information theory channel capacity communication systems theory and practice Die Informationstheorie wurde von Claude Elwood Shannon. Der Claude E. Shannon Award, benannt nach dem Begründer der Informationstheorie Claude E. Shannon, ist eine seit von der IEEE Information Theory. provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a.
Claude E. Shannon AwardThis book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon's information theory, discussing the fundamental. Der Claude E. Shannon Award, benannt nach dem Begründer der Informationstheorie Claude E. Shannon, ist eine seit von der IEEE Information Theory. Die Informationstheorie ist eine mathematische Theorie aus dem Bereich der Claude E. Shannon: A mathematical theory of communication. Bell System Tech.
Shannon Information Theory Primary Sidebar VideoIntroduction to Complexity: Shannon Information Part 1
Today we call that the bandwidth of the channel. Shannon demonstrated mathematically that even in a noisy channel with a low bandwidth, essentially perfect, error-free communication could be achieved by keeping the transmission rate within the channel's bandwidth and by using error-correcting schemes: the transmission of additional bits that would enable the data to be extracted from the noise-ridden signal.
Today everything from modems to music CDs rely on error-correction to function. A major accomplishment of quantum-information scientists has been the development of techniques to correct errors introduced in quantum information and to determine just how much can be done with a noisy quantum communications channel or with entangled quantum bits qubits whose entanglement has been partially degraded by noise.
The Unbreakable Code A year after he founded and launched information theory, Shannon published a paper that proved that unbreakable cryptography was possible.
He did this work in , but at that time it was classified. The scheme is called the one-time pad or the Vernam cypher, after Gilbert Vernam, who had invented it near the end of World War I.
The idea is to encode the message with a random series of digits--the key--so that the encoded message is itself completely random.
I download it on PDF but it was not completed. Thank you very much. The information is so simple to understand. May you describe and draw a relationship between this model and its application in effective communication practices, please?
Could you please explain to me the application of Shannon and Weaver model by using an example of business communication? Is the Shannon and Weaver model is by using technology like cellphone, computer and etc..??
How you could reply sir thank you.. We would like to request permission to use the chart in an upcoming textbook.
Please contact me. Kirito March 18, , am. 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.
Unfortunately, many of these purported relationships were of dubious worth. I personally believe that many of the concepts of information theory will prove useful in these other fields—and, indeed, some results are already quite promising—but the establishing of such applications is not a trivial matter of translating words to a new domain, but rather the slow tedious process of hypothesis and experimental verification.
Information theory Article Media Additional Info. Article Contents. Home Science Mathematics. It was originally proposed by Claude Shannon in to find fundamental limits on signal processing and communication operations such as data compression , in a landmark paper titled " A Mathematical Theory of Communication ".
The field is at the intersection of probability theory , statistics , computer science, statistical mechanics , information engineering , and electrical engineering.
A key measure in information theory is entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process.
For example, identifying the outcome of a fair coin flip with two equally likely outcomes provides less information lower entropy than specifying the outcome from a roll of a die with six equally likely outcomes.
Some other important measures in information theory are mutual information , channel capacity, error exponents , and relative entropy.
Important sub-fields of information theory include source coding , algorithmic complexity theory , algorithmic information theory , and information-theoretic security.
Applications of fundamental topics of information theory include lossless data compression e. ZIP files , lossy data compression e.
Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc , the feasibility of mobile phones and the development of the Internet.
The theory has also found applications in other areas, including statistical inference ,  cryptography , neurobiology ,  perception ,  linguistics, the evolution  and function  of molecular codes bioinformatics , thermal physics ,  quantum computing , black holes, information retrieval , intelligence gathering , plagiarism detection ,  pattern recognition , anomaly detection  and even art creation.
Information theory studies the transmission, processing, extraction, and utilization of information.
Abstractly, information can be thought of as the resolution of uncertainty. In the case of communication of information over a noisy channel, this abstract concept was made concrete in by Claude Shannon in his paper "A Mathematical Theory of Communication", in which "information" is thought of as a set of possible messages, where the goal is to send these messages over a noisy channel, and then to have the receiver reconstruct the message with low probability of error, in spite of the channel noise.
Shannon's main result, the noisy-channel coding theorem showed that, in the limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent.
