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7/17/2019 Chuong 3- Ma Hieu
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LYÙ THUYEÁT TRUYEÀN TINLYÙ THUYEÁT TRUYEÀN TIN
CHÖÔNG 3:CHÖÔNG 3:
MAÕ HIEÄUMAÕ HIEÄU
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Noäi dung c!n cu"# c$%ngNoäi dung c!n cu"# c$%ng
33&'&' ()n ng*# +#, i-äu()n ng*# +#, i-äu
.'.' C#/c 0o1ng 2o cu"# +#, i-äuC#/c 0o1ng 2o cu"# +#, i-äu
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<'<' M#, -ä 0ong co/ 0!n =>-?@M#, -ä 0ong co/ 0!n =>-?@
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&' M#, i-äu&' M#, i-äu
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i-äui-äu&'&' (i-4u 5i-än 7#1n 0#/c D$%c(i-4u 5i-än 7#1n 0#/c D$%c: i-äc +#,: i-äc +#,
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#+ c#u 0>u/c +#,:#+ c#u 0>u/c +#,: S$" dung #+ GniO 0>ong Do/:S$" dung #+ GniO 0>ong Do/:
o 9i-n ni 6# Doä d#i cu"# 0$ +#,9i-n ni 6# Doä d#i cu"# 0$ +#,
o Gi#/ 0>) cu"# #+ 6# 2o 0$ +#, co/Gi#/ 0>) cu"# #+ 6# 2o 0$ +#, co/Doä d#i ni 0$%ng $/ng'Doä d#i ni 0$%ng $/ng'
! du ! du : 9oä +#, i-äu & & &&: 9oä +#, i-äu & & &&&&&O&&&Oo H#+ c#u 0>u/c +#, 6#:H#+ c#u 0>u/c +#, 6#:3 khi ni=2
2 khi ni=3
G(ni) =
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9i-u di-;n +#, #\ng9i-u di-;n +#, #\ng
#+ c#u 0>u/c#+ c#u 0>u/c ! du: co nguo4n 0in co/ n#K+ 0in! du: co nguo4n 0in co/ n#K+ 0in
D$%c +#, o#/ 0-o +#, i-äu n$ 2#u:D$%c +#, o#/ 0-o +#, i-äu n$ 2#u:
o #& PQ #& PQ o #. PQ &#. PQ &o #3 PQ & PQ &&o #8 PQ & PQ &&
o #< PQ &&#< PQ && 9i-u di-;n oä +#, 0>-1n 0-o #+9i-u di-;n oä +#, 0>-1n 0-o #+
c#u 0>u/c'c#u 0>u/c'
Öukn$%c Di-+ cu"# 7$%ng 7#/7jÖukn$%c Di-+ cu"# 7$%ng 7#/7j
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9i-u di-;n +#, i-äu9i-u di-;n +#, i-äu
9#i 0#ä7: co nguo4n 0in co/ V 0in D$%c9#i 0#ä7: co nguo4n 0in co/ V 0in D$%c+#, o#/ 0-o +#, i-äu n$ 2#u:+#, o#/ 0-o +#, i-äu n$ 2#u:
o #& PQ &&#& PQ &&o #. PQ &#. PQ &o #3 PQ & PQ &&o #8 PQ && PQ &&&
o #< PQ &&#< PQ &&o # PQ &# PQ &o #^ PQ &&#^ PQ &&o #V PQ &&&#V PQ &&&
9i-u di-;n oä+#, 0-o:
P9#"ng Doi ci-u
P M#0 7#ng 0o#Doä
P (o4 `n c#1F
P H#+ c#u 0>u/c'
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T!n =>-?@ T!n =>-?@
