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Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Cowolutubn lodls
chasachuisH¢8
.Th cocdes enonotok +he Onccdes aue non-BYSeh
Set to o2. Fplopa Que inAal)y
. p o h enoden n egpon Se it c
Callad s impulse 8ponge
4
Chauacieiati o, each patb deptnou on itdootoris
Polynomial
&Granonakov poyomfal o poh 8rven
D M
Lghe
D Uh't olelay vauiade
Exompl
oP
Pouh
Thven Convoluforad encodas has 2 pouths umbeod 1 2
T impolso Bponseo oh u) m (1o)
T m0 e loo Fino Code woysuguon uu
pon A
9 (D) +D+D
n impulse espons o lo
3(D) +D
oo
ol opon
c(D a'CD) mCD)
DD) (14 D)
lP o pah
o o
ofP o path
D 9*lo) tm D)
(»2)1+4)
D24D +DD54
rMuliple ed o
CI 1o1 4
Lah o o BRqLara h C1tm
25a)
bift>
Exmple -
Conshrucf Hh Convolotional den ho Hh op Lov
Aequonc Tha spe coonS o ha Onuade
Cocle rat e ong k . The gneoy
a 3 (, o)
No Fe'a Mk -)
2-1
M
Sin C h:2 ho o roslolo - addee's
Polh ired
poth
a'(5): "+2
8 (o)
m Io
e'CD) 3'(D m(D),
4D) (up3 D*)
D 4
ole Peh 1 o o
R (D) D n(D)
I4D DtD)
olP o pah a oIo
mulltpl01ed oP I 1,0
ENCODIN CODE TREE
TRELLIS AND 9TATE DIA
H-
A he8e diog ramS ghahle us to
Teprasn
ruoder n
to al propent ros o convowtrona
D
toDE TRe E a loo-loo MM COman -
Fraol Halsall
oGecla îmea oRrxocter
ConsTUtfom
2
Cai ven Hha
b con8ryraol
pofr o callad hela
eachbranchs Covespordîng
Branchir
eochbhodo
o e
T/P .
O
Jha Uppe Curch Co s poncl So e o 4 Thouoe ourd
ory egp9r oAs to
foach bancha ole oopon'r
jncdf co ed on
ootRAclo o each, braich '2 8Cnueckeos
Example
for h qi ven
Crtoder, duothaConvoluHonal
Sequonce
Jnifally
m, m
1
to 2eto (vi
olP P xRa fshe
Conien
r
niially1.
A n a h l a s
R o g ie c o n k e n
Cod
1
sioe)
loo o1
L
ExampleR.
ov h Cohvolutfonal
enccdes hoen belo, dya
m: lo IO
Coclo tTRL Kon on
m
4
X
m ma m
1 3
I o I O
path
Cens9)
Regiatea -t ole
Contet I,243
Drd Stabe8hodlet beL
OoO 14
oloO
o 10
oro
L10
O o
of
' o 0
olo
ojoo
)Whale
weesing wf Ha label on ka branch
et.sinaas olP Codouscd o ms9 Ruence)
CU1ent glahe:
a ms oon nolcote CunenBahe
Alext Akate:
' z
E ampn ts a L9B ndiat e Next Be
Exanple
fo aen Cenvolutfonal encodea, draLoHu 'Alabe
tnol he Coceoond bor h msg sanLoNa io)) .
11 mg
ofP
for evoy m birs
mma s
de ereatcd.
