D:\sbornik\...\Mac-random.DVI


Mathematical Problems of Computer Science 24, 2005, 42{61.

B ounds of E-capacity Region for M ultiple-access

Channel With Random P ar ameter ¤

Ma r ia m E . H a r o u t u n ia n

Institue for Informatics and Automation Problems of NAS of RA

e-mail armar@ipia.sci.am

Abstract

The discrete memoryless multiple-access channel with random parameter is inves-
tigated. Various situations, when the state of the channel is known or unknown on
the encoders and decoder, are considered. Some bounds of E-capacity and capacity
regions for average error probability are obtained.

Refer ences

[1 ] R . F. A h ls we d e ," Mu lt y-wa y c o m m u n ic a t io n c h a n n e ls " , 2nd Intern. Sympos. In-
form. Theory. Tsahkadsor, Armenia, 1971, B u d a p e s t : A ka d . K ia d o , p p . 2 3 { 5 2 , 1 9 7 3 .

[2 ] R . F. A h ls we d e ," Th e c a p a c it y r e g io n o f a c h a n n e l wit h t wo s e n d e r s a n d t wo r e c e ive r s " ,
AnnalsP robability, vo l. 2 . n o . 2 . p p . 8 0 5 { 8 1 4 , 1 9 7 4 .

[3 ] E . A . H a r o u t u n ia n , M. E . H a r o u t u n ia n a n d A . E . A ve t is s ia n ," Mu lt ip le -a c c e s s c h a n n e l
a c h ie va b le r a t e s r e g io n a n d r e lia b ilit y" , Izvestiya Akademii Nauk Armenii, M atematika,
vo l. 2 7 , n o . 5 , p p . 5 1 { 6 8 , 1 9 9 2 .

[4 ] M. E . H a r o u t u n ia n , " On E-c a p a c it y r e g io n o f m u lt ip le -a c c e s s c h a n n e l" , ( in R u s s ia n )
Izvestiya Akademii Nauk Armenii, M atematika, vo l. 3 8 , n o . 1 , p p . 3 { 2 2 , 2 0 0 3 .

[5 ] R . G. Ga lla g e r , " A p e r s p e c t ive o n m u lt ia c c e s s c h a n n e ls " , IE E E Trans. Inform. Theory,
vo l. 3 1 , n o . 1 , p p . 1 2 4 { 1 4 2 , 1 9 8 5 .

[6 ] A . G. D ya c h ko v, " R a n d o m c o n s t a n t c o m p o s it io n c o d e s fo r m u lt ip le a c c e s s c h a n n e ls " ,
P roblems of Control and Inform. Theory, vo l. 1 3 , n o . 6 , p p . 3 5 7 { 3 6 9 , 1 9 8 4 .

[7 ] J. P o ko r n y a n d H .M. W a llm e ie r , " R a n d o m c o d in g b o u n d a n d c o d e s p r o d u c e d b y p e r -
m u t a t io n s fo r t h e m u lt ip le -a c c e s s c h a n n e l" , IE E E Trans. Inform. Theory, vo l. IT-3 1 ,
p p . 7 4 1 { 7 5 0 , 1 9 8 5 .

[8 ] Y . S . L iu a n d B . L . H u g h e s , " A n e w u n ive r s a l c o d in g b o u n d fo r t h e m u lt ip le -a c c e s s
c h a n n e l" , IE E E Trans. Inform. Theory, vo l. IT-4 2 , p p . 3 7 6 { 3 8 6 , 1 9 9 6 .

¤Work was partially supported by INTAS grant 00-738.

4 2



M. E. Haroutunian 4 3

[9 ] S . I. Ge lfa n d , M. S . P in s ke r , " Co d in g fo r c h a n n e l wit h r a n d o m p a r a m e t e r s " , P roblems
of Control and Inform. Theory, vo l. 8 , n o . 1 , p p . 1 9 { 3 1 , 1 9 8 0 .

[1 0 ] E . A . H a r o u t u n ia n a n d M. E . H a r o u t u n ia n , " E-c a p a c it y u p p e r b o u n d fo r c h a n n e l wit h
r a n d o m p a r a m e t e r " , P roblems of Control and Information Theory, vo l. 1 7 , n o .2 , p p .
9 9 { 1 0 5 , 1 9 8 8 .

[1 1 ] M. E . H a r o u t u n ia n , " B o u n d s o f E-c a p a c it y fo r t h e c h a n n e l wit h r a n d o m p a r a m e t e r " ,
P roblemi P eredachi Informatsii, ( in R u s s ia n ) , vo l. 2 7 , n o . 1 , p p . 1 4 { 2 3 , 1 9 9 1 .

