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Typical set

In information theory, the typical set is a set of sequences whose probability is approximately 2 − n H ( X ) {\displaystyle 2^{-nH(X)}} , where H ( X ) {\displaystyle H(X)} is the entropy of the source and n {\displaystyle n} is the sequence length. That this set has total probability close to one is a consequence of the asymptotic equipartition…

Art, (Weakly) typical sequences (weak typicality, entropy typicality) & Strongly typical sequences (strong typicality, letter typicality)

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(Weakly) typical sequences (weak typicality, entropy typicality)

Independent identically-distributed random variableLogarithmCardinalityStochastic processDegree of freedom
9 related topics

Strongly typical sequences (strong typicality, letter typicality)

Joint distributionMemoryless
2 related topics

Overview

Information theoryProbabilityAsymptotic equipartition propertyLaw of large numbersStationary ergodic processes
8 related topics

Topics to explore

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Overview

(Weakly) typical sequences (weak typicality, entropy typicality)

Strongly typical sequences (strong typicality, letter typicality)

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Map overview Semantic statistics

Typical set

Nodes23
Edges22
Triples23
Avg. degree1.91
Density0.086957
Components1

How this topic connects Entity context

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Typical set

Top relations

related to Example · 6
Typical set → Bernoulli, Counter-intuitively, For, Here, In, So
related to Properties · 6
Typical set → An, Aε, Formally, If, Pr, The
related to Typical set encoding · 4
Typical set → AEP, Asymptotically, In, Since
related to (Weakly) typical sequences (weak typicality, entropy typicality) · 3
Typical set → Aε, If, IID
related to Strongly typical sequences (strong typicality, letter typicality) · 2
Typical set → Aε, If
is a · 1
Typical set → set of sequences whose probability is approximately 2
related to Typical set decoding · 1
Typical set → In

Important terminology Word statistics

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Important terminology

typical set sequences displaystyle sequence probability entropy random information theory source defined large coding data aep jointly typicality channel independent

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Typical setis aset of sequences whose probability is approximately 20.90text
Typical setrelated to (Weakly) typical sequences (weak typicality, entropy typicality)If0.60section
Typical setrelated to (Weakly) typical sequences (weak typicality, entropy typicality)IID0.60section
Typical setrelated to (Weakly) typical sequences (weak typicality, entropy typicality)Aε0.60section
Typical setrelated to ExampleCounter-intuitively0.60section
Typical setrelated to ExampleFor0.60section
Typical setrelated to ExampleBernoulli0.60section
Typical setrelated to ExampleIn0.60section
Typical setrelated to ExampleHere0.60section
Typical setrelated to ExampleSo0.60section
Typical setrelated to PropertiesAn0.60section
Typical setrelated to PropertiesFormally0.60section

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