Ralph Hartley

Considering all possible multi-level and multi-phase encoding techniques, the theorem gives that the theoretical maximum rate of clean (or arbitrarily low bit error rate) data C with a given average signal power that can be sent through an analog communication channel subject to additive, white, Gaussian-distribution noise interference is: where C is the channel capacity in bits per second, net of error correction; BW is the bandwidth of the channel in hertz; and

Considering all possible multi-level and multi-phase encoding techniques, the theorem gives that the theoretical maximum rate of clean (or arbitrarily low bit error rate) data C with a given average signal power that can be sent through an analog communication channel subject to additive, white, Gaussian-distribution noise interference is: where C is the channel capacity in bits per second, net of error correction; BW is the bandwidth of the channel in hertz; ...

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Shannon–Hartley theorem, Shannon–Hartley theorem - Introduction, Shannon–Hartley theorem - Noisy channel coding theorem, Shannon–Hartley theorem - Shannon-Hartley theorem, Shannon–Hartley theorem - Capacity of the additive white Gaussian noise channel, Shannon–Hartley theorem - Examples

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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 ...

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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

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1970 - January. January 6 - Gabrielle Reece, American volleyball player and model January 13 - Keith Coogan, American actor January 13 - Marco Pantani, Italian cyclist (d. 2004) January 15 - Shane McMahon, American Wrestler January 17 - Jeremy Roenick, American hockey player January 17 - Gennady Tartakovsky Russian animator January 20 - Skeet Ulrich, American actor January 22 - Alex Ross, American comic artist January 29 - Heather Graha ...

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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

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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 ...

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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 - Mathematical preliminaries

1970 - January. January 4 - Jean-Etienne Valluy, French general (b. 1899) January 5 - Max Born, German physicist, Nobel Prize laureate (b. 1882) January 10 - Pavel Belyayev, cosmonaut (b. 1925) January 18 - David O. McKay, president of The Church of Jesus Christ of Latter-day Saints (b. 1873) January 25 - Jane Bathori, French mezzo-soprano (b. 1877) January 27 - Rita Angus, New Zealand painter (b. 1908) January 29 - Basil Liddell Hart, British military h ...

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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

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The work done by Bell Labs was broadly divided into three categories: research, systems engineering, and development. Research created the theoretical underpinnings for telecommunications. It covered subjects such as mathematics, physics, material sciences, behavioral sciences, and computer programming theory. Systems engineering concerned itself with conceiving the highly complex systems that make up the telecommunication networks. Development, by far the largest of Bell Labs' activities designed the specific systems -- both hardware and software -- needed to build the Bell Sy ...

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Bell Labs, Bell Labs - History, Bell Labs - Basis, Bell Labs - Calculators built by Bell Labs

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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 ...

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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

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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 | +-------+ | V +-----------+ Y +-------+ X +--------+ |Transmitter|-------->|Channel|-------->|Receiver ...

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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 - Channel Capacity

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 ...

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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 - Fundamental Theorem

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 ...

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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 - Source Theory

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 ...

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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 - Related Concepts