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Ralph Hartley | A Wisdom Archive on Ralph Hartley | | Ralph Hartley A selection of articles related to Ralph Hartley | |
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Ralph Hartley
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ARTICLES RELATED TO Ralph Hartley | |
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| | |  Ralph Hartley: Encyclopedia II - 1970 - Events
1970 - January.
January 1 - Construction begins on Arcosanti, by Paolo Soleri, in Mayer, Arizona, located 65 miles north of Phoenix, Arizona.
January 1 - Unix epoch at 00:00:00 UTC.
January 5 - The first episode of All My Children was broadcast on the ABC television network.
January 12 - Biafra capitulates, ending the Nigerian civil war.
January 15 - After a 32-month fight for independence from Nigeria, Biafran forces under General Effiong formally surrender to Gen ...
See also:1970, 1970 - Events, 1970 - January, 1970 - February, 1970 - March, 1970 - April, 1970 - May, 1970 - June, 1970 - July, 1970 - August, 1970 - September, 1970 - October, 1970 - November, 1970 - December, 1970 - Unknown date, 1970 - Births, 1970 - January, 1970 - February, 1970 - March, 1970 - April, 1970 - May, 1970 - June, 1970 - July, 1970 - August, 1970 - September, 1970 - October, 1970 - November, 1970 - December, 1970 - Unknown date, 1970 - Deaths, 1970 - January, 1970 - February, 1970 - March, 1970 - April, 1970 - May, 1970 - June, 1970 - July, 1970 - August, 1970 - September, 1970 - October, 1970 - November, 1970 - December, 1970 - Unknown date, 1970 - Nobel Prizes, 1970 - Fields Medalists Read more here: » 1970: Encyclopedia II - 1970 - Events |
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| | | | Ralph Hartley: Encyclopedia II - Information theory - Basic Concepts for Discrete Channels
Information theory - Self-information.
Shannon defined a measure of information content called the self-information or surprisal of a message m:
where p(m) = Pr(M = m) is the probability of the message m taken from an implicit message space M.
Note: Strictly speaking, p(m) is the probability density func ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Information theory - Basic Concepts for Discrete Channels |
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| | | | Ralph Hartley: Encyclopedia II - 1888 - Births
1888 - January-March.
January 1 - Victor Goldschmidt, Swiss geochemist (d. 1947)
January 8 - Matt Moore, Irish-born actor (d. 1960)
January 24 - Vicki Baum, Austrian writer (d. 1960)
Ernst Heinkel, German aircraft designer (d. 1958)
February 2 - Frederick Lane, Australian swimmer (d. 1969)
February 17 - Otto Stern, German physicist, Nobel Prize laureate (d. 1969)
February 19 - José Eustasio Rivera, Colombian writer (d. 1928)
Februar ...
See also:1888, 1888 - Events, 1888 - Births, 1888 - January-March, 1888 - April-June, 1888 - July-October, 1888 - November-December, 1888 - Deaths, 1888 - Marriages Read more here: » 1888: Encyclopedia II - 1888 - Births |
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| | | | Ralph Hartley: Encyclopedia II - Channel Capacity Let us return for the time being to our consideration of the communications process over a discrete channel. At this time it will be helpful to have a simple model of the process:
+-------+
| Noise |
+-------+
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V
+-----------+ Y +-------+ X +--------+
|Transmitter|-------->|Channel|-------->|Receiver ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Channel Capacity |
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| | | | Ralph Hartley: Encyclopedia II - Continuous Channels Shannon information is appropriate for measuring uncertainty over a discrete space. Its basic measures have been extended by analogy to continuous spaces. The continuous entropy, joint entropy, and conditional entropy are not quite as meaningful as the corresponding measures in the discrete case. Here they can take on negative as well as positive values, and they are not invariant under linear transformation. The mutual information has the distinction of being the only one of Shannon's basic measures of information that remains fundamentally ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Continuous Channels |
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| | | | Ralph Hartley: Encyclopedia II - Basic Concepts for Discrete Channels
Information theory - Self-information.
Shannon defined a measure of information content called the self-information or surprisal of a message m:
where p(m) = Pr(M = m) is the probability of the message m taken from an implicit message space M.
