thesis.pdf [Aland orollari]

§
´
 
624)B¤62H4&
&)(@$'&
02I¦6¨AYQ'08 
$'I
02BB¤A'B
¥
B¤0¨QRH@6Y4I
§
6A2QR0
C
T(©¨

5fsY@#„T5
d¨XVC#¡@4s)(%}#&¨s#&¨%0¨1d¨Bv#&¨%0T#d5
 Q5
!C1%
!6—T(©¨
1!CB¨%c!C1HT(¨
8
¨ 6¡
¢0(Y@41YBf% 5
Ba¨
I

1XQ()5
%l©(@)s©"¨#"u
T(©¨
1!CB¨%c!C1zQ(¨
#d5
VC(
¢0(Y@41YB
%S5
¨z!6
Q(¨

5fsY@#„T5
"¨zVC#¡@)s4(%}(Y@©¨zY@48f2¨%
T(Y@©c@#„¨
B¨d¨#"7'5U1©¨B

9XT(©¨
1!CB¨%}!C1XT(©¨
8
¨ 6¡
¢0(@)1Bf%S5xB¨
I
q
b—t'e4ET6…”bPYcf7W•…hƒaW“sRƒkT7W“Y1Yce)d7bk—6t'b‰rCƒke'd7b¡ 

¤
¦
e4wlsRrxYcb
 
#
¼
Uu†p7–•rƒaW“t'iYcf'b1Vdb5…c…cr4igbdU7W“YR…
r4Y1Ycf'brW“t'p'T'YR…1YaeyYaf'b)ƒaW`skƒkT7W`YCr4t6dFT6…8W“t'izYaf'bCeT'Ycp'T'YR…1exw{Ycf'bCp6r4s”W“Y”†ziurxYcb5…1r…%Ycf'b)ƒcf'b5ƒaƒFU7W`Yk…qw
˜hf'b)ƒke'd7bChbCYcf'bqscbqU7†seU'Ykr‡W“tzW•…rr)f'egscs”W“U7–“b)bqscscegscuƒkescscb5ƒkY‚W`t'izƒke'd7b´rW“Ydf6r…dr’hesRd€e4w{hbkW“if7Y
6Hd
¥
ˆ”…”bqb
“
W`igT'scb
¼
u
 
ŽRw
%‡ehbq|bqs‡'W˜wlYaf'b—igsRr4p'f’W•…errieue'dCbk'p6r4t6d7bqs%isRr4p'f¤Ycf'bqtzYcf7W•…eƒke'd7b%W„…
0
0
0
0
0
1
1
1
1
0
`
#$wDt%Hc
5
´D 
7
ARS
¥
ST024
§¡(&
6A2Q'0YSTA'B¤Q
¥UA'I¦7
C
ARI0U4I
V
H@&4)&
44 £¢¥¤
$'IQ
A'I7
C
&)(@A
 W0
V!$'B¨4)&5C
§R$'&508 
&)(@$'&
B¤0$'Q
&)(44 

4&
$'B¤0£¢¥¦G$'7)7A'&)(@0YB 3$'B¤0¨§
C
rPieue'd’bqscscesau!scb5d7T6ƒaW“t'iyƒke'd7bw

YiW•…ieU7|W“eT6…iYaf6r4Y{hbdƒqr4t’bqt6ƒkejd7bdYaf7W„…eƒke'd7b1W“t’–˜W`t'b5rxshY”W“VdbCˆ8lb
t'bqb5d’Vdbqscbk–“†yƒkegVdp'T'Ycb1Ycf'bh|4r‡–“T'b5…ee4w¨Yaf'bhp6r4s”W“Y”†)i7r4Ycb5…q'b5rgƒcfe4wvf7W•ƒcf€f6r…{rrƒket6…”Ykr4tuYit7T'V—Ubqs
e4wGW“t'p'T'YR…kŽRw
q
be¦W™–˜–t'e4
…”f'e4#Ycf6r4Y¦W`Y‡W•…vpeu…c…8W“U7–“b1Ycedpbqs”wžegscV¤bqsascescu!scb5d7T6ƒkY‚W`egt)etCYcf7W•…iƒkejd7b™W“t
–˜W“t'b5r4s{Y‚W`VPbw

 
 
