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Establishes the limits to possible data compression
Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is
Shannon's source coding theorem
Shannon's_source_coding_theorem
Theorem that tells the maximum rate at which information can be transmitted
coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's
Shannon–Hartley_theorem
Limit on data transfer rate
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise
Noisy-channel_coding_theorem
Alleged data encoding technique
compression which is mathematically impossible according to Shannon's source coding theorem.[citation needed] Sloot demonstrated the technology by recording
Sloot_Digital_Coding_System
Problem in information theory and communication
X and Y, Slepian–Wolf theorem includes theoretical bound for the lossless coding rate for distributed coding of the two sources as below: R X ≥ H ( X
Distributed_source_coding
Lossless data compression scheme
entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem
Entropy_coding
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Average uncertainty in variable's states
data source, and proved in his source coding theorem that the entropy represents an absolute mathematical limit on how well data from the source can be
Entropy_(information_theory)
American mathematician (1916–2001)
Shannon–Hartley theorem Shannon's expansion Shannon's source coding theorem Shannon-Weaver model of communication Whittaker–Shannon interpolation formula
Claude_Shannon
Data compression algorithms
compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is one of two related techniques for constructing a prefix code based on a
Shannon–Fano_coding
Topic in mathematics
other results) the source coding theorem for non-stationary source (with independent output symbols) and noisy-channel coding theorem for non-stationary
Asymptotic equipartition property
Asymptotic_equipartition_property
Form of entropy encoding used in data compression
on this compression is given by the entropy of the source, which Shannon's source coding theorem establishes as the minimum average number of bits per
Arithmetic_coding
Technique to compress data
can be left out of the formula above.) As a consequence of Shannon's source coding theorem, the entropy is a measure of the smallest codeword length that
Huffman_coding
compression which is mathematically impossible according to Shannon's source coding theorem. Contrary to his claims, the playback device he used was discovered
List_of_spurious_inventions
Time density of the average information in a stochastic process
In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the
Entropy_rate
Compact encoding of digital data
transmission, it is called source coding: encoding is done at the source of the data before it is stored or transmitted. Source coding should not be confused
Data_compression
Topics referred to by the same term
Shannon's law may refer to: Shannon's source coding theorem, which establishes the theoretical limits to lossless data compression Shannon–Hartley theorem
Shannon's_law
Slepian–Wolf theorem gives a theoretical bound for the lossless coding rate for distributed coding of the two sources. The bound for the lossless coding rates
Slepian–Wolf_coding
Information-theoretic measure
information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value x i {\displaystyle
Cross-entropy
Notion in information theory
limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy. It was formulated by Edwin Thompson Jaynes to
Limiting density of discrete points
Limiting_density_of_discrete_points
Shannon–Hartley theorem (information theory) Shannon's source coding theorem (information theory) Shannon's theorem (information theory) Ugly duckling theorem (computer
List_of_theorems
Scientific study of digital information
channel capacity. These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. In the latter
Information_theory
Type of set in information theory
properties of typical sequences, efficient coding schemes like Shannon's source coding theorem and channel coding theorem are developed, enabling near-optimal
Typical_set
Information-theoretical limit on transmission rate in a communication channel
over a communication channel. Following the terms of the noisy-channel coding theorem, the channel capacity of a given channel is the highest information
Channel_capacity
Measure of information in probability and information theory
2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. New York: Dover Publications. ISBN 0-486-41147-8
Joint_entropy
Information theory
1016/s0019-9958(78)90026-8. Dobrushin, R. L. (1959). "General formulation of Shannon's main theorem in information theory". Uspekhi Mat. Nauk. 14: 3–104. Cover, Thomas;
Conditional mutual information
Conditional_mutual_information
Topics referred to by the same term
with Shannon All pages with titles containing Shannon Shannon index, a biodiversity index Noisy-channel coding theorem, sometimes called Shannon Limit
Shannon
Study of the properties of codes and their fitness
