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124 relations: A Mathematical Theory of Communication, Adversary (cryptography), Alphabet (formal languages), Analog signal, Analog signal processing, Analogue electronics, Authentication, Automated teller machine, Automatic repeat request, Baseband, BCH code, Bell Labs, Binary Golay code, Bipolar encoding, Brain, Cambridge University Press, Claude Shannon, Code, Code word, Code-division multiple access, Coding gain, Communication protocol, Communications system, Computational hardness assumption, Computer, Computer science, Confidentiality, Convolution, Covering code, Cross-interleaved Reed–Solomon coding, Cryptography, Cyclic code, Data compression, Data integrity, Data storage, Data transmission, David J. C. MacKay, Decoding methods, Digital data, Digital signal, Dirty paper coding, Distance, E-commerce, Electrical engineering, Elwyn Berlekamp, Encryption, Entropy (information theory), Entropy encoding, Error correction code, Error detection and correction, ..., Fading, Fax, Folded Reed–Solomon code, Goppa code, Group testing, Hamming bound, Hamming code, Hamming distance, Hamming weight, Information, Information security, Information theory, Information-theoretic security, Injective function, Integer factorization, Internet Engineering Task Force, Johnson–Nyquist noise, Joint source and channel coding, Lee distance, Line code, Linear time-invariant theory, Linearity, Linguistics, List of algebraic coding theory topics, Low-density parity-check code, Manchester code, Mathematics, MIMO, NASA Deep Space Network, Neural coding, Neural network, Neuron, Neuroscience, Non-repudiation, Non-return-to-zero, Nonsense, Norbert Wiener, One-time pad, Parity bit, Password, Phase (waves), Polynomial code, Random variable, Reed–Muller code, Reed–Solomon error correction, Regular number, Repetition code, Richard Hamming, Robert Dorfman, Run-length encoding, Secure communication, Shaping codes, Space–time code, Spatial multiplexing, Sphere packing, Stimulus (physiology), Synchronization, Synchronous Data Link Control, Syphilis, Timeline of information theory, Transmission (telecommunications), Transmission Control Protocol, Turbo code, Turing Award, Unipolar encoding, United States Army Air Forces, Vera Pless, Viterbi algorithm, Waveform, Wide area network, Window function, World War II, X.25, Zip (file format). Expand index (74 more) »
A Mathematical Theory of Communication
"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in Bell System Technical Journal in 1948.
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Adversary (cryptography)
In cryptography, an adversary (rarely opponent, enemy) is a malicious entity whose aim is to prevent the users of the cryptosystem from achieving their goal (primarily privacy, integrity, and availability of data).
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Alphabet (formal languages)
In formal language theory, a string is defined as a finite sequence of members of an underlying base set; this set is called the alphabet of a string or collection of strings.
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Analog signal
An analog signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal.
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Analog signal processing
Analog signal processing is a type of signal processing conducted on continuous analog signals by some analog means (as opposed to the discrete Digital Signal Processing where the signal processing is carried out by a digital process).
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Analogue electronics
Analogue electronics (also spelled analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels.
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Authentication
Authentication (from authentikos, "real, genuine", from αὐθέντης authentes, "author") is the act of confirming the truth of an attribute of a single piece of data claimed true by an entity.
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Automated teller machine
An automated teller machine (ATM) is an electronic telecommunications device that enables customers of financial institutions to perform financial transactions, such as cash withdrawals, deposits, transfer funds, or obtaining account information, at any time and without the need for direct interaction with bank staff.
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Automatic repeat request
Automatic repeat request (ARQ), also known as automatic repeat query, is an error-control method for data transmission that uses acknowledgements (messages sent by the receiver indicating that it has correctly received a data frame or packet) and timeouts (specified periods of time allowed to elapse before an acknowledgment is to be received) to achieve reliable data transmission over an unreliable service.
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Baseband
Baseband is a signal that has a very narrow and near-zero frequency range, i.e. a spectral magnitude that is nonzero only for frequencies in the vicinity of the origin (termed f.
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BCH code
In coding theory, the BCH codes or Bose–Chaudhuri–Hocquenghem codes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called Galois field).
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Bell Labs
Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.
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Binary Golay code
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications.
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Bipolar encoding
In telecommunication, bipolar encoding is a type of return-to-zero (RZ) line code, where two nonzero values are used, so that the three values are +, −, and zero.
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Brain
The brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".
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Code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form or representation, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium.
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Code word
In communication, a code word is an element of a standardized code or protocol.
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Code-division multiple access
Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies.
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Coding gain
In coding theory and related engineering problems, coding gain is the measure in the difference between the signal-to-noise ratio (SNR) levels between the uncoded system and coded system required to reach the same bit error rate (BER) levels when used with the error correcting code (ECC).
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Communication protocol
In telecommunication, a communication protocol is a system of rules that allow two or more entities of a communications system to transmit information via any kind of variation of a physical quantity.