¡
 T§§©§¢¡
§©¥'¦)£
£

©
¥
 
 
˜¦f'bXd7b5ƒke'd7bqs1t6r4YcT'sRr–™–“†zr…c…‚ejƒaW•r4Ycb5…ib5rgƒcfzU7W“Y%e4wlYcf'bPlegsRdCYcf6rxYiW`Y%scb5ƒkbkW“|b5…e¦W`Yafzet'bde4whYcf'b
iur4Yab5…W“tyYaf'bhbqt6ƒke'dgW`t'i)ƒaW“sRƒkT7W“Y5w
q
b%hW˜–˜–n…cr‡†CYcf6rxY{r1p6r4s”W“Y”†Ciur4YabiW`tYcf'b1ƒaW“sRƒkT7W“YiW„… $'&54! ©¨
0¨QiU7†)r
hesRdPW˜w¨Ycf'beU7W“Yer…c…”e'ƒaW•r4Ycb5dC¦W`YafCYcf'bhiurxYcbiW•…hYcf'bhp6rxs”W“Y‰†re4wYcf'bhU7W“YR…‡r…c…”e'ƒaW•r4Ycb5dC¦W`YafCW“YR…W“t'p'T'YR…qw
xvYcf'bqsc¦W„…‚b6hbehW˜–˜–n…ar5†rYcf6r4Y¦W`Y‡W•…DHI" $'&54! ©¨
0¨Q%ˆ‰…‚bqb
“
W`igT'scb
¼
u
¼
ŽRw¨˜hf'b1d7b5ƒkejd7bqsihW˜–˜–n…”T6ƒqƒkb5…a…8W“|bk–“†
0
1
0
0
1
1
(a)
1
(b)
1
`
#$wDh%
c
%
´¡ 
$£¢
44 D$
 $'&544 
¨
0Q
V!$'B¨4)&5C
§'$'&50C¤ V¥¢
4! DH@I
 W$R&544 
¨
0Q
C
¥'W“pdYcf'bU7W`Yk…r…c…”e'ƒaW•r4Ycb5d%hW“Ycf1Ycf'bW“t'p'T'Yiur4Ycb5…¶W“tXrxt—b ¤esaY¤Yceed7b5ƒkscb5r…”bhYcf'bht7T'V—Ubqse4w6T't6…cr4Y‚W„…‰—6b5d
p6r4s”W“Y”†riur4Ycb5…qw
§
D©¨qCDP©#rAp`DH"Cc
DH
 "#$©
Ap$wu"#$
¥@er‘


wvYcf'bqscb1W•…1r4tW“t'p'T'Y1Ycf6r4YiW•…1r4tW“t'p'T'Y1YceCVdegscbdT't6…cr4Y‚W„…‰—6b5dzYcf6rxts…cr4Y”W•…8—6b5dvp6r4s”W“Y”†yi7r4Ycb5…q
Ycf'bqt
¥'W“p)Ycf'b%|r‡–“T'bhexw€Ycf6rxY¨W“t'p'T'Y5w

(hbqp6b5r4YiT't7Y”W˜–Št'e¢…”T6ƒafCW“t'p'T'YR…‡scbqV¢r‡W“t¤w
˜hf7W•…ir‡–“ies”W“Ycf'V
W•…vb5…c…‚bqtuY”W•r‡–˜–“†)Yaf'bh…cr4Vdb1r…hYcf'bh…”b5fgT'bqt7Y”W•r‡–€bk'p6r4t6d7bqscuƒke'd7bdd7b5ƒkejdgW“t'i)r‡–“iegs”W“Ycf'V
e4wSb5ƒkY”W“et
 
w
¼
u…”e™W“Y¨W•…hb5rg…”†1YceeW“Vdp7–“bqVdbqt7YhW“Yv…”e1Ycf6r4YW“YhYRr4ƒgb5…¨ƒket6…”Ykr4tuYY”W“Vdb‡wžesb5rƒafdW“YcbqsRrxY”W“et¤w
«vYb5rƒcfPW“YcbqsRr4Y‚W`egt¤W“Yvd7b5ƒkscb5r…‚b5…¨Yaf'b{YcegYRr‡–6t7T'V—Ubqshe4w¤T't6…cr4Y”W•…8—6b5drp6r4s‚W`Y”†di7r4Ycb5…q…”e%W“Yvƒqr4trscT'tdw!es
r4YvVPeu…”Yvr%–˜W“t'b5r4s{t7T'V1U6bqsie4w¤W“YcbqsRrxY”W“et6…qw
Y
DPesegAh%~£
5™£a§i¦©¨
 

¤
¦

¨
Ba¨#"5
©¨B‡6w#„!C7F@hB¨V…#&¨¨
ˆA6§
 
6‘Ž

5UsY@a#&T5
"¨VC#¡@)s4(

¨¡—¨¨1r@v%w¨'!6
¢
5f1)s)2d%
@)1B
¢
#
 
sY@a#"5
¡9
V
@©"¨%H%S2©(gT(Y@©'@)8f8|%0¨d%o!a6‚@©H7z!)%0
i
¢
5f1)s)2d%
¨
sY@41YB

9@f6"@ "!$#‰!6
@©'8
¨@©%0
–
&
U
6zd
¥
˜
I
§
%0% 2)7z¨AQ(Y@©XT(©¨A%0¨k$2¨1©T5
@48—¨#"#„!$#
¢0#&¨Bm2Y T5
!C1
@48
V4!
#d5
Q()7
5
%HVC5
©¨1
@f—!$#yBnT(Y@©
#&¨%0¨7

8
¨%
@z !CB¨—!$#yB
!6
 

¤
¦
¨a ¨s
T(Y@©c@©
7z!)%0
i
¢
#
 
!6
Q(¨'5U14s)2"%x(Y@©¨

¨¨1o !$#"#"24s"¨B
@41YB
@©}7
!4%w
i
¢
#
 
!6‰Q(¨XV
@©d¨%X(Y@©©¨

¨¨1A !
#d#"2)s©"¨B
I}p
(¨1)u~@{6yd¨#—T(¨'"¨#d7'5U1Y@©T5
!C1'!6
Q(¨'%0¨k$2¨1Q5
@48
¨#"#„!$#
¢0#&¨Bm2Y T5
!C1o@48
V)!$#d5
T(47ouC@©c7z!)%0
i
¢
#
 