There are four types of coding: Data compression (or source coding) Error control (or channel coding) Cryptographic coding Line coding Data compression attempts
Coding_theory
Theory about lossy data compression
bits/symbol of information from the source must reach the user. We also know from Shannon's channel coding theorem that if the source entropy is H bits/symbol,
Rate–distortion_theory
Measure of relative information in probability theory
variable X {\displaystyle X} is known. Here, information is measured in shannons, nats, or hartleys. The "entropy of Y {\displaystyle Y} conditioned on
Conditional_entropy
the information entropy and redundancy of a source, and its relevance through the source coding theorem; the mutual information, and the channel capacity
History_of_information_theory
Concept in information theory
absolutely continuous probability distributions which generalizes the Shannon entropy to continuous probability distributions. In terms of measure theory
Differential_entropy
Measure of dependence between two variables
specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing
Mutual_information
1948 scholarly article by Claude Shannon
of information entropy, redundancy and the source coding theorem, and introduced the term bit (which Shannon credited to John Tukey) as a unit of information
A Mathematical Theory of Communication
A_Mathematical_Theory_of_Communication
State-dependent measures that converge to the mutual information
equipartition property Rate–distortion theory Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem v t e
State-dependent_information
Scheme for controlling errors in data over noisy communication channels
telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors
Error_correction_code
Process of using data analysis for predicting population data from sample data
generating mechanism" does exist in reality, then according to Shannon's source coding theorem it provides the MDL description of the data, on average and
Statistical_inference
Subfield of information theory and computer science
theoretical computer science and cryptography Simplicity theory Shannon's source coding theorem – Establishes the limits to possible data compression Solomonoff's
Algorithmic information theory
Algorithmic_information_theory
Overview of computer engineering topics
Information theory Channel capacity Shannon–Hartley theorem Nyquist–Shannon sampling theorem Shannon's source coding theorem Zero-order hold Data compression
Computer engineering compendium
Computer_engineering_compendium
data compression, error correcting codes and related subjects. 1872 – Ludwig Boltzmann presents his H-theorem, and with it the formula Σpi log pi for
Timeline of information theory
Timeline_of_information_theory
Statistical distance measure
the prior distribution π {\displaystyle \pi } (see Holevo's theorem). Quantum Jensen–Shannon divergence for π = ( 1 2 , 1 2 ) {\displaystyle \pi =\left({\frac
Jensen–Shannon_divergence
Mathematical algorithm for eliminating variables from a system of linear inequalities
solution set. The second acceleration theorem detects minimal history sets: Theorem (Imbert's second acceleration theorem). If the inequality i {\displaystyle
Fourier–Motzkin_elimination
Mathematical statistics distance measure
information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value x i {\displaystyle
Kullback–Leibler_divergence
German mathematician
Ahlswede–Daykin inequality Ahlswede–Khachatrian_theorem Information-theoretic security Linear network coding Ahlswede, R; Ning Cai; Li, S.-Y.R; Yeung, R.W
Rudolf_Ahlswede
Maximum rate of a quantum channel
classical capacity theorem is proved in two parts: the direct coding theorem and the converse theorem. The direct coding theorem demonstrates that the
Entanglement-assisted classical capacity
Entanglement-assisted_classical_capacity
Reliable digital data delivery methods on unreliable channels
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control
Error detection and correction
Error_detection_and_correction
Digital representation of sampled analog signals
some equipment, but the benefits have been debated. The Nyquist–Shannon sampling theorem shows PCM devices can operate without introducing distortions within
Pulse-code_modulation
wrong. Noisy channel coding theorem See Deppe 2007 and Hill 1995. Berlekamp 1964. Deppe 2007. Berlekamp, Elwyn R. (1964). Block coding with noiseless feedback
Error-correcting codes with feedback
Error-correcting_codes_with_feedback
Israeli-American mathematician (born 1930)
Shapley on the Aumann–Shapley value. He is also known for Aumann's agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists
Robert_Aumann
Information held in the state of a quantum system
Claude Shannon. Shannon developed two fundamental theorems of information theory: noiseless channel coding theorem and noisy channel coding theorem. He also
Quantum_information
Technique used in signal processing and data compression
motion-compensated DCT or adaptive scene coding, in 1981. Motion-compensated DCT later became the standard coding technique for video compression from the
