noisy-channel coding theorem
E624507
The noisy-channel coding theorem is a fundamental result in information theory that establishes the maximum rate at which information can be transmitted over a noisy communication channel with arbitrarily low error using appropriate encoding schemes.
All labels observed (7)
| Label | Occurrences |
|---|---|
| channel coding theorem | 2 |
| Gaussian channel coding theorem | 1 |
| Shannon capacity | 1 |
| Shannon coding theorem | 1 |
| Shannon’s channel coding theorem | 1 |
| Shannon’s noisy-channel coding theorem | 1 |
| noisy-channel coding theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6858987 — 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: noisy-channel coding theorem Context triple: [information theory, hasCoreConcept, noisy-channel 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.
-
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.
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.
-
D.
information theory
Information theory is a mathematical framework for quantifying information, communication, and data compression, foundational to modern digital communication and signal processing.
-
E.
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.
- 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: noisy-channel coding theorem Target entity description: The noisy-channel coding theorem is a fundamental result in information theory that establishes the maximum rate at which information can be transmitted over a noisy communication channel with arbitrarily low error using appropriate encoding schemes.
-
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.
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.
-
D.
information theory
Information theory is a mathematical framework for quantifying information, communication, and data compression, foundational to modern digital communication and signal processing.
-
E.
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.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
result in information theory
ⓘ
theorem ⓘ |
| alsoKnownAs |
Shannon coding theorem
ⓘ
linked to:
noisy-channel coding theorem
channel coding theorem ⓘ
linked to:
noisy-channel coding theorem
|
| appliesTo |
additive white Gaussian noise channels
ⓘ
discrete memoryless channels ⓘ |
| assumes |
discrete memoryless channel
ⓘ
probabilistic channel model ⓘ sufficiently long block length ⓘ |
| characterizes | maximum achievable reliable communication rate ⓘ |
| defines | channel capacity ⓘ |
| doesNotSpecify | explicit construction of optimal codes ⓘ |
| field | information theory ⓘ |
| formulatedBy |
Claude E. Shannon
ⓘ
linked to:
Claude Shannon
|
| foundationFor | modern digital communication theory ⓘ |
| hasConverse |
strong converse for channel coding
ⓘ
weak converse for channel coding ⓘ |
| hasVariant |
Gaussian channel coding theorem
ⓘ
linked to:
noisy-channel coding theorem
continuous-time version ⓘ |
| historicalSignificance | cornerstone of Shannon’s information theory ⓘ |
| implies |
existence of long block codes with low error probability
ⓘ
trade-off between rate and reliability ⓘ |
| influencedField |
coding theory
ⓘ
data compression theory ⓘ digital communications ⓘ network information theory ⓘ
linked to:
information theory
|
| inspired |
development of coding theory
ⓘ
development of error-correcting codes ⓘ |
| involvesQuantity |
channel transition probabilities
ⓘ
input distribution ⓘ mutual information between input and output ⓘ |
| mathematicallyExpresses | channel capacity as maximum mutual information over input distributions ⓘ |
| publishedIn | A Mathematical Theory of Communication ⓘ |
| relatesConcept |
coding rate
ⓘ
entropy ⓘ error probability ⓘ mutual information ⓘ |
| statesThat |
for any rate below channel capacity there exist codes with arbitrarily small error probability
ⓘ
reliable communication over a noisy channel is possible if and only if the transmission rate is less than channel capacity ⓘ |
| usedIn |
analysis of data transmission limits
ⓘ
design of communication systems ⓘ |
| usesConcept |
asymptotic equipartition property
ⓘ
random coding argument ⓘ 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: noisy-channel coding theorem Description of subject: The noisy-channel coding theorem is a fundamental result in information theory that establishes the maximum rate at which information can be transmitted over a noisy communication channel with arbitrarily low error using appropriate encoding schemes.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem
linked to: noisy-channel coding theorem