!6—T(¨
5U1)s42"%z‚5U8U8

¨' !$#"#"24s"¨B
I

 R 
 
£¦¥
¡'§¢¡
¥
 
¥S¥
£
©
¡¢¡
¢W¥
¡R£


¥'©
¡£¡£¢W¥
¥¡§§©@§¢¡
©§§©¥'¥£
£
©
¥c
§1C© ‘
q
brhW˜–˜–v–“bqY
¤
d7bqt'egYcbCYcf'b)ƒkescsaT'p'Ycb5dW“t'p'T'YR…±
€Ycf'bC…8W“­qb)e4w
¤P
 Yaf'bCtuT'V1U6bqs1e4w
T't6…cr4Y‚W„…‰—6b5dp6r4s”W“Y”†)iurxYcb5…ihW“Ycf’W“t'p'T'YR…iW“t¤r¤r4t6d
¤XYcf'b1tuT'V1U6bqs%e4w¦…ar4Y”W•…8—6b5d’p6r4s”W“Y”†)iurxYcb5…ihW“Ycf
W“t'p'T'YR…‡W“t
¤¢w
q
b—¦W™–˜–¨|gW“bq
Ycf'b1p6r‡W“s%ˆ
 ¤§!'Ž¨r…‡Ycf'bd…”YRrxYcbee4w¨Ycf'b1r‡–“ies”W“Ycf'V)w
q
bh¦W™–˜–—6sR…‚Y¸…”f'e4
Ycf6r4Y‡W˜w
i
¢
#
 
(

(
i
¢GYcf'bqtzYcf'bqscb%W•…e…”eVPbhW“t'p'T'Y™W`t€Vdescb1T't6…cr4Y‚W„…‰—6b5dYcf6r4tz…cr4Y‚W„…‰—6b5d)p6rxs”W“Y‰†
iur4Yab5…qw˜hf'bhbk'p6r4t6…8W“et’e4wŠYcf'b%isRr4p'frW“Vdp7–˜W“b5…iYcf6r4Y
 'd¦¤
e
€
¼
 
6zd
¥
ƒ
'
ˆ
¼
w
¥
Ž
0rƒafyi7r4YcbdhW“YcfFr4tW“t'p'T'Y%W`t
¤ rƒqƒkeT't7YR…‡wžegs—r4Yi–“b5r…”Y%et'bdhW“scbX–`b5r‡|gW“t'i
¤rw

YeW•…™p6eu…c…‰W`U7–“b
Ycf6r4Yhrg…eV¢r4t7†yrg…
i
¢#
 
e4wvYcf'b¢…cr4Y‚W„…‰—6b5dp6r4s”W“Y”†iur4Ycb5…ihW“YcfvW`t'p'T'Yk…eW“t
¤¤rxscb¢…cr4Y‚W„…‰—6b5dU6b5ƒqr4T6…‚b
Ycf'bq†f6r‡|b1et7–“†et'bdhW“scb1w!sceV
¤r2U'T'YhYcf'bq†f6r‡|b1U6bqbqtƒkescscT'p'Yab5dw¢˜hf'b1scb5…”Y%V1T6…”Yef6r‡|b1Y‰he
hW“scb5…¦wžsaeV
¤¢w
#†)ƒkeT't7Y”W“t'idYcf'b¦6
1¦W`sab5…h–“b5r‡|W“t'i
¤d'hbeeU'Ykr‡W“t
6

e§ 
d¦¤cdˆ
¤
 3i
¢
#
 
Ž

6
xd
i
¢
#
 
e§ 'd
 
¤
ˆ
¼
w
 
Ž
¹¨eV1U7W“t7W“t'i¢b5fgT6r4Y”W“et6…™ˆ
¼
w
¥
Ž€r4t6dvˆ
¼
w
 
ŽRhbi—6t6d
¤
(
€
¥
 
6
 V¥
ƒ
}d
i
¢
#
 
§
rxt6d
 
e
€
¥
 
6}d
 
ƒ

 3i
¢
#
 
'
ˆ
¼
w
¼
Ž
q
f'bqt
i
¢‡e

e
i
¢
#
 
‘lbif6r‡|b
 ’›
6

#
 
7…”edYcf'bqsabeV—T6…‚YvU6bh…”egVdbiW“t'p'T'YvW“t)VPescbeT't6…cr4Y‚W„…‰—6b5d
Ycf6r4t)…ar4Y”W•…8—6b5dCp6rxs”W“Y‰†riur4Yab5…qw
˜2eh…”f'e4‚Yaf6r4YYcf'b{r‡–“iegs”W“Ycf'VµV1T6…”YYcbqsaV1W“t6r4YcbvhW“Ycf
$(
i
¢
#
 
ghb¦…‚f'eœYcf6r4Y%™V—T6…‚Ylr‡–“vr‡†j…
U6b’–“b5…c…rYcf6rxt
i
¢Gw
q
byr…a…”T'VdbYcf6r4Yd‡f'bqtŒYaf'bvr–`iges”W“Ycf'V
U6bqi4W“t6…

