Shannon's information theory deals with source coding [ ] Claude Shannon established the mathematical basis of information theory and published [ ]. Die Informationstheorie ist eine mathematische Theorie aus dem Bereich der Claude E. Shannon: A mathematical theory of communication. Bell System Tech. In diesem Jahr veröffentlichte Shannon seine fundamentale Arbeit A Mathematical Theory of Communication und prägte damit die moderne Informationstheorie.
Claude E. Shannon AwardDer Claude E. Shannon Award, benannt nach dem Begründer der Informationstheorie Claude E. Shannon, ist eine seit von der IEEE Information Theory. This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon's information theory, discussing the fundamental. A First Course in Information Theory is an up-to-date introduction to information Shannon's information measures refer to entropy, conditional entropy, mutual.
Shannon Information Theory Historical background VideoClaude Shannon - Father of the Information Age
This was of great utility to engineers, who could focus thereafter on individual cases and understand the specific trade-offs involved. Shannon also made the startling discovery that, even in the presence of noise, it is always possible to transmit signals arbitrarily close to the theoretical channel capacity.
This discovery inspired engineers to look for practical techniques to improve performance in signal transmissions that were far from optimal. Before Shannon, engineers lacked a systematic way of analyzing and solving such problems.
Though information theory does not always make clear exactly how to achieve specific results, people now know which questions are worth asking and can focus on areas that will yield the highest return.
They also know which sorts of questions are difficult to answer and the areas in which there is not likely to be a large return for the amount of effort expended.
The section Applications of information theory surveys achievements not only in such areas of telecommunications as data compression and error correction but also in the separate disciplines of physiology, linguistics, and physics.
The communications channel to one's memories--one's past and one's very personality--is progressively degraded until every effort at error correction is overwhelmed and no meaningful signal can pass through.
The bandwidth falls to zero. The extraordinary pattern of information processing that was Claude Shannon finally succumbed to the depredations of thermodynamic entropy in February But some of the signal generated by Shannon lives on, expressed in the information technology in which our own lives are now immersed.
Graham P. Collins is on the board of editors at Scientific American. You have free article s left. Already a subscriber? Sign in. One early commercial application of information theory was in the field of seismic oil exploration.
Work in this field made it possible to strip off and separate the unwanted noise from the desired seismic signal.
Information theory and digital signal processing offer a major improvement of resolution and image clarity over previous analog methods.
Semioticians Doede Nauta and Winfried Nöth both considered Charles Sanders Peirce as having created a theory of information in his works on semiotics.
Concepts from information theory such as redundancy and code control have been used by semioticians such as Umberto Eco and Ferruccio Rossi-Landi to explain ideology as a form of message transmission whereby a dominant social class emits its message by using signs that exhibit a high degree of redundancy such that only one message is decoded among a selection of competing ones.
Information theory also has applications in Gambling and information theory , black holes , and bioinformatics. From Wikipedia, the free encyclopedia.
Theory dealing with information. Not to be confused with Information science. This article may contain indiscriminate , excessive , or irrelevant examples.
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May Main article: History of information theory. Main article: Quantities of information. Main article: Coding theory. Main article: Channel capacity.
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Hartley, R. History of information theory Shannon, C. Timeline of information theory Yockey, H. Coding theory Detection theory Estimation theory Fisher information Information algebra Information asymmetry Information field theory Information geometry Information theory and measure theory Kolmogorov complexity List of unsolved problems in information theory Logic of information Network coding Philosophy of information Quantum information science Source coding.
Rieke; D. Spikes: Exploring the Neural Code. The MIT press. Scientific Reports. Bibcode : NatSR Bibcode : Sci Bibcode : PhRv.. Scientific American.
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An Introduction to Information Theory. Dover Publications, Inc. Example: An example of a sender might be the person reading a newscast on the nightly news.
They will choose what to say and how to say it before the newscast begins. The encoder is the machine or person that converts the idea into signals that can be sent from the sender to the receiver.
The Shannon model was designed originally to explain communication through means such as telephone and computers which encode our words using codes like binary digits or radio waves.
However, the encoder can also be a person that turns an idea into spoken words, written words, or sign language to communicate an idea to someone.
Examples: The encoder might be a telephone, which converts our voice into binary 1s and 0s to be sent down the telephone lines the channel.
Another encode might be a radio station, which converts voice into waves to be sent via radio to someone. The channel of communication is the infrastructure that gets information from the sender and transmitter through to the decoder and receiver.
Examples: A person sending an email is using the world wide web internet as a medium. A person talking on a landline phone is using cables and electrical wires as their channel.
There are two types of noise: internal and external. Internal noise happens when a sender makes a mistake encoding a message or a receiver makes a mistake decoding the message.
External noise happens when something external not in the control of sender or receiver impedes the message. Now, in the first page of his article, Shannon clearly says that the idea of bits is J.
And, surely enough, the definition given by Shannon seems to come out of nowhere. But it works fantastically. Meanwhile, in Vietnam, people rather use my full first name.
A context corresponds to what messages you expect. More precisely, the context is defined by the probability of the messages.
Thus, the context of messages in Vietnam strongly differs from the context of western countries. But this is not how Shannon quantified it, as this quantification would not have nice properties.
Because of its nice properties. But mainly, if you consider a half of a text, it is common to say that it has half the information of the text in its whole.
This is due to the property of logarithm to transform multiplication which appears in probabilistic reasonings into addition which we actually use.
This is an awesome remark! Indeed, if the fraction of the text you read is its abstract, then you already kind of know what the information the whole text has.
It does! And the reason it does is because the first fraction of the message modifies the context of the rest of the message. In other words, the conditional probability of the rest of the message is sensitive to the first fraction of the message.
This updating process leads to counter-intuitive results, but it is an extremely powerful one. Find out more with my article on conditional probabilities.
The whole industry of new technologies and telecommunications! But let me first present you a more surprising application to the understanding of time perception explain in this TedED video by Matt Danzico.
As Shannon put it in his seminal paper, telecommunication cannot be thought in terms of information of a particular message. Indeed, a communication device has to be able to work with any information of the context.
This has led Shannon to re -define the fundamental concept of entropy , which talks about information of a context.
You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name.
In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
In , Ludwig Boltzmann shook the world of physics by defining the entropy of gases, which greatly confirmed the atomic theory. He defined the entropy more or less as the logarithm of the number of microstates which correspond to a macrostate.
For instance, a macrostate would say that a set of particles has a certain volume, pressure, mass and temperature. Meanwhile, a microstate defines the position and velocity of every particle.
This is explained in the following figure, where each color stands for a possible message of the context:. Because there are just two digits and each has a very specific state that can be recognized, even after the signal has experienced extensive entropy, it becomes possible to reconstruct the information with greater accuracy.
Using the information theory, a base 2 is used for the mathematical logarithms so that we can obtain total informational content. In the instance of a coin flip, the value received is one bit.
The same would be true when dice are rolled. This is another bit of information. You could expand this to a twenty-sided die as well.
This principle can then be used to communicate letters, numbers, and other informational concepts that we recognize. Take the alphabet, for example.