source coding theorem
E624506
The source coding theorem is a fundamental result in information theory that establishes the minimum average number of bits needed to losslessly encode symbols from a given information source, linking this limit to the source’s entropy.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Shannon source coding theorem | 2 |
| noiseless coding theorem | 1 |
| source coding theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6858986 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: source coding theorem Context triple: [information theory, hasCoreConcept, source coding theorem]
-
A.
Coding and Information Theory
"Coding and Information Theory" is a foundational textbook by Richard W. Hamming that introduces the mathematical principles underlying error-correcting codes and the transmission of information.
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B.
Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
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C.
Mathematical Foundations of Information Theory
Mathematical Foundations of Information Theory is a seminal monograph by Aleksandr Khinchin that rigorously develops the probabilistic and mathematical basis of Shannon’s information theory.
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D.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
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E.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: source coding theorem Target entity description: The source coding theorem is a fundamental result in information theory that establishes the minimum average number of bits needed to losslessly encode symbols from a given information source, linking this limit to the source’s entropy.
-
A.
Coding and Information Theory
"Coding and Information Theory" is a foundational textbook by Richard W. Hamming that introduces the mathematical principles underlying error-correcting codes and the transmission of information.
-
B.
Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
-
C.
Mathematical Foundations of Information Theory
Mathematical Foundations of Information Theory is a seminal monograph by Aleksandr Khinchin that rigorously develops the probabilistic and mathematical basis of Shannon’s information theory.
-
D.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
-
E.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf | theorem in information theory ⓘ |
| alsoKnownAs |
Shannon source coding theorem
ⓘ
linked to:
source coding theorem
noiseless coding theorem ⓘ
linked to:
source coding theorem
|
| appliesTo |
discrete memoryless sources
ⓘ
stationary ergodic sources ⓘ |
| assumes |
large block length coding
ⓘ
probabilistic model of the source ⓘ |
| category | fundamental theorem of information theory ⓘ |
| concerns | noiseless communication ⓘ |
| contrastsWith | channel coding theorem ⓘ |
| field | information theory ⓘ |
| formulatedBy |
Claude E. Shannon
ⓘ
linked to:
Claude Shannon
|
| goal | minimize average number of bits per symbol for lossless representation ⓘ |
| guarantees | existence of asymptotically optimal codes ⓘ |
| hasApplication |
coding for storage systems
ⓘ
entropy coding in multimedia standards ⓘ file compression ⓘ |
| hasConsequence |
Huffman coding is optimal among prefix codes for a given source
ⓘ
no lossless code can have average rate below the source entropy ⓘ universal codes aim to approach the entropy without full source knowledge ⓘ |
| implies | entropy is the fundamental limit of lossless compression ⓘ |
| influences |
design of practical compression algorithms
ⓘ
entropy coding methods ⓘ rate–distortion theory ⓘ |
| isPartOf |
Shannon’s information theory
ⓘ
linked to:
A Mathematical Theory of Communication
|
| mathematicalForm |
L̄ ≥ H(X) for any uniquely decodable code
ⓘ
for every ε > 0 there exists a code with L̄ < H(X) + ε ⓘ |
| publishedIn | A Mathematical Theory of Communication ⓘ |
| relatesConcept |
average codeword length
ⓘ
data compression ⓘ entropy ⓘ lossless compression ⓘ optimal coding ⓘ prefix codes ⓘ |
| requires |
prefix-free or instantaneous codes for practical realization
ⓘ
uniquely decodable codes ⓘ |
| statesThat |
for any uniquely decodable code the average codeword length is at least the source entropy
ⓘ
the minimum achievable average codeword length per source symbol is lower bounded by the entropy of the source ⓘ there exist codes whose average codeword length is arbitrarily close to the source entropy ⓘ |
| upperBoundGivenBy | H(X)+1 for optimal prefix codes of a discrete memoryless source ⓘ |
| usesConcept |
Kraft–McMillan inequality
ⓘ
law of large numbers ⓘ typical sequences ⓘ |
| yearProposed | 1948 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: source coding theorem Description of subject: The source coding theorem is a fundamental result in information theory that establishes the minimum average number of bits needed to losslessly encode symbols from a given information source, linking this limit to the source’s entropy.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: source coding theorem
linked to: source coding theorem
linked to: source coding theorem