(
i
¢
#
 
r4t6dªYcf'bqscbkw!escb
 
(
6
i
¢
#
 
d
i
¢
#
 
we«e…iYcf'bdr‡–“ies”W“Ycf'V
p'sce'ƒkbqb5d'…q
 vV—T6…‚Y¸…”Yab5rdgW˜–`†zd7b5ƒkscb5rg…”bw
%‡e4hbq|bqs5‘W™whYcf'b
r‡–“ies‚W`Yaf'V
W„…™bq|bqsiW“tsrr…”YRr4Ycbrˆ
 2§‘ŽW“tzvf7W•ƒaf
C¨
i
¢GYcf'bqtzb5fgT6r4Y”W“etFˆ
¼
w
¼
ŽlheT7–•d…W“Vdp7–“†zYcf6r4Y
 ve
6
i
¢
#
 
d
¼)i
¢
#
 
7vf7W•ƒaf)heT7–•dCUb—rdƒket7YcsRrgdgW„ƒkY‚W`egt¤w
˜¦fuT6…qgYcf'b{r‡–“iegs”W“Ycf'VµV1T6…”Y¨r‡–“vr‡†j…nV¢r‡W“t7YRr‡W“tdYcf'b{ƒkegt6dgW`Y‚W`egtCYcf6r4Y%d–
i
¢Gw¨˜hf7W•…nW“Vdp7–˜W“b5…hYcf6r4Y
Ycf'bhr‡–“iegs”W“Ycf'V¤ƒqr4t't'eY‡YcbqscV1W“t6r4Ycb%T't7–“b5…c…hW“YhW•…¦W“tyrd…”Ykr4Ycb‡W`t’vf7W•ƒcfP–
i
¢
#
 
w
q
bvf6r‡|bvp'sce4|b5d1Yaf6r4Y
 

¤
¦
W•…hr4tdbqscscegscu!scb5d7T6ƒaW“t'idƒkejd7bie4w¤sRr4Ycb
 
#
¼
rxt6d1bqscscesau!scb5d7T6ƒkY”W“et
¥
#
 
w

 
 
¡
 T§§©§¢¡
§©¥'¦)£
£

©
¥
 


YhW•…{r–„…‚edp6eu…a…8W“U7–`b1Yce1pbqs”wžegscV„bqscscegscu!scb5d7T6ƒkY”W“et’etCYcf7W•…{ƒke'd7biW“t)p6r4skr‡–˜–`bk–w
§
AAp
p$DHp
DE"ucvDE "#rB©VAp$wC
#$
¥qe

“
eshb5rƒafrW“t'p'T'Y5ƒkeT'tuY‡Ycf'betuT'V1Ubqs{e4wT't6…cr4Y‚W„…‰—6b5dCp6r4s”W“Y”†riur4Ycb5…Yced‡f7W„ƒafCW“YhW•…ir4trW“t'p'T'Y5w

“
eseb5rgƒcfW“t'p'T'Y1Ycf6r4Y™W•…—rxtW“t'p'T'Y—YaeCVdescbdT't6…ar4Y”W•…8—6b5d€Ycf6r4ts…crxY”W•…8—6b5dzp6rxs”W“Y‰†iurxYcb5…q
¥'W“pFYcf'b
|r‡–“T'b%e4w€Yaf6r4YW`t'p'T'Y‡w

YhW•…vb5rg…”†¢YaehW“Vdp7–“bqVdbqt7YeYcf7W•…vr‡–“iegs”W“Ycf'V¤r…vrPƒket6…”YRr4t7Ycud7bqp'Ycf)ƒaW“sRƒkT7W“Yee4wG–˜W“t'b5r4s¸…‰W`­qbw
Y
DPesegAh%~£
5™£
5q¦©¨
 

¤
¦

¨ABa¨#"5
©¨Bf60#&!C7
@fB¨VC#„¨¨
ˆA6§
 
6‘Ž

5UsY@a#&Q5
"¨
VC#y@4s)(

¨¡—¨¨1g@
%0¨}!6
¢
5U14s)2"%
@41YB
¢
#
 
sY@a#"5
¡9fV
@©"¨%z% 2Y©(Q(Y@©X@)8f8|%0¨d%X!6c@H7z!)%0
i
¢
5U14s)2"%'¨$sY@41YB

9
@
6"@Y d!$#‰!6l@©
8
¨@©%0
–
&
U
dsš
˜
6
u™6¡!$#
@419
še›
 
#
6
I
§
%0% 2)7z¨'T(Y@©}T(¨s@#y@48f8
¨8
¨#d#&!$#
¢0#„¨B$2Y Q5
!C1A@48
V4!
#d5
Q()7D5
%cVC5
¨1A@
—!$#yBxT(Y@©c#„¨%0¨7

8
¨%
@H !mBa¨—!
#¡BH!6
 

¤
¦
¨a ¨s
T(Y@©
@
7z!)%0

(
i
¢
#
 
!6~Q(¨'5U1)s42"%z(@©¨

¨¨1
 !$#"#d2)s"¨Bmu
@41YBf@©l7z!)%0

(
i
¢
#
 
!6
Q(¨'V
@©"¨%z(@©¨

¨¨1A !$#"#"24s"¨B
Icp
(¨1)u~@{6yd¨#
Q(¨X¨¨©2T5
!C1
!6—T(¨
sY@#¡@48U8
¨8)¨#d#&!$#
¢0#„¨B$2Y Q5
!C1o@48
V)!$#"5
Q()7'um@©}7z!)%0
xd¡ 
¦
ˆ
 