M#, co/ 0!n 7#1n 0#/c D$%c:M#, co/ 0!n 7#1n 0#/c D$%c: $ieàu kieän$ieàu kieäncaàn vaø ñuû ñe% maõ coù tính phaân taùchcaàn vaø ñuû ñe% maõ coù tính phaân taùchñöôïc laø &aát k#ø to% hôïp maõ naøo cuõngñöôïc laø &aát k#ø to% hôïp maõ naøo cuõng
khoâng ñöôïc t"uøng vôùi phaàn ñaàu cuûa to%khoâng ñöôïc t"uøng vôùi phaàn ñaàu cuûa to%hôïp maõ khaùchôïp maõ khaùc''o ! du:! du: +oä0 nguo4n 0in co/ 8 0in a# c db' T# +#,+oä0 nguo4n 0in co/ 8 0in a# c db' T# +#,
o#/ %/i +#, i-äu n$ 2#u:o#/ %/i +#, i-äu n$ 2#u:]
# PQ _ PQ &_ c PQ &_ d PQ &&# PQ _ PQ &_ c PQ &_ d PQ &&
] Nguo4n 0in n#F 0o#" +#,n Di-4u 5i-än 7#1n 0#/c D$%c'Nguo4n 0in n#F 0o#" +#,n Di-4u 5i-än 7#1n 0#/c D$%c'
o N-u T# +#, o#/ %/i +#, i-äu n$ 2#u:N-u T# +#, o#/ %/i +#, i-äu n$ 2#u:] # PQ _ PQ &_ c PQ &_ d PQ &&# PQ _ PQ &_ c PQ &_ d PQ &&] Nguo4n 0in 5o1ng 0o#" +#,n Di-4u 5i-än 7#1n 0#/cNguo4n 0in 5o1ng 0o#" +#,n Di-4u 5i-än 7#1n 0#/c
D$%cD$%c
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T!n =>-?@ T!n =>-?@
Co +oä0 0$ +#, 7>-?@ cu"# 0$ +#,Co +oä0 0$ +#, 7>-?@ cu"# 0$ +#,Do/ 6# 0#0 c#" c#/c 0i-4n 0o cu"# 0$Do/ 6# 0#0 c#" c#/c 0i-4n 0o cu"# 0$
+#, D#, co'+#, D#, co'o ! du:! du: co 0$ +#, &&&& 7>-?@ cu"#co 0$ +#, &&&& 7>-?@ cu"#0$ +#, n#F 6# c#/c 0o %7 +#,:0$ +#, n#F 6# c#/c 0o %7 +#,:] &&&&&&&&] &&&&&&] &&&&&&] &&&&] &&&&] &&&&
] &&
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T!n =>-?@ T!n =>-?@
M#, co/ 0!n 7>-?@:M#, co/ 0!n 7>-?@: 'oä maõ ñöôïc goïi'oä maõ ñöôïc goïilaø coù tính p"e() neáu &aát k#ø to% hôïplaø coù tính p"e() neáu &aát k#ø to% hôïp
maõ naøo cuõng khoâng phaûi laø p"e()maõ naøo cuõng khoâng phaûi laø p"e()cuûa to% hôïp maõ khaùc t"ong cuøng &oäcuûa to% hôïp maõ khaùc t"ong cuøng &oämaõ*maõ*
#äF +#, co/ 0!n 7>-?@ 0o#" +#,n#äF +#, co/ 0!n 7>-?@ 0o#" +#,n
Di-4u 5i-än 7#1n 0#/c D$%c'Di-4u 5i-än 7#1n 0#/c D$%c' T>-1n Do4 `n c#1F c#/c 0$ +#, cu"# T>-1n Do4 `n c#1F c#/c 0$ +#, cu"#
oä +#, co/ 0!n 7>-?@ c D$%c 0!n %"oä +#, co/ 0!n 7>-?@ c D$%c 0!n %"c#/c nu/0 cuoi 5o1ng D$%c 0!n c#/cc#/c nu/0 cuoi 5o1ng D$%c 0!n c#/c
nu/0 gi$,#'nu/0 gi$,#'
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T!n =>-?@ T!n =>-?@