This derote a m m3
L5e 3 mg bys
M )
k 9
) Sfne k3 , Pos'He satea aue 3
Consjclee
or
C O s s
ont
8 B a i e
Slate
e n i c e e l a s t
Trarsit oor 1
oP bars
onen Nal ,
a)
o 0 o0
o o O
b) o
O
C0 ol
O
)
Koo
o
) Coda oord
o ms o
Slaatom 00 oure
i 1 lplou
Example
ov H ven encocde dus he tdte d fog an
Find H Loco uwovd t.lo 0
m, mg m4
Porá Pori ble stak e CuR a a'
(1e LOO lo
Torans °Hfon
CoAen
Ste Raq f e
Con Neo
Sote
ooO
ooo
o 0 00
o01 ooo
0lo
0o
o10''lo
o lo
.oo O
OOO 0
00
o o
olo
0o
o
o O o
o10
Stote Dicora
000
o o0o () To ffn
too
Ofo
Stu rom o oo Sata
C ft o1o 10o ro ootOo
lo
TRE LLIS
Ce Pa 393 -
394 digital comens FOndanas
DIAhRAN
APplica ior and edi
mone,
Th brorh
Pcduq,by i panrad, sioa Soiod b
A
Brosh produceel b ie
At an K . ell,A dicaTao heed red3
epgtesgnt'
-
PoRBe
[late
Tho t rou9 haAA hoole% 'Coepords to Bhet e o0
Coond
T
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications
Error control problems in Digital Communications

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Error control problems in Digital Communications

  • 36. Cowolutubn lodls chasachuisH¢8 .Th cocdes enonotok +he Onccdes aue non-BYSeh Set to o2. Fplopa Que inAal)y . p o h enoden n egpon Se it c Callad s impulse 8ponge 4 Chauacieiati o, each patb deptnou on itdootoris Polynomial &Granonakov poyomfal o poh 8rven D M Lghe D Uh't olelay vauiade Exompl oP Pouh Thven Convoluforad encodas has 2 pouths umbeod 1 2 T impolso Bponseo oh u) m (1o) T m0 e loo Fino Code woysuguon uu pon A 9 (D) +D+D n impulse espons o lo 3(D) +D
  • 37. oo ol opon c(D a'CD) mCD) DD) (14 D) lP o pah o o ofP o path D 9*lo) tm D) (»2)1+4) D24D +DD54 rMuliple ed o CI 1o1 4 Lah o o BRqLara h C1tm 25a) bift>
  • 38. Exmple - Conshrucf Hh Convolotional den ho Hh op Lov Aequonc Tha spe coonS o ha Onuade Cocle rat e ong k . The gneoy a 3 (, o) No Fe'a Mk -) 2-1 M Sin C h:2 ho o roslolo - addee's Polh ired poth a'(5): "+2 8 (o) m Io e'CD) 3'(D m(D), 4D) (up3 D*) D 4 ole Peh 1 o o
  • 39. R (D) D n(D) I4D DtD) olP o pah a oIo mulltpl01ed oP I 1,0 ENCODIN CODE TREE TRELLIS AND 9TATE DIA H- A he8e diog ramS ghahle us to Teprasn ruoder n to al propent ros o convowtrona D toDE TRe E a loo-loo MM COman - Fraol Halsall oGecla îmea oRrxocter ConsTUtfom 2 Cai ven Hha b con8ryraol pofr o callad hela eachbranchs Covespordîng Branchir eochbhodo o e T/P . O Jha Uppe Curch Co s poncl So e o 4 Thouoe ourd ory egp9r oAs to foach bancha ole oopon'r jncdf co ed on ootRAclo o each, braich '2 8Cnueckeos
  • 40. Example for h qi ven Crtoder, duothaConvoluHonal Sequonce Jnifally m, m 1 to 2eto (vi olP P xRa fshe Conien r niially1. A n a h l a s R o g ie c o n k e n Cod 1 sioe) loo o1 L
  • 41. ExampleR. ov h Cohvolutfonal enccdes hoen belo, dya m: lo IO Coclo tTRL Kon on m 4 X m ma m 1 3 I o I O path Cens9) Regiatea -t ole Contet I,243 Drd Stabe8hodlet beL OoO 14 oloO o 10 oro L10 O o of ' o 0 olo ojoo
  • 42. )Whale weesing wf Ha label on ka branch et.sinaas olP Codouscd o ms9 Ruence) CU1ent glahe: a ms oon nolcote CunenBahe Alext Akate: ' z E ampn ts a L9B ndiat e Next Be Exanple fo aen Cenvolutfonal encodea, draLoHu 'Alabe tnol he Coceoond bor h msg sanLoNa io)) . 11 mg ofP for evoy m birs mma s de ereatcd. This derote a m m3 L5e 3 mg bys M ) k 9 ) Sfne k3 , Pos'He satea aue 3
  • 43. Consjclee or C O s s ont 8 B a i e Slate e n i c e e l a s t Trarsit oor 1 oP bars onen Nal , a) o 0 o0 o o O b) o O C0 ol O ) Koo o ) Coda oord o ms o Slaatom 00 oure i 1 lplou
  • 44. Example ov H ven encocde dus he tdte d fog an Find H Loco uwovd t.lo 0 m, mg m4 Porá Pori ble stak e CuR a a' (1e LOO lo Torans °Hfon CoAen Ste Raq f e Con Neo Sote ooO ooo o 0 00 o01 ooo 0lo 0o o10''lo o lo .oo O OOO 0 00 o o olo 0o o o O o o10
  • 45. Stote Dicora 000 o o0o () To ffn too Ofo Stu rom o oo Sata C ft o1o 10o ro ootOo lo TRE LLIS Ce Pa 393 - 394 digital comens FOndanas DIAhRAN APplica ior and edi mone, Th brorh Pcduq,by i panrad, sioa Soiod b A Brosh produceel b ie At an K . ell,A dicaTao heed red3 epgtesgnt' - PoRBe [late Tho t rou9 haAA hoole% 'Coepords to Bhet e o0 Coond T