d
 
š‹Ž
¥
d
 
š
'
ˆ
¼
w
 
Ž
!6—T(¨
5U1)s42"%}c5f8U8

¨o !$#d#"2)sd¨B
I
§1C© ‘
q
bhhW˜–˜––“bqY
¤„d7bqt'egYcbhYcf'b1…”bqYie4wlƒkescscT'p'Yab5drW“t'p'T'YR…q
G
Ycf'b—…”bqYie4wlƒkesascT'p'Ycb5drW“t'p'T'YR…
Ycf6r4YPwr‡W˜–¸Yce¥'W“p¤er4t6d@¥
Yaf'by…”bqYCe4weW“t'p'T'YR…rYaf6r4Y¢hbqscb’es”W“i4W“t6r‡–˜–“†
ƒa–“b5r4t¤vU'T'YC‡f7W„ƒaf@U6b5ƒkeVPb
ƒkescsaT'p'Ycb5drUu†rYcf'bep6r4skr‡–˜–`bk–Gbqscscescu!sab5d7T6ƒkY”W“et)r‡–“ies”W“Ycf'V’w
q
behW˜–˜–Š–“bqY{©€ˆ¥¤XŽR7Ycf'bet'bkW“if7U6esR…¦e4w&¤P
d7bqt'eYcbrYcf'b)…”bqY%e4w{p6r4s‚W`Y”†zi7r4Ycb5…eYaf6r4YdƒketuYkr‡W“tzW“t'p'T'YR…%W“t¤Pw
q
b¢¦W™–˜–v–“bqY
F¨
 
¤
 ˜
 
F¨
 
G
 ˜
¢¢%¨
 
¥
 ˜'r4t6d@Q6
X¨
 
©€ˆ¥¤1Ž
 ˜w
q
beU6bqi4W“tUu†CegU'YRr‡W“t7W“t'i)r1U6eT't6d’et
 …W`tYcbqsaV¢…he4wQ7w¤0|bqsc†PW“t'p'T'YiW“t
G
W•…{r4t…W“t'p'T'Y{YceCr4Y
–“b5r…”Y{rg…hV¢r4t7†‰…ar4Y”W•…8—6b5d)rg…hT't6…cr4Y”W•…8—6b5d…p6r4s”W“Y”†¢i7r4Ycb5…qwG«vYvVPeu…”Y
ie4wYcf'b5…”bh…cr4Y‚W„…‰—6b5dCp6r4s”W“Y”†riur4Ycb5…
r4scb1…cr4Y”W•…8—6b5d…U6b5ƒqr4T6…‚b—Yaf'bq†Cf6r5|gbeU6bqbqtzƒkescscT'p'Yab5dwv˜hfuT6…±²r4Y¦–`b5rg…”Y
¦£¢
¢
"
 
ee4wYcf'b%hW“scb5…h–“b5r‡|gW`t'i
G
bqt6d’W“trrp6r4s”W“Y”†iur4Ycb1Ycf6r4YhƒkegtuYRrW`t6…er…hW“scb1w!sceV
r4t'egYcf'bqsebk–“bqVdbqtuY%e4w¤dwd˜hf7T6…q2Ycf'b¢…”bqY
¤
ƒqr4tCf6r‡|bhr4Y‡Vdeu…”Y
6

 
6© 

 
d

 

 e 
 
£¦¥
¡'§¢¡
¥
 
¥S¥
£
©
¡¢¡
¢W¥
¡R£


¥'©
¡£¡£¢W¥
¥¡§§©@§¢¡
©§§©¥'¥£
£
©
¥c
t'bkW“if7U6esR…±w
#b5ƒqr4T6…”behbef6r‡|bh…”bqY‡Ycf'betuT'V1Ubqs{e4wt'bkW“if7U6esR…‡e4w'¤‘YcePU6b
Q6
67hbeeU'YRrW`t
Q6

(
6

 
6© 

 
d

 
6
© 
 
(
ˆ
¥
 
QgŽA6
}d

 
 
(
 
ˆ
¥
 
QgŽ~d
 

6

ˆ
¼
w
ˆjŽ
‡bkjY5‘lbe¦W™–˜–U6eT't6d
¢CW“t)YabqscV¢…he4w
QhU7†)…”f'e4hW“t'idYcf6rxY
¢’–
Q
 
–
&
U
d
š
˜
d
 
¦
¢
®
U
dsš
'
ˆ
¼
w
 
Ž
«e…c…”T'VdbvU7†dvr‡†he4w¤ƒket7YcsRrdgW•ƒkY”W“etrYcf6r4YYcf7W•…GW•…nwr‡–•…”b7r4t6dX–`bqYh¥
'Ub¸r%…”T'U6…”bqY¨exw2¥¦e4w¤…8W“­qbebk‘rƒkY‚–`†
s
’
ˆ


¯'°
Ž
¯¡ 
¡£¢


¯'°
w
0¨rgƒcf1W“t'p'T'YhW“t)¥7W„…hr4tPW“t'p'T'YvYce1r4Y–“b5r…”Y
6
#
 
T't6…ar4Y”W•…8—6b5drp6r4s”W“Y”†diurxYcb5…qw¤«‡YlVPeu…”Y

e4wYcf'b5…”b%iur4Ycb5…vƒqrxt)U6b%T't6…cr4Y”W•…8—6b5d’Ub5ƒqr4T6…”bhYaf'bkW`sep6rxs”W“Y‰†riur4Yabef6r…hU6bqbqtzƒkesascT'p'Ycb5dwv˜hf'beeYaf'bqsR…
V1T6…”YhUb¢T't6…ar4Y”W•…8—6b5dFU6b5ƒqrxT6…”bCYcf'bq†f6r‡|b‰rxtW“t'p'T'Y1W“t
¤rw)˜hf7T6…qGYcf'brtuT'V1Ubqs—exw¦p6rxs”W“Y‰†€iur4Ycb5…
ƒket7YRr‡W“t7W“t'idW“t'p'T'YR…¦W“t)Ycf'bh…‚bqY¤
#¢¥