Note: Strictly speaking, p(m) is the probability density func ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Basic Concepts for Discrete Channels |
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| | | | Ralph Hartley: Encyclopedia II - Mathematical preliminaries Information theory is based on and intimately connected with probability theory.
In information theory, logarithms are used extensively. The base of the logarithms used here is deliberately left unspecified, following standard practice in information theory. As in many other applications of logarithms, it really does not matter much what base is used as long as one is consistent. In the case of information theory, the choice of logarithmic base merely determines the unit that is used to measure information. Common choices of logarithm ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Mathematical preliminaries |
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| | | | Ralph Hartley: Encyclopedia II - Source Theory Any process that generates successive messages can be considered a source of information. Sources can be classified in order of increasing generality as memoryless, ergodic, stationary, and stochastic, (with each class strictly containing the previous one). The term "memoryless" as used here has a slightly different meaning than it normally does in probability theory. Here a memoryless source is defined as one that generates successive messages independently of one another and with a fixed probability distribution. However, the position of t ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Source Theory |
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| | | | Ralph Hartley: Encyclopedia II - Fundamental Theorem
Information theory - Statement Noisy-Channel Coding Theorem.
1. For every discrete memoryless channel, the channel capacity
has the following property. For any ε > 0 and R < C, for large enough N, there exists a code of length N and rate ≥ R and a decoding algorithm, such that the maximal probability of block error is ≤ ε.
2. If a probability of bit error pb is acceptable, ra ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Fundamental Theorem |
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| | | | Ralph Hartley: Encyclopedia II - History Claude E. Shannon (1916–2001) founded information theory with his classic paper "A Mathematical Theory of Communication", published in the Bell System Technical Journal in July and October of 1948. This work drew on earlier publications by Harry Nyquist and Ralph Hartley. At the beginning of his paper, Shannon asserted that
"The fundamental problem of communication is that of reproducing at one point, either exactly or approximately ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - History |
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| | | | Ralph Hartley: Encyclopedia II - Related Concepts
Information theory - Measure Theory.
Here is an interesting and illuminating connection between information theory and measure theory:
If to arbitrary discrete random variables X and Y we associate the existence of sets and , somehow representing the information borne by X and Y, respectively, such that:
and are disjoint whenever X and Y are independent, and
whenever X and Y are such that either one is completel ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Related Concepts |
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| | | | Ralph Hartley: Encyclopedia II - Applications
Information theory - Coding Theory.
Coding theory is the most important and direct application of information theory. It can be subdivided into data compression theory and error correction theory. Using a statistical description for data, information theory quantifies the number of bits needed to describe the data. There are two formulations for the compression problem -- in lossless data compression the data must be reconstructed exactly, whereas lossy data compression examines how many bits are needed to recons ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography, Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Applications |
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| | | | Ralph Hartley: Encyclopedia II - Information theory - History Claude E. Shannon (1916–2001) founded information theory with his classic paper "A Mathematical Theory of Communication", published in the Bell System Technical Journal in July and October of 1948. This work drew on earlier publications by Harry Nyquist and Ralph Hartley. At the beginning of his paper, Shannon asserted that
"The fundamental problem of communication is that of reproducing at one point, either exactly or approximately ...
See also:Information theory, Information theory - Mathematical preliminaries, Information theory - Basic Concepts for Discrete Channels, Information theory - Self-information, Information theory - Entropy, Information theory - Joint Entropy, Information theory - Conditional Entropy Equivocation, Information theory - Mutual Information Transinformation, Information theory - Continuous Channels, Information theory - Channel Capacity, Information theory - Source Theory, Information theory - Rate, Information theory - Fundamental Theorem, Information theory - Statement Noisy-Channel Coding Theorem, Information theory - Channel capacity of particular model channels, Information theory - Related Concepts, Information theory - Measure Theory, Information theory - Kolmogorov Complexity, Information theory - Applications, Information theory - Coding Theory, Information theory - Cryptography Cryptanalysis, Information theory - Relation with thermodynamic entropy, Information theory - Quantum Information Theory, Information theory - Detection and Estimation Theory, Information theory - Gambling, Information theory - Intelligence, Information theory - Music, Information theory - History Read more here: » Information theory: Encyclopedia II - Information theory - History |
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More material related to Ralph Hartley can be found here:
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