Discrete_cosine_transform
Improved efficiency encoding
Correcting Codes is about 1.53 dB higher than minimum SNR required by a Gaussian source(>30% more transmitter power) as given in the Shannon–Hartley theorem C
Shaping_codes
Power law growth of entropy of language or a stochastic process
There is a general result concerning stationary processes, called the theorem about facts and words, which states that the mutual information between
Hilberg's_hypothesis
strings Shannon–Fano coding Shannon–Fano–Elias coding: precursor to arithmetic encoding Entropy coding with known entropy characteristics Golomb coding: form
List_of_algorithms
American mathematician (1923–2013)
mathematician and coding theorist, a longtime researcher at Bell Laboratories. His accomplishments include the Gilbert–Varshamov bound in coding theory, the
Edgar_Gilbert
Israeli computer scientist
Breiman (1957, 1960). Shannon Theorems are based on AEP. Shannon provided in 1959 the first source-compression coding theorems. But neither he nor his
Ilan_Sadeh
Computer technology
"Burrows-Wheeler Transform and combination of Move-to-Front coding and Run Length Encoding for lossless audio coding". 2014 9th International Conference on Computer
Silence_compression
1956 computer program written by Allen Newell, Herbert A. Simon and Cliff Shaw
artificial intelligence program". Logic Theorist proved 38 of the first 52 theorems in chapter two of Whitehead and Bertrand Russell's Principia Mathematica
Logic_Theorist
Hungarian and American mathematician and physicist (1903–1957)
for the Radon–Nikodym theorem. His lecture notes on measure theory at the Institute for Advanced Study were an important source for knowledge on the topic
John_von_Neumann
Facts provided or learned about something or someone
fundamental topics of information theory include source coding/data compression (e.g. for ZIP files), and channel coding/error detection and correction (e.g. for
Information
Formal information theory restatement of Occam's Razor
(2018). Coding Ockham's Razor. Springer. doi:10.1007/978-3-319-76433-7. ISBN 978-3319764320. S2CID 19136282., on implementing MML, and source-code. Related
Minimum_message_length
Subfield of set theory
This fact—that all closed games are determined—is called the Gale–Stewart theorem. Note that by symmetry, all open games are determined as well. (A game
Determinacy
Type of stable matching problem
provides a free, web-based implementation of the algorithm, including source code for the website and solver written in JavaScript. MATLAB: The algorithm
Stable_roommates_problem
Error-correcting codes
In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon
Reed–Solomon_error_correction
Type of error-correcting code using convolution
data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant
Convolutional_code
Overuse of a shared resource
including, for example: Source code and software documentation in software projects that can get "polluted" with messy code or inaccurate information
Tragedy_of_the_commons
Device or program that encodes/decodes audio data in some bitstream format
algorithms are based on modified discrete cosine transform (MDCT) coding and linear predictive coding (LPC). In hardware, audio codec refers to a single device
Audio_codec
Standard example in game theory
Abilene paradox Centipede game Collective action problem Externality Folk theorem (game theory) Free-rider problem Gift-exchange game Hobbesian trap Innocent
Prisoner's_dilemma
Study of computation
Claude Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data. Coding theory
Computer_science
Technology that records, stores, and reproduces sound
predictive coding (APC), a perceptual coding algorithm that exploited the masking properties of the human ear, followed in the early 1980s with the code-excited
Digital_audio
Function in discrete mathematics
the star denotes complex conjugation. The Plancherel theorem is a special case of Parseval's theorem and states: ∑ n = 0 N − 1 | x n | 2 = 1 N ∑ k = 0 N
Discrete_Fourier_transform
Mathematical models of strategic interactions
von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard
Game_theory
Search heuristic for combinatorial games
192. Bruce Moreland's Programming Topics: Aspiration Windows Stockfish source code - direct aspiration window mention Computer Chess Programming Theory:
Aspiration_window
Sequence of operations for a task
computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code: Algorithm LargestNumber Input: A list of numbers
Algorithm
Information rate that can be transmitted over a given bandwidth
channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the Shannon–Hartley theorem. Example 7: If the SNR is 1, corresponding
Spectral_efficiency
Subfield of computer science and mathematics
other fields. Important sub-fields of information theory are source coding, channel coding, algorithmic complexity theory, algorithmic information theory
Theoretical_computer_science
Game theory solution
Algorithmic game theory (note an important typo) [1] Iskander Karibzhanov. MATLAB code to plot the set of correlated equilibria in a two player normal form game