N-u oä +#, i-äu co/ c% 2o + 0`N-u oä +#, i-äu co/ c% 2o + 0`c#/c nu/0 5o1ng 7#"i nu/0 cuoi 2-,c#/c nu/0 5o1ng 7#"i nu/0 cuoi 2-,
noi %/i + nu/0 %" +$/c 0i-7 0-onoi %/i + nu/0 %" +$/c 0i-7 0-o%/i +%/i + ≤≤ ++o N-u + Z + 0# co/ +#, D#4FN-u + Z + 0# co/ +#, D#4Fo N-u + + 0# co/ +#, %i'N-u + + 0# co/ +#, %i'
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T!n =>-?@ T!n =>-?@
N$ #äF #+ 5-0 c#u cu"# c#/c +$/c n$N$ #äF #+ 5-0 c#u cu"# c#/c +$/c n$2#u:2#u:
G&OG&O ≤ m≤ m
G(2) ≤ mG(2) ≤ m22 – G(1).m – G(1).m
G(3) ≤ mG(3) ≤ m33 – G(1).m – G(1).m22 – G(2).m – G(2).m
……
G(n) ≤ mG(n) ≤ mnn – G(1).m – G(1).mn-1n-1 – G(2).m – G(2).mn-2n-2 - …-G(n-1).m- …-G(n-1).m
o Ci# . - co +Ci# . - co +nn 0# co/: 0# co/:
o (#1F 6# Di-4u 5i-än D- 0i-0 6#ä7 +#, co/ 0!n 7>-?@(#1F 6# Di-4u 5i-än D- 0i-0 6#ä7 +#, co/ 0!n 7>-?@
∑=
−≥n
j
j jGm1
)(.1
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@=>-?@ M#, -ä 0ong co/ 0!n 7>-?@M#, -ä 0ong co/ 0!n 7>-?@ 6#6#
+oä0 0>ong #i 6o#i +#, c+oä0 0>ong #i 6o#i +#, coù tínhoù tính
p"e() pho% &ieán* p"e() pho% &ieán* %/i +oä0 oä +#, i-äu 0# co/ #%/i +oä0 oä +#, i-äu 0# co/ #
gi#i Do#n 0$c i-än:gi#i Do#n 0$c i-än:o T#n 6#ä7 +#, T#n 6#ä7 +#,
o M#, o#/M#, o#/o Gi#"i +#,Gi#"i +#,
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] T#n 6#ä7 +#,=>-?@ ] T#n 6#ä7 +#, T#n 6#ä7 +#, -ä 0ong co/ 0!n T#n 6#ä7 +#, -ä 0ong co/ 0!n
7>-?@7>-?@ #o go4+ 3 $%/c:#o go4+ 3 $%/c:o
9$%/c &9$%/c &: Con +oä0 oä +#,: Con +oä0 oä +#, D%n gi#"n co/D%n gi#"n co/0!n 7>-?@0!n 7>-?@o 9$%/c .9$%/c .: L#F +oä0 2o 0o %7 +#, %" $%/c: L#F +oä0 2o 0o %7 +#, %" $%/c
& 6#+& 6#+ 0o %7 c% 2%"0o %7 c% 2%" c#/c 0o %7 con 6#i c#/c 0o %7 con 6#icu"# $%/c & D$%c goi 6#cu"# $%/c & D$%c goi 6# 0o %7 cuoi0o %7 cuoi''
o 9$%/c 39$%/c 3:: G-/7 +oä0 o#c +oä0 2o 0o %7G-/7 +oä0 o#c +oä0 2o 0o %7c% 2%" %/i n#u >o4i coäng 0-1+ #o cuoic% 2%" %/i n#u >o4i coäng 0-1+ #o cuoi+oä0 0o %7 cuoi 0# D$%c & 0$ +#,+oä0 0o %7 cuoi 0# D$%c & 0$ +#,' T$c' T$ci-än n$ #äF co D-n 5i co/ Du" 2o 0$i-än n$ #äF co D-n 5i co/ Du" 2o 0$+#, c#4n dung'+#, c#4n dung'
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] T#n 6#ä7 +#,=>-?@ ] T#n 6#ä7 +#, ! du&! du&: 0#n 6#ä7 oä +#, -ä: 0#n 6#ä7 oä +#, -ä
0ong co/ 0!n 7>-?@ D- +#, o#/0ong co/ 0!n 7>-?@ D- +#, o#/
