having the same volume.

To TW log N P+N Formulas similar to C = W log for the white noise case have been developed independently N by several other writers, although with somewhat different interpretations. We may mention the work of N. Wiener,7 W. G. Tuller,8 and H. Sullivan in this connection. In the case of an arbitrary perturbing noise (not necessarily white thermal noise) it does not appear that the maximizing problem involved in determining the channel capacity C can be solved explicitly. However, upper and lower bounds can be set for C in terms of the average noise power N the noise entropy power N1 .

Download PDF sample

A Mathematical Theory of Communication by Claude E. Shannon


by Thomas
4.5

Rated 4.72 of 5 – based on 6 votes