Correlated_equilibrium
Part of the history of physics
conservation of mechanical energy. Over the next three decades, Carnot's theorem was taken as a statement that in any machine the accelerations and shocks
History_of_entropy
Cochran's Q test Cochran's theorem Cochran–Armitage test for trend Cochran–Mantel–Haenszel statistics Cochrane–Orcutt estimation Coding (social sciences) Coefficient
List_of_statistics_articles
Algebraic manipulation of "true" and "false"
the theorem proved by the proof. Every nonempty initial segment of a proof is itself a proof, whence every proposition in a proof is itself a theorem. An
Boolean_algebra
Representation of a signal as a rectangular wave with varying duty cycle
waveform is two-level or three-level. For comparison, the Nyquist–Shannon sampling theorem can be summarized as: If you have a signal that is bandlimited
Pulse-width_modulation
Intelligence of machines
generative models to generate text, images, videos, audio, software code (vibe coding) or other forms of data. These models learn the underlying patterns
Artificial_intelligence
Chatbot developed by DeepSeek
praised for its open weights and infrastructure code, energy efficiency and contributions to open-source artificial intelligence. On 10 January 2025, DeepSeek
DeepSeek_(chatbot)
Hungarian mathematician (1941–2019)
conjecture of Marton". arXiv:2311.05762 [math.NT]. Marton, K. (1979). "A coding theorem for the discrete memoryless broadcast channel". IEEE Transactions on
Katalin_Marton
Cryptographic attack
vulnerability having to do with the use of RSA with Chinese remainder theorem optimizations. The actual network distance was small in their experiments
Timing_attack
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems
Mathematics
Min-Hsiu; Wilde, Mark M. (2013). "Quantum rate distortion, reverse Shannon theorems, and source-channel separation". IEEE Transactions on Information Theory
Mark_Wilde
Analysis of datasets using techniques from topology
first classification theorem for persistent homology appeared in 1994 via Barannikov's canonical forms. The classification theorem interpreting persistence
Topological_data_analysis
Methodic assignment of colors to elements of a graph
introduced by Shannon. The conjecture remained unresolved for 40 years, until it was established as the celebrated strong perfect graph theorem by Chudnovsky
Graph_coloring
Canadian computer scientist and mathematician
Princeton to work under John von Neumann. There he developed the first theorems of core (game theory) in his PhD thesis. Gillies moved to England for two
Donald_B._Gillies
Encryption technique
So, if key material begins with XMCKL and the message is hello, then the coding would be done as follows: h e l l o message 7 (h) 4 (e) 11 (l) 11 (l) 14
One-time_pad
Codes with the property that slight modifications of messages are difficult to make
inefficient) coding scheme which is non-malleable w.r.t. F. Moreover, for a fixed "small enough" function family F {\displaystyle F} , a random coding scheme
Non-malleable_code
True when either but not both inputs are true
Converse Theorems: The Elements of Symbolic Logic. Translated by Boddington, T. Oxford, London, New York and Paris: Pergamon Press. Shannon, C. E. (1938)
Exclusive_or
and contains "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians
Timeline_of_mathematics
Device that converts a digital signal into an analog signal
that a signal's bandwidth meets the requirements of the Nyquist–Shannon sampling theorem (i.e., a baseband signal with bandwidth less than the Nyquist frequency)
Digital-to-analog_converter
Overview of democracy measures
assesses democratic performance using different types of sources: expert surveys, standards-based coding by research groups and analysts, observational data
Democracy_indices
Diplomatic policy of concessions
London), the House of Lords, and media such as the BBC and The Times.[better source needed] As alarm grew about the rise of fascism in Europe, Chamberlain resorted
Appeasement
from the original (PDF) on 2006-05-25. Ling, San; Xing, Chaoping (2004). Coding Theory: a First Course. Cambridge: Cambridge University Press. ISBN 978-0-521-82191-9
List of pioneers in computer science
List_of_pioneers_in_computer_science
Norton theorem Norton's theorem Notch filter NTSC Nuclear power Numerical control Nuvistor Nyquist frequency Nyquist stability criterion Nyquist–Shannon sampling
Index of electrical engineering articles
Index_of_electrical_engineering_articles
characteristic 1946 – Cox's theorem derives the axioms of probability from simple logical assumptions, 1948 – Claude Shannon's Mathematical Theory of Communication
Timeline of probability and statistics
Timeline_of_probability_and_statistics
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
Girl/Female
Christian & English(British/American/Australian)
Wise
Surname or Lastname
English
English : patronymic from Middle English sour ‘sour’, ‘tart’, used as a nickname for a sour-tempered, sharp-tongued person.