nguo4n 0in: AZa#& #. #3 #8 #<bnguo4n 0in: AZa#& #. #3 #8 #<bo 9$%/c &9$%/c &: Con oä +#, D%n gi#"n co/: Con oä +#, D%n gi#"n co/0!n 7>-?@:0!n 7>-?@: & & && & &
o 9$%/c .9$%/c .::
] ConCon & & & & 6#+6#+ 0o %7 c% 2%"0o %7 c% 2%"] To %7 con 6#i: To %7 con 6#i: && 6#6# 0o %7 cuoi0o %7 cuoi''
o 9$%/c 39$%/c 3: G-/7 0#n c#/c 0o %7 +#,:: G-/7 0#n c#/c 0o %7 +#,:] &&&&__ &&&& &&&& &&&&&& &&
#& #. #3 #8 #<#& #. #3 #8 #<
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Tingoc #& #. #3 #8 #<
T$+#,
&&
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&& &&& &
M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] T#n 6#ä7 +#,=>-?@ ] T#n 6#ä7 +#, T# D$%c #"ng +#, -ä 0ong co/ 0!n =>-?@ n$ 2#u:
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] T#n 6#ä7 +#,=>-?@ ] T#n 6#ä7 +#, ! du ! du : 0#n 6#ä7 oä +#, -ä: 0#n 6#ä7 oä +#, -ä
0ong co/ 0!n 7>-?@ D- +#, o#/0ong co/ 0!n 7>-?@ D- +#, o#/
nguo4n 0in: AZa#& #. #3 #8 #< #nguo4n 0in: AZa#& #. #3 #8 #< ##^ #Vb#^ #Vb
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] M#, o#/=>-?@ ] M#, o#/ M#, o#/M#, o#/ : 0$c i-än 0#i D#4u 7#/0: 0$c i-än 0#i D#4u 7#/0
0in 6# i-n Doi c#/c 0in cu"# #"n0in 6# i-n Doi c#/c 0in cu"# #"n
0in 0#n c#/c 0o %7 +#, 0$%ng0in 0#n c#/c 0o %7 +#, 0$%ng$/ng'$/ng' ! du! du nguo4n 0in 0>-1n 7#/0 #"n 0in:nguo4n 0in 0>-1n 7#/0 #"n 0in:
lZ#lZ#&& # #33 # #<< # #88 # #.. # #&& # #&&O'O'o M#, o#/ 0# D$%c:M#, o#/ 0# D$%c:
&&&&&&&&&&&&&&&&&&&&&&&&&&&O&O
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] Gi#"i +#,=>-?@ ] Gi#"i +#, Gi#"i +#,Gi#"i +#, #o go4+ 3 $%/c 0$c#o go4+ 3 $%/c 0$c
i-än 0#i D#4u 0u 0in:i-än 0#i D#4u 0u 0in:
o 9$%/c &9$%/c &: =#1n 0#/c cuo;i 0in 0u D$%c: =#1n 0#/c cuo;i 0in 0u D$%c0#n c#/c 0o %7 c% 2%" # 0o %70#n c#/c 0o %7 c% 2%" # 0o %7cuoicuoi
o 9$%/c .9$%/c .: No/+ 0#n c#/c 0o %7 +#,: No/+ 0#n c#/c 0o %7 +#,
-ä 0ong'-ä 0ong'o 9$%/c 39$%/c 3: 9i-n Doi 0$ c#/c 0o %7 +#,: 9i-n Doi 0$ c#/c 0o %7 +#,-ä 0ong 0#n c#/c 0in 0$%ng $/ng'-ä 0ong 0#n c#/c 0in 0$%ng $/ng'
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] Gi#"i +#,=>-?@ ] Gi#"i +#, ! du 0>-1n! du 0>-1n: cuo;i 0in 0u D$%c 6#:: cuo;i 0in 0u D$%c 6#:
&&&&&&&&&&&&&&&&&&&&&&&&&&&&