W•…{r4YhVde7…”Y
6¡Q
}d
6
 
 
¥

 ©d
"'
q
bd¦W™–˜–{…”bqY1šd›
 
#662vf7W•ƒcfFhW˜–˜–lW“Vdp7–“†zYaf6r4Y
 
¥
##¤@ G–
i
¢G…”e’Ycf7W•…—…‚bqYhV1T6…”Yebk'p6r4t6dzU7†zr
wrƒkYceshe4w¨r4Yh–“b5r…”Y
–
&
U
d
š
˜
w¨˜hf7T6…q'hbeeU'YRrW`t
€
¼
 
dš0ƒ
 
¥

#
¤
 '–
6
Q
}d
6
 
 
¥

 ©d
4§
vf7W•ƒafyƒket7YcsRrdgW•ƒkYR…¦eT's{r…c…‚T'Vdp'Y”W“et)r4UeT'YvYcf'b1…8W“­qbhe4w¨¥
†w
#†zƒkeV1U7W“t7W“t'iyb5fgT6r4Y”W“et6…Xˆ
¼
w
ˆjŽ¦r4t6d
ˆ
¼
w
 
Žk6hb1—6t6d€Ycf6r4YeYcf'bPtuT'V1U6bqs%e4w¦ƒkegscscT'p'Ycb5d’W“t'p'T'YR…
r‡w!Ycbqsvr4t)bk'b5ƒkT'Y”W“et’e4w€Yaf'bep6r4sRr‡–˜–“bk–€bqsascescu!scb5d7T6ƒkY‚W`egt)r‡–“ies”W“Ycf'VW•…ir4YvVde7…”Y
ˆ 
d
¢GŽ

(

Q
 
–
&
U
dsš
˜
d
 
¦
¢
®
U
d
š
d
 
ˆ
¥
 
QgŽ~d
 

6
¨

–
®
U
d
¼
š
 
 
š$Q
˜
d
 
¦
d
–
®
U
dš
˜
"
 
¦
®
U
dsš
–
xd
 
¦
ˆ
 
d
 
škŽ
¥
d
 
š
'

 
 ¡ 
 T§§©§¢¡

©@§§©¥'
¥¨)£
£

©
¥
 
 
message
Good Code
parity
bits
bits
`
#$wD
%
c
£
´«³ie7ejdCƒke'd7bhbqV1U6b5d'd7b5d…W“tyrxtCbqscscescu!sab5d7T6ƒkY”W“etyƒke'd7bw
q
b¢ƒqr4t’W“YcbqsRrxYcbdYcf7W•…hr–`iges”W“Ycf'V
rCƒket6…”Ykr4tuYet7T'V1U6bqsee4whY”W“Vdb5…iW“tzegsRd7bqshYcePw!T'scYcf'bqshsab5d7T6ƒkbdYcf'b
t7T'V—Ubqs{exw€ƒkescscT'p'Yab5drW“t'p'T'Y{U7W“YR…±w
¢
£¢
"2131¡8165“&(¡41313)9&@©3•B
&(¡pE”)uG
˜hf'b%V¢r‡W“trW•d7b5rPW`t’eT's{ƒket6…‚YcscT6ƒkY”W“et’e4wŠ–˜W“t'b5r4scu!Y‚W`VPb—bqt6ƒke'd'r4U7–“bdr4t6dCd7b5ƒke'd'r4U7–“b—bqsascescuƒkesascb5ƒkY”W“t'i
ƒke'd7b5…eW•…1Yae)T6…”brYcf'bP–™W“t'b5r4sau!Y”W“Vdb)bqt6ƒke'd'r4U7–“b)r4t6dFd7b5ƒkejd'r4U7–“b’bqscscescu!sab5d7T6ƒaW`t'izƒke'd7b5…1scb5ƒkT'sR…‰W`|gbk–`†w

Vrr4i4W“t'b1vf6r4Yvf6r4p'pbqt6…ivf'bqt)hb%YRr4ƒbhrPie7ejdrbqscsaescuƒkescsab5ƒkY”W“t'i‰ƒke'd7bhe4w–“bqt'iYafy¢Fr4t6dCT6…”b%Ycf'b
hesRd'…e4wYcf7W•…{ƒke'd7b—rg…hYcf'beVdb5…c…ar4ibeU7W“YR…he4w¨r4tCbqscsaescu!scb5d7T6ƒaW“t'iCƒkejd7bPˆcSbqb
“
W“iT'scb
¼
u
 