[1 2 ] M. E . H a r o u t u n ia n , " N e w b o u n d s fo r E-c a p a c it ie s o f a r b it r a r ily va r yin g c h a n n e l a n d
c h a n n e l wit h r a n d o m p a r a m e t e r " , Trans. IIAP NAS R A and YSU, M athematical P rob-
lems of Computer sciences, v. 2 2 , p . 4 4 { 5 9 , 2 0 0 1 .

[1 3 ] J. Ja h n , " Co d in g o f a r b it r a r ily va r yin g m u lt iu s e r c h a n n e ls " , IE E E Trans. Inform. The-
ory, vo l. IT-2 7 , n o . 2 , p p . 2 1 2 { 2 2 6 , 1 9 8 1 .

[1 4 ] R . F. A h ls we d e , A r b it r a r ily va r yin g c h a n n e ls wit h s t a t e s s e qu e n c e kn o wn t o t h e s e n d e r ,
IE E E Trans. Inform. Theory, vo l. IT-3 2 , n o . 5 , p p . 6 2 1 { 6 2 9 , 1 9 8 6 .

[1 5 ] R . F. A h ls we d e a n d N . Ca i, " A r b it r a r ily va r yin g m u lt ip le a c c e s s c h a n n e ls " , P a r t 1 ,
IE E E Trans. Inform. Theory, vo l. IT-4 5 , n o . 2 , p p . 7 4 2 { 7 4 9 , 1 9 9 9 .

[1 6 ] R . F. A h ls we d e a n d N . Ca i, " A r b it r a r ily va r yin g m u lt ip le a c c e s s c h a n n e ls " , P a r t 2 ,
IE E E Trans. Inform. Theory, vo l. IT-4 5 , n o . 2 , p p . 7 4 9 { 7 5 6 , 1 9 9 9 .

[1 7 ] A . D a s a n d P . N a r a ya n , " Ca p a c it ie s o f t im e -va r yin g m u lt ip le -a c c e s s c h a n n e ls wit h s id e
in fo r m a t io n " , IE E E Transactions on Information Theory, vo l. 4 8 , n o . 1 , p p . 4 { 2 5 , 2 0 0 2 .

[1 8 ] M. S . P in s ke r , " Mu lt i-u s e r c h a n n e ls " , II J oint Swedish-Soviet Intern. workshop on In-
form. Theory, Gr ¶a n n a , S we d e n , p p . 1 6 0 -1 6 5 , 1 9 8 5 .

[1 9 ] I. Cs is z ¶a r a n d J. K ¶o r n e r , Information Theory. Coding Theorems for D iscrete M emoryless
Systems, B u d a p e s t : A ka d . K ia d o , 1 9 8 1 .

[2 0 ] I. Cs is z ¶a r , " Th e m e t h o d o f t yp e s " , IE E E Trans. Inform. Theory, vo l. IT-4 4 , p p . 2 5 0 5 -
2 5 2 3 , 1 9 9 8 .

öá÷áËíáÕ å³ñ³Ù»ïñáí µ³½Ù³Ùáõïù ϳåáõÕáõ
E-áõݳÏáõÃÛ³Ý ïÇñáõÛÃÇ ·Ý³Ñ³ï³Ï³ÝÝ»ñÁ

Ø. º. гñáõÃÛáõÝÛ³Ý

²Ù÷á÷áõÙ

²ß˳ï³Ýùáõ٠ѻﳽáïí³Í ¿ ÷á÷áËíáÕ å³ñ³Ù»ïñáí ÁÝ¹Ñ³ï ³é³Ýó
ÑÇßáÕáõÃÛ³Ý µ³½Ù³Ùáõïù ϳåáõÕÇÝ: àõëáõÙݳëÇñí³Í »Ý ï³ñµ»ñ ¹»åù»ñ, »ñµ
ϳåáõÕáõ íÇ׳ÏÁ ѳÛïÝÇ ¿ ϳ٠³ÝѳÛï Ïá¹³íáñÇãÇÝ ¨ ³å³Ïá¹³íáñÇãÇÝ: êï³óí³Í
»Ý áñáß³ÏÇ ·Ý³Ñ³ï³Ï³ÝÝ»ñ E-áõݳÏáõÃÛ³Ý ¨ áõݳÏáõÃÛ³Ý Ñ³Ù³ñ, ÙÇçÇÝ ë˳ÉÇ
ѳí³Ý³Ï³ÝáõÃÛ³Ý ¹»åùáõÙ: