Chng 4. M ho knh kim sot li trong truyn dn v tuyn s 90 Chng 4 M
HA KNH KIM SOT LITRONG TRUYN DN V TUYN S 4.1. GII THIU CHUNG 4.1.1.
Cc ch c trnh by trong chng Cc phng php m ha knh kim sot li Cc m khi
tuyn tnh Cc m xon Cc m turbo v gii m MAP 4.1.2. Hng dn Hc k cc t
liu c trnh by trong chng Tham kho thm [1],[2], [7],[8]. 4.1.3. Mc
ch chng Hiu nguyn tc m ha knh kim sot li Hiu c hot ng ca cc b m ha
knh kim sot li in hnh nht trong cc h thng thng tin v tuyn hin i
Thit k c cc b m ha knh kim sot lin gin 4.2. M U Thng thng m ho knh
l qu trnh x l tn hiu s c thc hin sau ngun tin s v trc iu ch. Mt
trong cc nhim v ca m ho knh l kim sot li. M ho knh kim sot li l qu
trnh x l tn hiu s m bo truyn dn thng tin s tin cy knh thc t. Trong
phn ny chng ta s xem xt cc k thut m ho kim sot li bng cch b sung
cho h thng cc k hiu d n thng tin pht c th thc hin c hai nhim v pha
thu: pht hin li v sa li.Nhim v ca nh thit k h thng truyn dn s l
cung cp mt h thng kinh t truyn thng tin t ni pht n ni nhn tc v mc
tin cy m ngi s dngchpthun.Haithngsquantrngmnhthitkctrongtaykhinyl:
thng s tn hiu c pht v rng bng tn ca knh truyn dn. Hai thng s ny cng
vi mt ph cng sut ca tp m thu xc nh t s gia nng lng mt bit PDF
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http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 91 tnhiuvmtcngsuttpm,Eb/N0.Tsnyxcnhntrtsbitli BER (Bit
Error Rate) i vi mt s iu ch cho trc. Cc thit k thc t thng t ra mt
gii hn gi tr m ta cth phn b cho Eb/N0. Trong thc t tu theo hon cnh
ta thng phi s dng mt s iu ch m vi s ny khng th m bo cht lng s liu.
i vi t s Eb/N0 c nh cch duy nht t c cht lng s liu quy nh l s dng m
ho knh. Mtngcthctinkhcdnnvicsdngmhoknhlgimts Eb/N0yu cu i vi t s
bit li (BER) cnh. Nh vic gim ny ta c th gim
cngsutphthaygimgithnhphncngchnghnsdngantenkchcnh hn. Kim sot li m
bo s ton vn ca s liu c th c thc hin bng hiu chnh li trc FEC
(Forward Error Correction). Hnh 4.1a cho thy m hnh ca mt h thng
thng tin s s dng phng phpny. B m ho knh nhn cc bit ca bn
tinvbsungthmccbitdtheomtquytccquynhtrc,vthtora lung bit c m ho c tc
cao hn. B gii m s dng cc bit d quyt nh bit no ca bn tin l bit thc t
c pht. Mc ch ca vic kt hp gia m ho v iu ch (hnh4.1.b) l gim thiu
nhhng ca tp m. Ngha l gim thiu s li gia u vo ca b m ho (ly t ngun
tin) v u ra ca b gii m knh (cung cp cho ngi s dng).
NgoiFECcncmtphngphpkhccgilyucuphtlitng
(ARQ:AutomaticRetransmissionRequest)cngcsdnggiiquytvn kim sot li.
ARQ s dng cc bit k hiu d pht hin li. Datrn kt qu pht hin limy thuyu
cu pht li bn tin bmc li, v th cn phi cmtknh hi tip.
Hnh4.1.Mhnhngincahthngtruyndns.a)Mhaviuch knh ring bit; b) M ha knh
v iu ch kt hp. Vic b sung cc bit d vo bn tin dc m ho cn dn n vic cn
thit tng rng bng thng.PDF created with FinePrint pdfFactory Pro
trial version http://www.fineprint.comChng 4. M ho knh kim sot li
trong truyn dn v tuyn s 92 Ngai ra vic s dng m ho cn lm tng tnh phc
tp ca h thng, nht l vic thc hin gii m knh my thu. Nh vy cc suy xt
khi la chn vic s dng m ho knh cn bao hm c cc cn nhc v rng bng tn v
tnh phc tp. T cc vn nu ra trn ta c th pht biu mc tiu ca m ho knh
kim sot li nh sau: 1. Pht hin li: Xc inh on no ca lung s thucha li.
Thng bo cho ni gi hay ni nhn v li. Gim thiu xc sut khng pht hin li.
2. Sa li: tcsgimxcsutli(haytsbitli,BER)chotsEb/N0nh trc. i vi xc
sut li cho trc gim gi tr Eb/N0. Lng gim c gi li ca m ho i vi xc sut
li . Ccyucuphthinvsalicxcnhtrchtbikiuthngtinc pht. S khi chc nng ca
mt my pht s dng m ho knh c cho hnh 4.2.T hnh ny ta thy: Tc bit u ra
ca b m ho R lun lun ln hn tc bit,Rb.. T l m c th c nh ngha nh sau:
T l m = Rb/R . Hnh 4.2. S khi ca my pht s dng m ha knh 4.3. CC
NGUYN TC M HA KNH KIM SOT LI Ta xt mt s nguyn tc c s thc hin m ho
knh kim sot li. C th pht biu vn c bn khi thc hin m ho knh ny nh
sau: ta mun chuyn i m bn tin c th c vo m t m . Cc t m ny phi tha mn
cc mc tiu v pht hin v sa li. Chng hn ta xt mt bn tin bao gm 3 bit.
Vi 3 bit ny c th c: 23 = 8 bn
tincthc.Tamunthaythtngbntinnitrnbngmttm.Nhni PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 93 trn t c iu ny ta
s dng cc bit d. Khi ny cc t m s di hn bn tin tng ng m t n c to ra.
Ta c th phn tch cc kh nng pht hin li v sa li cu cc m d khc nhau
bngcchtrchtnhnghakhongcchHamminggiahaitm.Khongcch Hamming gia hait
m bt kc cng di c nh ngha l s v trm
chngkhcnhau.TacthmtkhongcchHammingnybngmtkhnggian nhiu chiu (hnh
4.3). Hnh 4.3. Trnh by t m ba bit khng gian ba chiu Gi s ta c mt bn
tin nguyn t bao gm mt s "0" hay mt s "1". Khi bn tin l 0 ta pht i
"000", cn khi n l "1" ta pht i "111". T hnh lp th hnh 4.3 ta
thykhongcchgiahaitmngnitrnlbng3vchuyntmttm ny sang t m khc phi
chuyn dch theo ba cnh. By gi ta li gi thit rng bn tin bao gm ba bit
v s dng tt c cc t hp bit cu ba bit ny truyn bn tin. T hnh v4.3 ta
thy tt cc ccnh ca hnh lp th u c s dng biu th cc bn tin. Mi li xy ra
mt trong ba bit u dn nchuynvomtnhbncnhvsdnnli.Trongtrnghpnynu khong
cch ca tpht v thu l mt th chc chn s mc mt li v t thu c l mt trong s
cc bn tinc th c.Ta ci thin tnh trng trn bng cch tng khong cch. Chng
hn cc t m : 0000, 0011, 0101, 1001, 1010, 1100, 1111 u c khong cch
ti thiu l 2. i vi bn t m ny ta cn mt hnh khng gian c 16 nh biu din.
Hay tng qut ta cn mt khng gian n chiu.
Gisxyramtlimtvtrcatmbnbitnitrn:tathuc1000 chng hn. My thu c th nhn
nh rng t m ny c th l mt trong hai t m gn t thu nht : 0000 hay
1010.Trnghpnychcthphthinclichkhngsacli.Bygita xt cc t m gm: 01111,
01000 v 10011. Khong cch cc tiu gia chng by gi l 3. Nu thu c mt t m
01001 th mt my thu thng minh c th nhn nh t m c pht phi l 01000 v y
l t m gn vi t thu c nht (c khong cch
nhnht=1).Byggithittthucl01011,mythuchcthnhnnh rng t pht c th l mt
trong hai t: 01000 v 10011, v khong cch cu t thu vi PDF created
with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 94 hai t ny u bng2. Vy trong trng hp ny my thu ch c th pht
hin c li ch khng sa cli. Khi ny ta ni rng m trn cho php pht hin li
kp v sa li n. Tccthdtrntacthnuracngthcchunglinquannkhongcch Hamming
ti thiu gia cc t m v s bitli m m cho php pht hin v sa nh sau: * Kh
nng pht hin li: dm = t+1 (4.1) * Kh nng sa li: dm 2t +1 (4.2) trong
dm l khong cch Hamming cc tiu gia cc t m c th c trong tp m cn t l s
li m cho php pht hin (trng hp th nht) v sa (trng hp hai). Cc m knh
thng c phn thnh hai loi : m khi tuyn tnh v m xon, di y ta s xt c th
hai loi m ny. 4.4. CC M KHI TUYN TNH Trong loim nylung thng tin c
chia thnh cc khi c di bng nhau c gi l cc khi bn tin. Cc bit nhn c u
ra ca b m ho c gi l t m. Cc bit d c b sung vo cc khi theo mt thut
ton nht nh ph thuc vo loimcsdng,ccbitnythngcgilccbitkimtra.Ccmkhi c
xc nh bng ba thng s: di khi bn tin k, di t m n v khong cch Hamming
cc tiu dm. T s r = k/n c gi l t l m. Cc bit kim tra c di n-k. B m
ho c k hiu (n,k). S khi tng qut ca mt b m ho khi tuyn tnh c cho hnh
4.4. . Hnh 4.4 S tng qut ca b m ha khi
Hotngcabmhocthcbiudintonhcdngmatrnhaya thc. Cc ma trn hay cc a thc
ny c gi l cc ma trn to m hay cc a thc to m. PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 95 4.4.1. Ma trn to
m Trong phn ny ta s nh ngha hai ma trn quan trng cho b m ha khi
tuyn tnh: ma trn to m cho php xc nh t m u ra v ma trn kim tra chn l
cho php kim tra tm nhn c ti pha thu.