ŽRw
q
bet'e4
f6r‡|bvr4t1bqscscesauƒkescscb5ƒkY”W“t'ieƒkejd7b‡e4w²isab5r4Ycbqs2–`bqt'igYcfdhW“Ycfdrif7W“if'bqs¨bqsascescu!Ycex–`bqskr4t6ƒkb
4f'e4lbq|gbqs5‡W“Yf6r…
Ycf'b1…cr4Vdb%tuT'V1U6bqsie4wVdb5…c…crxibhU7W“YR…ir…‡Ycf'bhes‚W`ixW`t6r–nƒke'd7bwv˜¤ePW“t6ƒkscb5r…”b1Ycf'b%tuT'V1Ubqs{e4wVdb5…c…ar4ib
U7W“YR…‡W“tYcf'b—ƒke'd7bhbhhW˜–˜–nƒksab5r4Ycb—rPt'bqµ…”bqYie4wVdescb%Vdb5…c…cr4igbhU7W“YR…qr4t6d’bqt6ƒkejd7b1Ycf'b5…‚bhVdb5…c…ar4ib
U7W“YR…¦W`tzr4t’bqscscesau!scb5d7T6ƒkY”W“etyƒke'd7bw
q
b%Ycf'bqt)T6…”b%Ycf'b—ƒaf'b5ƒaƒCU7W`Yk…ve4w¨Yaf7W„…‡bqscscegscu!scb5d7T6ƒkY”W“etƒkejd7b1r…
Ycf'beVdb5…a…cr4ibeU7W“YR…‡e4wŠYcf'b%bqscscesauƒkescscb5ƒkY”W“t'i¢ƒke'd7behbh·‰T6…‚Y{ƒket6…”YcsaT6ƒkYcb5dˆcSbqb
“
W“iT'sab
¼
uˆ7ŽRw
q
f'bqthbyrxp'p7–`†Yaf7W„…rƒket6…”YascT6ƒkY”W“et‚sab5ƒkT'sR…8W“|bk–“†vhbr—6t6dYaf6r4Ydt'eYdegt7–`†f6r‡|bChbd7bk—6t'b5d
Ycf'b1bqscscegscuƒkescscb5ƒkY‚W`t'iCƒke'd7bU'T'Yelb%f6r‡|b—ƒkscb5rxYcb5dr1–˜W“t'b5r4scu…8W“­qbCƒaW“sRƒkT7W“YhYcf6r4Y‡bqt6ƒkejd7b5…™Ycf'b1bqscscescu
ƒkescsab5ƒkY”W“t'i
ƒke'd7bw#y’escbqe4|bqs5Yaf'b)eT'Ycp'T'YPe4w¸b5rgƒcfœiur4YcbCe4weYcf7W•…rƒaW`skƒkT7W`YrW•…rrsƒaf'b5ƒaƒU7W`Yre4weYcf'b
bqscscegscuƒkescscb5ƒkY‚W`t'iƒke'd7bwµ˜hf7W•…rhW˜–˜–hU6bYcscT'bhW“Ycfœet'bz…”V¢r‡–˜–ebk‘ƒkbqp'Y”W“et¤´Fhby…‚f'eT7–•d#ƒcf'e7eu…”br
U6bqYaYcbqs1U6r…”bCƒqr…”bPwžes%eT'shsab5ƒkT'sR…8W“et¤wz˜hf'brp6bqs”w!escVrr4t6ƒkb¢exw{eT's—ƒke'd7bChW˜–˜–vU6b)dgW•ƒkYRr4Ycb5d€U7†zYcf'b

 
 
 
£¦¥
¡'§¢¡
¥
 
¥S¥
£
©
¡¢¡
¢W¥
¡R£


¥'©
¡£¡£¢W¥
¥¡§§©@§¢¡
©§§©¥'¥£
£
©
¥c
(a)
R
k
message
Good Code
parity
bits
bits
(b)
C
k+1
R’
k-1
`
#$wD
%
c
x
´
8(@0
B
062HBg W4
©20U6¨ARI" &5B¨H62&54)A'IPA¤E1¥
¥
C
 
$
¢
4! 
&)(@0U02BB
ARB¦¥¤B
0Q'H624)I¨§
6¨AYQ'0UA'I
&)(0
I¦02S
1308 I W$
§'0
4)&6 
C
 0
¢
44 D&)(@0
02BB
ARB¦¥¤B
0Q'H624)I¨§U6A2Q'0
V
7
$'60¨Q
A'I
&5AV
A¤E
&)(0
0YB¨B¤A'B
¥
6A'BB¤0¨6Y&54I
§
6A2QR0
C
fgT6r‡–˜W`Y”†dexw¶Yaf'b¸ƒke'd7b{Yaf6r4Y¨hb{ƒaf'eue7…”b¸rg…eT'sU6r…”bw¨˜hf7T6…qglbiV¢r‡†hvr4t7Y¨Yae—ƒaf'eueu…‚b{r%p6r4scY”W•ƒkT7–•r4s”–“†
ie7ejdCƒke'd7bhexw€…”V¢r‡–˜–ŠU7–“e'ƒcƒr–“bqt'iYaf¤w¨«it'eYcf'bqs{ƒkegt6…”YcsRr‡W“t7YW„…‡Ycf6r4Yhhbhd7et

Y‡ƒut'e4@Ycf6r4YvhbehW˜–˜–ŠUb
r4U7–“beYce%—6t6drie7ejdrbk'p6r4t6d7bqsvigsRr4p'f6…e4w€…”Vrr‡–˜–€…8W“­qbw
%‡ehbq|bqs‡Ycf'bqscbhd7bk—6t7W“Ycbk–“†…W„…‡…”eVdbeƒket6…”YRrxtuY
…8W“­qb—rwžYcbqshvf7W•ƒaf)hbehW˜–˜–€Ubhr4U7–“bhYce%—6t6d…ieue'drbk'p6r4t6d7bqs{igsRr4p'f6…q'r4t6drvf7W•ƒaf)hbehW˜–˜–nƒaf'e7eu…”beYce
U6b%Ycf'beU7–“ejƒaƒr–“bqt'iYcf’e4w€egT'svU6r…”bhƒke'd7bw
q
behW˜–™–Gt'e¦p'scb5…”bqt7Y{r%w!escV¢r‡–¤d7b5…cƒks”W“p'Y”W“ete4wŠegt'bewr4V1W˜–“†¢e4w¨…”T'pbqsRƒket6ƒkbqt7YcsRr4Ycegs{ƒkejd7b5…±w
q
b
p'sce4|gW„d7b%Ycf7W•…vd7b5…cƒks”W“p'Y”W“etU7†‰d7b5…aƒks”W“U7W`t'iCYaf'bhbqt6ƒke'dgW`t'iCƒaW“sRƒkT7W“YR…‡w!eshYcf'b5…”b—ƒke'd7b5…qw
 
