D:\sbornik\...\tpel.DVI


Mathematical Problems of Computer Science 35, 53{62, 2011.

Random Coding B ound for E-capacity Region of

Asymmetr ic B r oadcast Channel With Stochastic

E ncoding

N a s r in A fs h a r

Institute for Informatics and Automation Problems of NAS of RA

Abstract

E-capacity (rate-reliability) region of the asymmetric broadcast channel with
stochastic encoding is studied. The asymmetric broadcast channel involves two dis-
crete memoryless channels with a common input. A common message is transmitted
to both receivers and one private message to the intended receiver. We derive an inner
bound for rate-reliability region.

Key words: Asymmetric broadcast channel, E-capacity, error exponent, random
coding bound, rate-reliability region, stochastic encoding.

Refer ences

[1 ] T. M. Co ve r , \ B r o a d c a s t c h a n n e ls " , IE E E Trans. Inform. Theory, vo l. IT-1 8 , n o 1 , p p .
2 -1 4 , 1 9 7 2 .

[2 ] I. Cs is z ¶a r a n d J. K Äo r n e r , \ B r o a d c a s t c h a n n e l wit h c o n ¯ d e n t ia l m e s s a g e s " , IE E E Trans-
action on IT, vo l. IT-2 4 ( 3 ) , p p . 3 3 9 -3 4 8 , 1 9 7 8 .

[3 ] I. Cs is z ¶a r a n d J. K Äo r n e r , \ In fo r m a t io n Th e o r y: Co d in g Th e o r e m s fo r D is c r e t e Me m o -
r yle s s S ys t e m s " , New York, W iley, 1 9 8 1 .

[4 ] E . A . H a r o u t u n ia n , \ U p p e r e s t im a t e o f t r a n s m is s io n r a t e fo r m e m o r yle s s c h a n n e l wit h
c o u n t a b le n u m b e r o f o u t p u t s ig n a ls u n d e r g ive n e r r o r p r o b a b ilit y e xp o n e n t " , in 3rd
All Union Conference on Theory of Information Transmisssion and Coding, Uzhgorod,
P ublishing House of the Uzbek Academy of sciences, p p . 8 3 -8 6 , Ta s h ke n t , 1 9 6 7 .

[5 ] E . A . H a r o u t u n ia n , \ On t h e o p t im a lit y o f in fo r m a t io n t r a n s m is s io n b y a c h a n n e l wit h
¯ n it e n u m b e r o f s t a t e s kn o wn a t t h e in p u t " , ( in R u s s ia n ) , Izvestia Academii Nauk
Armenii, M atematika, vo l. 4 , n o . 2 , p p .8 1 -9 0 , 1 9 6 9 .

[6 ] E . A . H a r o u t u n ia n , \ On B o u n d s fo r E -Ca p a c it y o f D MC" , IE E E Trans. Inform. Theory,
vo l. IT-5 3 , n o . 1 1 , p p . 4 2 1 0 -4 2 2 0 , 2 0 0 7 .

[7 ] 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 . N . H a r o u t u n ia n , \ R e lia b ilit y c r it e r ia in
in fo r m a t io n t h e o r y a n d in s t a t is t ic a l h yp o t h e s is t e s t in g " , F oundations and Trends in
Communications and Information Theory, vo l. 4 , n o s . 2 -3 , 2 0 0 8 .

[8 ] M. E . H a r o u t u n ia n , \ R a n d o m c o d in g b o u n d fo r E -c a p a c it y r e g io n o f t h e b r o a d c a s t
c h a n n e l" , M athematical problems of computer science, n o . 2 1 , p p . 5 0 -6 0 , 2 0 0 0 .

5 3



5 4 Random Coding Bound for E-capacity Region of Asymmetric Broadcast Channel With Stochastic Encoding

[9 ] J. K Äo r n e r a n d K . Ma r t o n , \ A n a c h ie va b le r a t e r e g io n fo r t h e b r o a d c a s t c h a n n e l" , IE E E
Trans. Inform. Theory, vo l. IT-2 3 , p p . 7 5 1 -7 6 1 , 1 9 7 7 .

[1 0 ] J. K Äo r n e r a n d K . Ma r t o n , \ Ge n e r a l b r o a d c a s t c h a n n e ls wit h d e g r a d e d m e s s a g e s e t s " ,
IE E E Trans. Inform. Theory, vo l. IT-2 3 , p p . 6 0 -6 4 , 1 9 7 7 .

[1 1 ] C. E . S h a n n o n , \ A m a t h e m a t ic a l t h e o r y o f c o m m u n ic a t io n " , B ell System Technical
J ournal, vo l. 2 7 , n o . 3 , p p . 3 7 9 -4 2 3 , 1 9 4 8 .

[1 2 ] C. E . S h a n n o n , \ P r o b a b ilit y o f e r r o r fo r o p t im a l c o d e s in Ga u s s ia n c h a n n e ls " , B ell Syst.
Tech. J ., vo l. 3 8 , n o 5 , p p . 6 1 1 -6 5 9 , 1 9 5 9 .

ȳÛݳë÷Ûáõé ³Ýѳٳã³÷ ëïá˳ëïÇÏ Ïá¹³íáñٳٵ ϳåáõÕáõ
E-áõݳÏáõÃÛ³Ý ïÇñáõÛÃÇ å³ï³Ñ³Ñ³Ý Ïá¹³íáñÙ³Ý ·Ý³Ñ³ï³Ï³ÝÁ

Ü. ²íß³ñ

²Ù÷á÷áõÙ

Ðá¹í³ÍáõÙ áõëáõÙݳëñíáõÙ ¿ ɳÛݳë÷Ûáõé ³Ýѳٳã³÷ ëïá˳ëïÇÏ Ïá¹³íáñٳٵ
ϳåáõÕÇÝ: γéáõóí³Í ¿ E-áõݳÏáõÃÛ³Ý (³ñ³·áõÃÛáõÝ-Ñáõë³ÉÇáõÃÛáõÝ) ïÇñáõÛÃÇ
å³ï³Ñ³Ï³Ý Ïá¹³íáñÙ³Ý ·Ý³Ñ³ï³Ï³ÝÁ: