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Area Digital technology – Fundamental concepts / Information theory

IEV ref171-07-18

Symbol
R

en
redundancy, <in information theory>
amount by which the decision content H0 exceeds the entropy H

R = H0 − H

EXAMPLE Let { a,b,c } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaomaacmaakeaajugibiaadggacaGGSaGaamOyaiaacYcacaWGJbaa kiaawUhacaGL9baaaaa@43FE@ be a set of three events and let p(a)=0,5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadggacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaiwdaaaa@43D9@ , p(b)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadkgacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4496@ and p(c)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadogacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4497@ be the probabilities of their occurrences. The redundancy of this set is: R=1,585 Sh1,50 Sh =0,085 ShMathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaqaaaaaaaaaWdbiaadkfacqGH9aqpcaaIXaGaaiilaiaaiwdacaaI 4aGaaeiiaiaabofacaqGObGaeyOeI0IaaGymaiaacYcacaaI1aGaaG imaiaabccacaqGtbGaaeiAaiaabccacqGH9aqpcaaIWaGaaiilaiaa icdacaaI4aGaaeiiaiaabofacaqGObaaaa@517B@ .

Note 1 to entry: Usually, messages can be represented with fewer characters by using suitable codes; the redundancy can be considered as a measure of the decrease of the average length of the messages accomplished by appropriate coding.


[SOURCE: IEC 80000-13:2008, 13-28, modified – Addition of information useful for the context of the IEV, and adaptation to the IEV rules]


fr
redondance, <en théorie de l'information> f
excès de la quantité de décision H0 sur l'entropie H

R = H0 − H

EXEMPLE Soit { a,b,c } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaomaacmaakeaajugibiaadggacaGGSaGaamOyaiaacYcacaWGJbaa kiaawUhacaGL9baaaaa@43FE@ un jeu de trois événements dont les probabilités de réalisation sont p(a)=0,5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadggacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaiwdaaaa@43D9@ , p(b)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadkgacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4496@ et p(c)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadogacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4497@ . La redondance de ce jeu est: R=1,585 Sh1,50 Sh =0,085 ShMathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaqaaaaaaaaaWdbiaadkfacqGH9aqpcaaIXaGaaiilaiaaiwdacaaI 4aGaaeiiaiaabofacaqGObGaeyOeI0IaaGymaiaacYcacaaI1aGaaG imaiaabccacaqGtbGaaeiAaiaabccacqGH9aqpcaaIWaGaaiilaiaa icdacaaI4aGaaeiiaiaabofacaqGObaaaa@517B@ .

Note 1 à l’article: En pratique, l'usage de codes convenables permet de représenter des messages avec un nombre réduit de caractères; la redondance peut être considérée comme une mesure de la diminution de la longueur moyenne des messages ainsi réalisée au moyen d'un codage approprié.


[SOURCE: IEC 80000-13:2008, 13-28, modifié – Ajout d’informations utiles pour le contexte de l’IEV, et adaptation aux règles de l’IEV]


ar
الزيادة, <في نظرية المعلومات>

de
Redundanz, <in der Informationstheorie> f

fi
redundanssi, <informaatioteoriassa>

ja
冗長量, <情報理論>

pl
redundancja, <w teorii informacji> f

pt
redundância, <em teoria da informação>

zh
冗余, <信息论中>

Publication date: 2019-03-29
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