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] N#än @-/0=>-?@ ] N#än @-/0 M#, -ä 0ong co/ 0!n =>-?@ co/M#, -ä 0ong co/ 0!n =>-?@ co/ $u$u
Di-+Di-+::
o Co/ 0!n cong ni-;uCo/ 0!n cong ni-;uo Co/ 0!n #"o +#ä0 c#oCo/ 0!n #"o +#ä0 c#o
N$%c Di-+N$%c Di-+::o T>ong ! du 0>-1n Doä d#i 0$ +#, 6%/nPQ T>ong ! du 0>-1n Doä d#i 0$ +#, 6%/nPQ
i-äu 2u#0 0>uF-4n 0in gi#"+' TuF ni-1ni-äu 2u#0 0>uF-4n 0in gi#"+' TuF ni-1nDoä d#i 0$ +#, c#ng 0#Kng 0` 0!nDoä d#i 0$ +#, c#ng 0#Kng 0` 0!n#"o +#ä0 c#ng 0#Kng'#"o +#ä0 c#ng 0#Kng'
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
=>-?@ ] T#n 6#ä7 +#,=>-?@ ] T#n 6#ä7 +#, ! du .! du .: 0#n 6#ä7 oä +#, -ä: 0#n 6#ä7 oä +#, -ä
0ong co/ 0!n 7>-?@ D- +#, o#/0ong co/ 0!n 7>-?@ D- +#, o#/
nguo4n 0in: UZau& u. u3 u8 u<nguo4n 0in: UZau& u. u3 u8 u<ub'ub'o Gi#" 2$" nguo4n 0in 0>-1n 7#/0 #"n 0in:Gi#" 2$" nguo4n 0in 0>-1n 7#/0 #"n 0in:
lZu u< u3 u. u. u3 u8 u&OlZu u< u3 u. u. u3 u8 u&O
M#, o#/ # gi#"i +#, #"n 0in 0-o oäM#, o#/ # gi#"i +#, #"n 0in 0-o oä+#, $# 0#n 6#ä7'+#, $# 0#n 6#ä7'
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M#, -ä 0ong co/ 0!nM#, -ä 0ong co/ 0!n
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0ong co/ 0!n 7>-?@ D- +#, o#/0ong co/ 0!n 7>-?@ D- +#, o#/
nguo4n 0in: UZa#& #. #3 #8 #< #nguo4n 0in: UZa#& #. #3 #8 #< ##^b'#^b'o Gi#" 2$" nguo4n 0in 0>-1n 7#/0 #"n 0in:Gi#" 2$" nguo4n 0in 0>-1n 7#/0 #"n 0in:
lZ#. #. #^ #^ # #< #3 #. #8 #&OlZ#. #. #^ #^ # #< #3 #. #8 #&O
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M#, 0ong 5-1 0oi $uM#, 0ong 5-1 0oi $u
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N-u +#, o#/ %/i oä +#, D-4u 0`N-u +#, o#/ %/i oä +#, D-4u 0`#"n 0in 2#u +#, o#/ 2-, d#i %n#"n 0in 2#u +#, o#/ 2-, d#i %n7$%ng 7#/7 +#, o#/ +# %" Do/:7$%ng 7#/7 +#, o#/ +# %" Do/:o Tin @u#0 i-än ni-4u dung 0$ +#, ng#fn Tin @u#0 i-än ni-4u dung 0$ +#, ng#fn
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o =$%ng 7#/7 p#no=$%ng 7#/7 p#noo =$%ng 7#/7 H#u+#n=$%ng 7#/7 H#u+#no =$%ng 7#/7 S#nnon=$%ng 7#/7 S#nnon
9#i 0o#/n:9#i 0o#/n: Co nguo4n 0in aU =uCo nguo4n 0in aU =u iiOOiZ&''nb' C#4n +#, o#/ nguo4n 0iniZ&''nb' C#4n +#, o#/ nguo4n 0in0>-1n 0-o +#, 0ong 5-1 0oi $u'0>-1n 0-o +#, 0ong 5-1 0oi $u'
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