Surname or Lastname
Danish
Danish : probably a habitational name from Kolding. This was originally the name of a river, from kaldr ‘cold’ + a derivational suffix -ung, hence ‘the cold river’.English : perhaps a spelling variant of Golding.
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Female
Scottish
Scottish feminine form of English Rodney, RODINA means "Hroda's fen/island."
Surname or Lastname
English
English : ethnic name for someone from Prussia, Middle English Spruce, Sprewse. Compare German Preuss. The adjective spruce ‘neat’, ‘dapper’, which probably derives from an attributive use of the name of the country, is not recorded until the late 16th century, too late for it to be a likely source of the surname. The tree (earlier called spruce fir) has likewise only come to be known by this name in the last couple of centuries.
Male
English
Variant spelling of English unisex Shannon, SHANNEN means "old river" or "river of wisdom."
Boy/Male
Irish American
Little old wise one. Surname and river name.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : from a double diminutive of Codd.English (Yorkshire) : from Old French ceur de lion ‘lion heart’, applied as a nickname for a brave man, or ironically for an exceptionally timorous one.
Boy/Male
American, Australian, British, Celtic, English, Irish
Form of Shannon; Wise One; Young Wolf
Female
English
Variant spelling of English Colleen, COLINE means "girl."
Girl/Female
Arabic, Indian, Muslim
Caring; Loving
Girl/Female
American, Australian, Chinese, Gaelic, Irish
Wise One; Old; Ancient; River Name; Form of Shannon
Boy/Male
American, Gaelic, Hindu, Indian
Little Old Wise One; Old; Ancient; Old River; River of Wisdom
Surname or Lastname
English
English : variant of Colling.
Girl/Female
American, British, Dutch, English, French, Gaelic, Irish
Small and Wise; Old; Ancient; Wise One; River Name; Old River; River of Wisdom
Girl/Female
Irish American
Old. Surname and river name.
Girl/Female
Arabic, Muslim
Caring; Loving
Surname or Lastname
English
English : variant of Gooding.German (Göding) : variant of Godding.
Female
French
Variant spelling of French Corinne, CORINE means "maiden."
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Punjabi, Sanskrit, Sikh, Telugu
Right; Truth; Liberty; Freedom; Own Country
Boy/Male
Indian, Sanskrit
Shining Forth; Radiant
Girl/Female
Hindu, Indian
Stream of Water; Life
Girl/Female
Hindu, Indian, Marathi
Arts of Eternal Knowledge
Female
English
English name derived from the name of a district in London, CHELSEA means "landing place" or "landing port."
Boy/Male
Hindu
Supreme spirit, Big soul
Boy/Male
Hindu, Indian
Psychic; Intelligent
Girl/Female
French Hebrew
Bitter.
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Mythological, Telugu
Wife of Kalketu
Girl/Female
Muslim
Favor, Grace (1)
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
SHANNONS SOURCE-CODING-THEOREM
n.
The act or process of one who, or that which, bores; as, the boring of cannon; the boring of piles and ship timbers by certain marine mollusks.
n.
Source. See Source.
v. t.
To pounce upon.
a.
Approaching; of the future, especially the near future; the next; as, the coming week or year; the coming exhibition.
n. & v.
See Souse.
v. t.
A roll of wool or other fiber as it comes from the carding machine.
n.
The highest or covering course of masonry in a wall, often with sloping edges to carry off water; -- sometimes called capping.
n.
See 1st Souse.
v. t.
To wet copiously, as by opening a sluice; as, to sluice meadows.
n.
Approach; advent; manifestation; as, the coming of the train.
n.
Alt. of Codling
v. i.
To have origin or source; to rise; to spring.
n.
A hole made by boring.
a.
Ever closing.
a.
Boding evil; inauspicious; ill-omened.
n.
The chips or fragments made by boring.
n.
Hence, an opening or channel through which anything flows; a source of supply.
n.
Any boxlike inclosure or recess; a casing.
v. t.
To sprinkle or rub with pounce; as, to pounce paper, or a pattern.
v. t. & i.
See Souse.