D:\sbornik\...\Article.DVI


Mathematical Problems of Computer Science 37, 7{16, 2012.

Upper and Lower B ounds of B iometr ic I denti¯cation

E-Capacity

Ma r ia m E . H a r o u t u n ia n , L ilit A . Te r -V a r d a n ya n a n d A r t h u r R . Mu r a d ya n

Institute for Informatics and Automation Problems of NAS RA

armar@ipia.sci.am, lilit@sci.am, mur¡art@yahoo.com

Abstract

In this paper we introduce a new concept of E-capacity for biometric indenti¯cation
system, which is the generalization of the capacity studied by Willems et al [1]. We
investigate this function by constructing upper and lower bounds. When E ! 0 we
derive the lower and upper bounds of the channel capacity which coincides with the
capacity obtained in [1].
Keywords: Biometric identi¯cation system, identi¯cation capacity, E-capacity
bounds, error exponents.

Refer ences

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8 Upper and Lower Bounds of Biometric Identi¯cation E-Capacity

[9 ] I. Cs is z ¶a r a n d J. K Äo r n e r , Information Theory: Coding Theorems for D iscrete M emory-
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n o . 6 , p p . 2 5 0 5 -2 5 2 3 , 1 9 9 8 .

λÝë³ã³÷³Ï³Ý ÝáõÛݳϳݳóÙ³Ý Ñ³Ù³Ï³ñ·Ç E-áõݳÏáõÃÛ³Ý
í»ñÇÝ ¨ ëïáñÇÝ ·Ý³Ñ³ï³Ï³ÝÝ»ñÁ

Ø. гñáõÃÛáõÝÛ³Ý, È. î»ñ-ì³ñ¹³ÝÛ³Ý ¨ ². Øáõñ³¹Û³Ý

²Ù÷á÷áõÙ

Ðá¹í³ÍáõÙ Ý»ñÙáõÍíáõÙ ¿ Ï»Ýë³ã³÷³Ï³Ý ÝáõÛݳϳݳóÙ³Ý Ñ³Ù³Ï³ñ·Ç E-
áõݳÏáõÃÛ³Ý Ýáñ ѳëϳóáõÃÛáõÝÁ, áñÝ ÁݹѳÝñ³óÝáõÙ ¿ ìÇÉ»ÙëÇ ¨ áõñÇßÝ»ñÇ [1]
áõëáõÙݳëÇñ³Í áõݳÏáõÃÛ³Ý ·³Õ³÷³ñÁ: лﳽáïíáõÙ ¿ ³Û¹ ýáõÝÏódzݑ í»ñÇÝ ¨
ëïáñÇÝ ·Ý³Ñ³ï³Ï³ÝÝ»ñÇ Ï³éáõóÙ³Ý ÙÇçáóáí: ºñµ E ! 0 , Ù»Ýù ëï³ÝáõÙ »Ýù
ϳåáõÕáõ áõݳÏáõÃÛ³Ý í»ñÇÝ ¨ ëïáñÇÝ ·Ý³Ñ³ï³Ï³ÝÝ»ñÁ, áñáÝù ѳÙÁÝÏÝáõÙ »Ý [1]-
áõÙ ëï³óí³Í áõݳÏáõÃÛ³Ý Ñ»ï:

Âåðõíÿÿ è íèæíÿÿ ãðàíèöû E-ïðîïóñêíîé ñïîñîáíîñòè
áèîìåòðè÷åñêîé ñèñòåìû èäåíòèôèêàöèè

Ì. Àðóòþíÿí, Ë. Òåð-Âàðäàíÿí è À. Ìóðàäÿí

Àííîòàöèÿ

 ñòàòüå ââîäèòñÿ íîâîå ïîíÿòèå Å-ïðîïóñêíîé ñïîñîáíîñòè äëÿ áèîìåò-
ðè÷åñêîé ñèñòåìû èäåíòèôèêàöèè, êîòîðàÿ ÿâëÿåòñÿ îáîáùåíèåì ïðîïóñêíîé
ñïîñîáíîñòè, èçó÷åííîé Âèëåìñîì è äð. â [1]. Ôóíêöèÿ èññëåäóåòñÿ ïóòåì
ïîñòðîåíèÿ âåðõíåé è íèæíåé ãðàíèö. Êîãäà E ! 0 , ìû ïîëó÷àåì âåðõíþþ
è íèæíþþ ãðàíèöû ïðîïóñêíîé ñïîñîáíîñòè êàíàëà, êîòîðûå ñîâïàäàþò ñ
ïðîïóñêíîé ñïîñîáíîñòüþ, ïîëó÷åííîé â [1].