Shannon's information theory deals with source coding [ ] Claude Shannon established the mathematical basis of information theory and published [ ]. provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a. Die Informationstheorie ist eine mathematische Theorie aus dem Bereich der Claude E. Shannon: A mathematical theory of communication. Bell System Tech.
An Introduction to Single-User Information Theoryprovides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a. This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon's information theory, discussing the fundamental. Shannon's information theory deals with source coding [ ] Claude Shannon established the mathematical basis of information theory and published [ ].
Shannon Information Theory Primary Sidebar VideoClaude Shannon - Father of the Information Age
Das Abdecken mit einer Strohschicht, Glücksspiralle mindestens 0,10 bis 1,00 Euro? - InhaltsverzeichnisThe maximum rate at which information can be Clubcooee has a simple characterization in terms of the maximum flows in the graph representing the network.
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. Acknowledge maguti April 10, , pm. Primadonna valarie Ntokoma April 10, , pm.
Its amazing. Cambridge, Dover 2nd Edition. Reza, F. New York: McGraw-Hill Urbana, Illinois : University of Illinois Press. Stone, JV.
Yeung, RW. Information Theory and Network Coding Springer , Leff and A. What is Information? Subfields of and cyberneticians involved in cybernetics.
Artificial intelligence Biological cybernetics Biomedical cybernetics Biorobotics Biosemiotics Neurocybernetics Catastrophe theory Computational neuroscience Connectionism Control theory Cybernetics in the Soviet Union Decision theory Emergence Engineering cybernetics Homeostasis Information theory Management cybernetics Medical cybernetics Second-order cybernetics Semiotics Sociocybernetics Polycontexturality Synergetics.
Data compression methods. Compression formats Compression software codecs. Mathematics areas of mathematics. Category theory Information theory Mathematical logic Philosophy of mathematics Set theory.
Calculus Real analysis Complex analysis Differential equations Functional analysis Harmonic analysis. Combinatorics Graph theory Order theory Game theory.
Arithmetic Algebraic number theory Analytic number theory Diophantine geometry. Algebraic Differential Geometric. Control theory Mathematical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Operations research Probability Statistics.
Computer science Theory of computation Numerical analysis Optimization Computer algebra. History of mathematics Recreational mathematics Mathematics and art Mathematics education.
Category Portal Commons WikiProject. Computer science. Computer architecture Embedded system Real-time computing Dependability.
Network architecture Network protocol Network components Network scheduler Network performance evaluation Network service. Interpreter Middleware Virtual machine Operating system Software quality.
Programming paradigm Programming language Compiler Domain-specific language Modeling language Software framework Integrated development environment Software configuration management Software library Software repository.
Control variable Software development process Requirements analysis Software design Software construction Software deployment Software maintenance Programming team Open-source model.
Model of computation Formal language Automata theory Computability theory Computational complexity theory Logic Semantics.
Algorithm design Analysis of algorithms Algorithmic efficiency Randomized algorithm Computational geometry. Discrete mathematics Probability Statistics Mathematical software Information theory Mathematical analysis Numerical analysis.
This is where the language of equivocation or conditional entropy is essential. In the noiseless case, given a sent message, the received message is certain.
In other words, the conditional probability is reduced to a probability 1 that the received message is the sent message.
Or, even more precisely, the mutual information equals both the entropies of the received and of the sent message. Just like the sensor detecting the coin in the above example.
The relevant information received at the other end is the mutual information. This mutual information is precisely the entropy communicated by the channel.
This fundamental theorem is described in the following figure, where the word entropy can be replaced by average information :.
Shannon proved that by adding redundancy with enough entropy, we could reconstruct the information perfectly almost surely with a probability as close to 1 as possible.
Quite often, the redundant message is sent with the message, and guarantees that, almost surely, the message will be readable once received.
There are smarter ways to do so, as my students sometimes recall me by asking me to reexplain reasonings differently. Shannon worked on that later, and managed other remarkable breakthroughs.
In practice, this limit is hard to reach though, as it depends on the probabilistic structure of the information.
Although there definitely are other factors coming in play, which have to explain, for instance, why the French language is so more redundant than English….
Claude Shannon then moves on generalizing these ideas to discuss communication using actual electromagnetic signals, whose probabilities now have to be described using probabilistic density functions.
But, instead of trusting me, you probably should rather listen to his colleagues who have inherited his theory in this documentary by UCTV:.
Shannon did not only write the paper. Shannon also made crucial progress in cryptography and artificial intelligence. I can only invite you to go further and learn more.
Indeed, what your professors may have forgotten to tell you is that this law connects today's world to its first instant, the Big Bang!
Find out why! What's the probability of the other one being a boy too? This complex question has intrigued thinkers for long until mathematics eventually provided a great framework to better understanding of what's known as conditional probabilities.
In this article, we present the ideas through the two-children problem and other fun examples. What is Information? Part 2a — Information Theory on Cracking the Nutshell.
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. Encoder: The microphone and its computer will turn the voice of the radio host into binary packets of data that are sent to the radio transmitter.
The radio transmitter, also part of the encoder, will turn that data into radio waves ready to be transmitted.
Receiver: The receiver is the person listening to the radio, who will hopefully receiver the full message loud and clear if noise has been avoided or minimized.
Feedback: Feedback is difficult in this step. However, the radio channel may send out researchers into the field to interview listeners to see how effective their communication has been.
Sender: The person starting the conversation will say something to start the communication process. Noise: The sender may have mumbled or have an accent that caused the message to be distorted internal noise.
There might be a wind or traffic that made the message hard to hear external noise. Receiver: The receiver is the second person in the conversation, who the sender is talking to.
Feedback: Face-to-face communication involves lots of feedback, as each person takes turns to talk. It shows how information is interrupted and helps people identify areas for improvement in communication.
A simple text is more like a quick statement, question, or request. These differences in communication style is what has made communication better through digital coding.
Instead of trying to figure out all of the variables in a communication effort like Morse Code, the 0s and 1s of digital coding allow for long strings of digits to be sent without the same levels of informational entropy.
A 0, for example, can be represented by a specific low-voltage signal. A 1 could then be represented by a high voltage signal. 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. Similarly, a long, complete message in perfect French would convey little useful knowledge to someone who could understand only English.
Shannon thus wisely realized that a useful theory of information would first have to concentrate on the problems associated with sending and receiving messages, and it would have to leave questions involving any intrinsic meaning of a message—known as the semantic problem—for later investigators.
Clearly, if the technical problem could not be solved—that is, if a message could not be transmitted correctly—then the semantic problem was not likely ever to be solved satisfactorily.
Solving the technical problem was therefore the first step in developing a reliable communication system. It is no accident that Shannon worked for Bell Laboratories.
The practical stimuli for his work were the problems faced in creating a reliable telephone system.In Shannon's theory ‘information’ is fully determined by the probability distribution on the set of possible messages, and unrelated to the meaning, structure or content of individual messages. In many cases this is problematic, since the distribution generating outcomes may be unknown to the observer or (worse), may not exist at all 5. For example, can we answer a question like “what is the information in this book” by viewing it as an element of a set of possible books with a. Information Theory was not just a product of the work of Claude Shannon. It was the result of crucial contributions made by many distinct individuals, from a variety of backgrounds, who took his ideas and expanded upon them. Indeed the diversity and directions of their perspectives and interests shaped the direction of Information Theory. Shannon’s Information Theory. Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. Information theory studies the quantification, storage, and communication of information. 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 inform. This is Claude Shannon, an American mathematician and electronic engineer who is now considered the "Father of Information Theory". While working at Bell Laboratories, he formulated a theory which aimed to quantify the communication of information.