DHG 
"#
9#$©
©)G"9qDH
 F© "D©PAH
C¤ F!BDHG)‘

¹¨f'e7eu…”bhr4U6…”ex–`T'Yabhƒket6…”YRr4t7YR…
er4t6d@6w

¹¨f'e7eu…”bhr1ƒkejd7b

 
e4wG–“bqt'iYcf
 
ƒ
 
 
uskr4Ycb
¥
#
 
jrxt6dCr…–•r4scibeVXW`t7W“V1T'V
dgW•…”YRr4t6ƒkb1r…p6eu…a…8W“U7–`bw

¬bqYe¥
 
U6b—rrƒaW“sRƒkT7W“YeYcf6r4YvYkr4ƒb5…
 
 
U7W`Yk…{r…¦W“t'p'T'Yhr4t6dCp'saejd7T6ƒkb5…
¼
ƒ
 
 
U7W`Yk…er…heT'Ycp'T'Ye…”erYcf6r4Y
Ycf'b5…”biU7W“YR…YRr4ƒbqtrYceibqYaf'bqsw!escV
r1ƒke'd7bqhesRdPe4wI
 
wˆ‰˜hf'b
 
 
W“t'p'T'YR…¦U7W`Yk…lrxscb{Yaf'b{Vdb5…a…cr4ibiU7W“YR…
e4wŠYcf'b1ƒkejd7br4t6drYcf'bhegYcf'bqsR…hr4scbeYcf'b1ƒcf'b5ƒaƒrU7W`Yk…qw˜Ž

“
es

›4x–`bqY¡ 
¥
r4t6d¢ 

¥
UbhƒaW`skƒkT7W`Yk…hYcf6r4Yhbqt6ƒke'd7bhr4t¢bqsascescu!scb5d7T6ƒkY‚W`egt‰ƒke'd7bee4w¤sRr4Ycb
 
#
¼
hW“Ycf

 
 ¡ 
 T§§©§¢¡

©@§§©¥'
¥¨)£
£

©
¥
 
£
 
¥
Vdb5…c…ar4ibeU7W“YR…vr4t6d
 
¥
#
 
ƒaf'b5ƒcƒCU7W“YR…qr…vd7b5…cƒks”W“Ub5dCW“t€Sb5ƒkY”W“et
¼
w
 
w

˜¤eXwžesaV¤ƒaW“sRƒkT7W“Y—¥
¥
wžscegV¤¥
¥
’
®
6Ykr4ƒbhrrƒkepu†Cexw
 
¥
r4t6d’T6…”bhYcf'b™W“t'p'T'YR…ie4w
 
¥
r…‡Ycf'beW“t'p'T'YR…
e4w¨¥
¥
wi«¸d'd¥
¥
’
®
YcedYcf'bdƒaW“sRƒkT7W“YhU7†rW•d7bqtuY‚W™w!†gW`t'i’Ycf'b1eT'Ycp'T'Yiiur4Ycb5…‡e4w
 
¥
hW“YcfYcf'beW“t'p'T'YR…ie4w
¥
¥
’
®
w
“
W“t6r‡–˜–“†²r4YaYRrƒaf‰rdƒkegpu†re4w
 

¥
¯®
U7†PW„d7bqt7Y”W˜w!†W“t'iCr‡–˜–ŠYcf'beW“t'p'T'Yer4t6dreT'Ycp'T'Y‡iur4Ycb5…e4wYcf'b
ƒkep7†Ce4wl¥
¥
’
®
hW“Ycf)Ycf'b%W“t'p'T'YR…ie4w
 

¥
¯®
we˜hf'b1eT'Ycp'T'Yiiur4Yab5…ve4wl¥
¥
hW˜–˜–¨U6bdr‡–˜–¨Ycf'b™W`t'p'T'Y1r4t6d
eT'Ycp'T'Yvi7r4Ycb5…e4w¨¥
¥
’
®
r‡–“et'idhW“Ycf’Ycf'beeT'Ycp'T'Yvi7r4Ycb5…he4w
 

¥
¯®
ˆcSbqb
“
W“iT'scb
¼
uˆjŽRw

¬bqY%
¥
UbdYcf'bdsRrxYcb
¥
#
 
ƒke'd7bdeU'YRr‡W“t'b5d€Uu†YRrxƒW“t'i
 
¥
VPb5…c…cr4ibPU7W`Yk…qw!bqb5dgW“t'iyYaf'bqV W“tuYae)¥
¥

r4t6drT6…8W“t'irYcf'b
¼
ƒ
 
¥
egT'Ycp'T'YvU7W“YR…ir…Ycf'bhp6r4s‚W`Y”†Cƒcf'b5ƒaƒ'…he4wYcf'bhƒkejd7bw
q
bhƒqr4t)d7b5ƒkejd7b%Ycf'b5…”b1ƒkejd7b5…¦W“tC–˜W“t'b5r4s¸…‚b5fT'bqt7Y”W•r‡–ŠY”W“Vdbw