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Communications system
In telecommunication, a communications system is a collection of individual communications networks, transmission systems, relay stations, tributary stations, and data terminal equipment (DTE) usually capable of interconnection and interoperation to form an integrated whole.
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Computational hardness assumption
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where efficiently typically means "in polynomial time").
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Confidentiality
Confidentiality involves a set of rules or a promise usually executed through confidentiality agreements that limits access or places restrictions on certain types of information.
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Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
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Covering code
In coding theory, a covering code is a set of elements (called codewords) in a space, with the property that every element of the space is within a fixed distance of some codeword.
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Cross-interleaved Reed–Solomon coding
In the compact disc system, cross-interleaved Reed–Solomon code (CIRC) provides error detection and error correction.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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Cyclic code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code.
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Data compression
In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.
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Data integrity
Data integrity is the maintenance of, and the assurance of the accuracy and consistency of, data over its entire life-cycle, and is a critical aspect to the design, implementation and usage of any system which stores, processes, or retrieves data.
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Data storage
Data storage is the recording (storing) of information (data) in a storage medium.
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Data transmission
Data transmission (also data communication or digital communications) is the transfer of data (a digital bitstream or a digitized analog signal) over a point-to-point or point-to-multipoint communication channel.
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David J. C. MacKay
Sir David John Cameron MacKay (22 April 1967 – 14 April 2016) was a British physicist, mathematician, and academic.
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Decoding methods
In coding theory, decoding is the process of translating received messages into codewords of a given code.
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Digital data
Digital data, in information theory and information systems, is the discrete, discontinuous representation of information or works.
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Digital signal
A digital signal is a signal that is being used to represent data as a sequence of discrete values; at any given time it can only take on one of a finite number of values.
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Dirty paper coding
In telecommunications, dirty paper coding (DPC) or Costa precoding is a technique for efficient transmission of digital data through a channel subjected to some interference known to the transmitter.
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Distance
Distance is a numerical measurement of how far apart objects are.
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E-commerce
E-commerce is the activity of buying or selling of products on online services or over the Internet.
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Electrical engineering
Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism.
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Elwyn Berlekamp
Elwyn Ralph Berlekamp (born September 6, 1940) is an American mathematician.
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Encryption
In cryptography, encryption is the process of encoding a message or information in such a way that only authorized parties can access it and those who are not authorized cannot.
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Entropy (information theory)
Information entropy is the average rate at which information is produced by a stochastic source of data.
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Entropy encoding
In information theory an entropy encoding is a lossless data compression scheme that is independent of the specific characteristics of the medium.
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Error correction code
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels.
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Error detection and correction
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of digital data over unreliable communication channels.
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Fading
In wireless communications, fading is variation or the attenuation of a signal with various variables.
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Fax
Fax (short for facsimile), sometimes called telecopying or telefax (the latter short for telefacsimile), is the telephonic transmission of scanned printed material (both text and images), normally to a telephone number connected to a printer or other output device.
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Folded Reed–Solomon code
In coding theory, folded Reed–Solomon codes are like Reed–Solomon codes, which are obtained by mapping m Reed–Solomon codewords over a larger alphabet by careful bundling of codeword symbols.
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Goppa code
In mathematics, an algebraic geometric code (AG-code), otherwise known as a Goppa code, is a general type of linear code constructed by using an algebraic curve X over a finite field \mathbb_q.
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Group testing
In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying certain objects into tests on groups of items, rather than on individual ones.
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Hamming bound
In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words.
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Hamming code
In telecommunication, Hamming codes are a family of linear error-correcting codes.
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Hamming distance
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
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Hamming weight
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used.
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Information
Information is any entity or form that provides the answer to a question of some kind or resolves uncertainty.
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Information security
Information security, sometimes shortened to InfoSec, is the practice of preventing unauthorized access, use, disclosure, disruption, modification, inspection, recording or destruction of information.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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Information-theoretic security
Information-theoretic security is a cryptosystem whose security derives purely from information theory.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.
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Internet Engineering Task Force
The Internet Engineering Task Force (IETF) develops and promotes voluntary Internet standards, in particular the standards that comprise the Internet protocol suite (TCP/IP).
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Johnson–Nyquist noise
Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage.
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Joint source and channel coding
In information theory, joint source–channel coding is the encoding of a redundant information source for transmission over a noisy channel, and the corresponding decoding, using a single code instead of the more conventional steps of source coding followed by channel coding.
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Lee distance
In coding theory, the Lee distance is a distance between two strings x_1 x_2 \dots x_n and y_1 y_2 \dots y_n of equal length n over the q-ary alphabet of size q ≥ 2.
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Line code
Some signals are more prone to error than others when conveyed over a communication channel as the physics of the communication or storage medium constrains the repertoire of signals that can be used reliably.
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Linear time-invariant theory
Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Linguistics
Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.
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List of algebraic coding theory topics
This is a list of algebraic coding theory topics.
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Low-density parity-check code
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel.