Information theory is closely associated with a collection of pure and applied disciplines that have been investigated and reduced to engineering practice under a variety of rubrics throughout the world over the past half-century or more: adaptive systems , anticipatory systems , artificial intelligence , complex systems , complexity science , cybernetics , informatics , machine learning , along with systems sciences of many descriptions.
Information theory is a broad and deep mathematical theory, with equally broad and deep applications, amongst which is the vital field of coding theory.
Coding theory is concerned with finding explicit methods, called codes , for increasing the efficiency and reducing the error rate of data communication over noisy channels to near the channel capacity.
These codes can be roughly subdivided into data compression source coding and error-correction channel coding techniques.
In the latter case, it took many years to find the methods Shannon's work proved were possible. A third class of information theory codes are cryptographic algorithms both codes and ciphers.
Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis. See the article ban unit for a historical application.
The landmark event that established the discipline of information theory and brought it to immediate worldwide attention was the publication of Claude E.
Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs , all implicitly assuming events of equal probability.
The unit of information was therefore the decimal digit , which has since sometimes been called the hartley in his honor as a unit or scale or measure of information.
Alan Turing in used similar ideas as part of the statistical analysis of the breaking of the German second world war Enigma ciphers.
Much of the mathematics behind information theory with events of different probabilities were developed for the field of thermodynamics by Ludwig Boltzmann and J.
Willard Gibbs. Connections between information-theoretic entropy and thermodynamic entropy, including the important contributions by Rolf Landauer in the s, are explored in Entropy in thermodynamics and information theory.
In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of , Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that.
Information theory is based on probability theory and statistics. Information theory often concerns itself with measures of information of the distributions associated with random variables.
They are the person or object, or thing — any information source who has the information to begin with. The information source starts the process by choosing a message to send, someone to send the message to, and a channel through which to send the message.
A sender can send a message in multiple different ways: it may be orally through spoken word , in writing, through body language, music, etc.
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.
Thus, in average, the conditional information of the coin is zero. In other words, the conditional entropy is nil. It surely is!
Indeed, if you try to encode a message by encoding each character individually, you will be consuming space to repeat mutual information.
In fact, as Shannon studied the English language, he noticed that the conditional entropy of a letter knowing the previous one is greatly decreased from its non-conditional entropy.
The structure of information also lies in the concatenation into longer texts. In fact, Shannon defined the entropy of each character as the limit of the entropy of messages of great size divided by the size.
As it turns out, the decrease of entropy when we consider concatenations of letters and words is a common feature of all human languages… and of dolphin languages too!
This has led extraterrestrial intelligence seekers to search for electromagnetic signals from outer spaces which share this common feature too, as explained in this brilliant video by Art of the Problem :.
In some sense, researchers assimilate intelligence to the mere ability to decrease entropy. What an interesting thing to ponder upon!
A communication consists in a sending of symbols through a channel to some other end. Now, we usually consider that this channel can carry a limited amount of information every second.
Shannon calls this limit the capacity of the channel. The channel is usually using a physical measurable quantity to send a message.
This can be the pressure of air in case of oral communication. For longer telecommunications, we use the electromagnetic field.
The message is then encoded by mixing it into a high frequency signal. The frequency of the signal is the limit, as using messages with higher frequencies would profoundly modify the fundamental frequency of the signal.
Imagine there was a gigantic network of telecommunication spread all over the world to exchange data, like texts and images. How fast can we download images from the servers of the Internet to our computers?
Using the basic formatting called Bitmap or BMP, we can encode images pixels per pixels. The encoded images are then decomposed into a certain number of bits.
In the example, using bitmap encoding, the images can be transfered at the rate of 5 images per second. In the webpage you are currently looking at, there are about a dozen images.
This means that more than 2 seconds would be required for the webpage to be downloaded on your computer.
This theory turned information into a mathematical unit that could be measured, manipulated and then transmitted from one individual or machine to another.
Shannon worked at Bell Labs throughout much of his career as an electronics engineer and a mathematician. During World War II, he worked on the processes that would help to make it easier to send messages securely and efficiently over great distances.
Using coding and principles of equation, his work would become the foundation of one of the most important theories that we use today.
Information theory is based on statistics and probabilities. It measures the distributions that are associated with random variables so that we can recognize a specific result.
Just as our brain sees a tree and recognizes it to provide you with information, a computer can do the same thing using a specific series of codes.
Everything in our world today provides us with information of some sort. If you flip a coin, then you have two possible equal outcomes every time.