THOMAS M. COVER is Professor jointly in the Departments of Electrical Engineering and Statistics at Stanford University. He is past President. Library of Congress Cataloging-in-Publication Data: Cover, T. M., – Elements of information theory/by Thomas M. Cover, Joy A. Thomas.–2nd ed. p. cm. ELEMENTS OF INFORMATION THEORY Second Edition THOMAS M. COVER JOY A. THOMAS A JOHN WILEY & SONS, INC., PUBLICATION E.
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Elements of information theory/by Thomas M. Cover, Joy A. Thomas.–2nd ed. p. cm. “A Wiley-Interscience publication.” Includes bibliographical references and. John Bellamy. Elements of Information Theory. Thomas M. Cover and Joy A. Thomas. Telecommunication System Engineering, 2nd Edition. Roger L. Freeman. Share. Email; Facebook; Twitter; Linked In; Reddit; CiteULike. View Table of Contents for Elements of Information Theory.
Channel coding is concerned with finding such nearly optimal codes that can be used to transmit data over a noisy channel with a small coding error at a rate near the channel capacity. Capacity of particular channel models[ edit ] A continuous-time analog communications channel subject to Gaussian noise — see Shannon—Hartley theorem. A binary symmetric channel BSC with crossover probability p is a binary input, binary output channel that flips the input bit with probability p. The possible channel outputs are 0, 1, and a third symbol 'e' called an erasure. The erasure represents complete loss of information about an input bit. Applications to other fields[ edit ] Intelligence uses and secrecy applications[ edit ] Information theoretic concepts apply to cryptography and cryptanalysis.
Print ISBN: In he received the Outstanding Paper Award in information Theory for his paper "Broadcast Channels," and he was selected in as the Shannon Lecturer, regarded as the highest honor in information theory.
Author of over 90 technical papers, he is coeditor of the book Open Problems in Communication and Computation. Professor Cover has devoted the last 20 years to developing the relationship between information theory and statistics. He received his PhD in electrical engineering from Stanford University. JOY A. Free Access.
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One of the questions that many of you had whether the bound derived in part a was actually achievable. For example, can one distinguish 13 coins in 3 weighings?
No, not with a scheme like the one above.
Yes, under the assumptions under which the bound was derived. The bound did not prohibit the division of coins into halves, neither did it disallow the existence of another coin known to be normal. Under both these conditions, it is possible to nd the odd coin of 13 coins in 3 weighings.
You could try modifying the above scheme to these cases. Drawing with and without replacement.
An urn contains r red, w white, and b black balls. Which has higher entropy, drawing k 2 balls from the urn with replacement or without replacement? Set it up and show why. There is both a hard way and a relatively simple way to do this.
Solution: Drawing with and without replacement. Intuitively, it is clear that if the balls are drawn with replacement, the number of possible choices for the i -th ball is larger, and therefore the conditional entropy is larger.
But computing the conditional distributions is slightly involved.
It is easier to compute the unconditional entropy. With replacement. In this case the conditional distribution of each draw is the same for every draw. Thus r with prob.
Thus the unconditional entropy H X i is still the same as with replacement. The conditional entropy H X i Xi1 ,. A metric.
By problem 2. Thus X, Y is 0 i X and Y are functions of each other - and therefore are equivalent up to a reversible transformation. Consider three random variables X , Y and Z. Entropy of a disjoint mixture. Solution: Entropy. We can do this problem by writing down the denition of entropy and expanding the various terms.
Instead, we will use the algebra of entropies for a simpler proof. A measure of correlation. Let X1 and X2 be identically distributed, but not necessarily independent.
H X2 X1. Solution: A measure of correlation. By symmetry, X1 is a function of X2 , i.