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Manchester code
In telecommunication and data storage, Manchester code (also known as phase encoding, or PE) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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MIMO
In radio, multiple-input and multiple-output, or MIMO (pronounced or), is a method for multiplying the capacity of a radio link using multiple transmit and receive antennas to exploit multipath propagation.
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NASA Deep Space Network
The NASA Deep Space Network (DSN) is a worldwide network of US spacecraft communication facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary spacecraft missions.
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Neural coding
Neural coding is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity of the neurons in the ensemble.
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Neural network
The term neural network was traditionally used to refer to a network or circuit of neurons.
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Neuron
A neuron, also known as a neurone (British spelling) and nerve cell, is an electrically excitable cell that receives, processes, and transmits information through electrical and chemical signals.
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Neuroscience
Neuroscience (or neurobiology) is the scientific study of the nervous system.
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Non-repudiation
Non-repudiation refers to a state of affairs where the author of a statement will not be able to successfully challenge the authorship of the statement or validity of an associated contract.
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Non-return-to-zero
In telecommunication, a non-return-to-zero (NRZ) line code is a binary code in which ones are represented by one significant condition, usually a positive voltage, while zeros are represented by some other significant condition, usually a negative voltage, with no other neutral or rest condition.
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Nonsense
Nonsense is a communication, via speech, writing, or any other symbolic system, that lacks any coherent meaning.
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Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher.
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One-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a one-time pre-shared key the same size as, or longer than, the message being sent.
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Parity bit
A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd.
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Password
A password is a word or string of characters used for user authentication to prove identity or access approval to gain access to a resource (example: an access code is a type of password), which is to be kept secret from those not allowed access.
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Phase (waves)
Phase is the position of a point in time (an instant) on a waveform cycle.
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Polynomial code
In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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Reed–Muller code
Reed–Muller codes are a family of linear error-correcting codes used in communications.
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Reed–Solomon error correction
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.
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Regular number
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently powers of 30).
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Repetition code
In coding theory, the repetition code is one of the most basic error-correcting codes.
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Richard Hamming
Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications.
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Robert Dorfman
Robert Dorfman (27 October 1916 – 24 June 2002) was emeritus professor of political economy at Harvard University.
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Run-length encoding
Run-length encoding (RLE) is a very simple form of lossless data compression in which runs of data (that is, sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original run.
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Secure communication
Secure communication is when two entities are communicating and do not want a third party to listen in.
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Shaping codes
In digital communications shaping codes are a method of encoding that changes the distribution of signals to improve efficiency.
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Space–time code
A space–time code (STC) is a method employed to improve the reliability of data transmission in wireless communication systems using multiple transmit antennas.
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Spatial multiplexing
Spatial multiplexing (often abbreviated SM or SMX) is a transmission technique in MIMO wireless communication, Fibre-optic communication and other communications technologies to transmit independent and separately encoded data signals, known as "streams".
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Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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Stimulus (physiology)
In physiology, a stimulus (plural stimuli) is a detectable change in the internal or external environment.
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Synchronization
Synchronization is the coordination of events to operate a system in unison.
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Synchronous Data Link Control
Synchronous Data Link Control (SDLC) is a computer communications protocol.
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Syphilis
Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum subspecies pallidum.
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Timeline of information theory
A timeline of events related to information theory, quantum information theory and statistical physics, data compression, error correcting codes and related subjects.
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Transmission (telecommunications)
In telecommunications, transmission (abbreviations: TX, Xmit) is the process of sending and propagating an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless.
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Transmission Control Protocol
The Transmission Control Protocol (TCP) is one of the main protocols of the Internet protocol suite.
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Turbo code
In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.
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Turing Award
The ACM A.M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) to an individual selected for contributions "of lasting and major technical importance to the computer field".
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Unipolar encoding
Unipolar encoding is a line code.
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United States Army Air Forces
The United States Army Air Forces (USAAF or AAF), informally known as the Air Force, was the aerial warfare service of the United States of America during and immediately after World War II (1939/41–1945), successor to the previous United States Army Air Corps and the direct predecessor of the United States Air Force of today, one of the five uniformed military services.
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Vera Pless
Vera Pless (née Stepen, born March 5, 1931) is an American mathematician specializing in combinatorics and coding theory.
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Viterbi algorithm
The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models.
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Waveform
A waveform is the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.
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Wide area network
A wide area network (WAN) is a telecommunications network or computer network that extends over a large geographical distance/place.
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Window function
In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.
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World War II
World War II (often abbreviated to WWII or WW2), also known as the Second World War, was a global war that lasted from 1939 to 1945, although conflicts reflecting the ideological clash between what would become the Allied and Axis blocs began earlier.
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X.25
X.25 is an ITU-T standard protocol suite for packet switched wide area network (WAN) communication.
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Zip (file format)
ZIP is an archive file format that supports lossless data compression.
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Algebraic Coding Theory, Algebraic coding theory, Analog coding, Analog encryption, Channel code, Code theory, Coding Theory, Frequency coding theory.
References
[1] https://en.wikipedia.org/wiki/Coding_theory