Taxtcchbiudinmatrntomchobmhokhituyntnh.Gasmt khi bn tin k bit : m0,
m1, ........, mk-1 c a vo b m ho, u ra ca b m ho cho ta t m dng
chui bit sau: b0,b1 ,....., bn-k-1, m0,m1, ......,mk-1 trong mj l
cc bit ca khi bn tin, cn bi l cc bit kim tra, cc bit ny c gi
lccbitchnl,ccbitcchscaolccbitcnghalnhnvctruyn trc. Nh vy u vo b m
ho c th c 2k khi bn tin v tng ng u ra c 2k t m c s dng trong s 2n t
m c th c. Ta c th biu din k bit bn tin vo dng vect v 1 k sau y: m =
[m0, m1, ..........,mk-1] (4.3) Tng t c th biu din n-k bit chn l vo
dng vect 1(n- k)sau: b = [b0, b1, ........., bn-k-1](4.4) Ta k hiu
c l vet u ra ca b m ho nh sau: c = [c0, c1, ..........., cn-1](4.5)
trong
' + +1 ...., , 1 , ,1 .., , 1 , 0 ,n k n k n i mk n i bcn k
iii(4.6) n-k bit chn l u ra cab to m c xc nh nh sau: b = mP(4.7)
trong P l ma trn k(n-k) xc nh theo cng thc sau: PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 96
11111111]1
1 , 1 1 , 1 1 , 01 , 1 1 , 1 1 , 00 , 1 0 , 1 0 , 0.....
........... . .. . .. . ...... ............... ..........k k n k kk
nk np p pp p pp p pP (4.8) vi i = 0,1,...,n-k-1 l ch s ca ct v j =
0,1, ..., k-1 l ch s ca hng, pij=0 hoc 1 ty thuc vo vic bi c ph
thuc vo bit bn tin mi hay khng. Ma trn to mc xc dnh nh sau: G =[
]kI PM (4.9)
trong Ik l ma trn n v kk:
1 0 .......... 00 1 .......... 0. . .. . .. . .0 0 .......... 1
1 1 1 1 1 ]kI(4.10)
Khi ny ma trn t m c xc nh nh sau: c = mG (4.11) Ma trn kim tra
chn l Hl ma trn (n-k)n c xc nh nh sau: [ ]Tk nP I H M (4.12)
Syndrome Syndrom cho php xc nh t m nhn c c b mc li hay khng v thm
ch c mu li khi tha mn iu kin trong phng trnh (4.2) Ta xt qu trnh
gii m. Ta k hiu y l mt vect thu c c kch thc l 1 n
nhnctvicphtivectxtrnmtknhctpm.Tabiudinvectyl tng ca vect thu x v
vect li egy ra do tp m: PDF created with FinePrint pdfFactory Pro
trial version http://www.fineprint.comChng 4. M ho knh kim sot li
trong truyn dn v tuyn s 97 y = c +e(4.13) Vect e c gi l vect li hay
mu li. Phn t ei ca vect ny bng khng nu phn t tng ng ca ybng phn t
tng ng ca c. Ngc li phn t ei bng 1 nu phn t tng ng ca y khc vi phn
t tng ng ca c, khi ny xy ra mt li v tr i. Nh vy vi i = 1, 2, ......
, n ta c:
ei = 1 khi mt li xy ra v tr i ei = 0 khi khng c li(4.14)
Mythucnhimvgiimvectctvectythuc.giimngita thng tnh ton mt vect 1
(n-k) c gi l Syndrome. c im ca Syndrome l n ch ph thuc vo mu li.
Syndrome c xc nh nh sau: s = y HT (4.15) Syndrome c cc thuc tnh
quan trng sau y. Thuctnh1:Syndromechphthucvomulichkhngphthucvotm c
pht. Thuctnh2:Ttcccmulikhcnhaunhiunhtmttmuccng Syndrome. i vi k bit
bn tin ta c 2k vect t m khc nhau c biu th bng : ci, i= 0,1, 2, 3,
.... , 2k-1. Tng ng i vi mt mu li e bt k ta c th nh nghi 2k vect ei
khc nhau nh sau: ei = e + ci i=0,1, 2, . . ., 2k-1 (4.16) ch khc
nhau nhiu nht mt t m. Tp cc vect {ei , i = 0,1,2,3, ... , 2k-1}
theo nh ngha trn c gi l Coset ca
m.NimtcchkhcmtCosetcng2kphntkhcnhaunhiunhtmtt m. S cc t hp t m c th
c ca mt m khi tuyn tnh (n,k)l 2n trong ch c mt b 2kt m l c s dng,
vy tng s b 2k t m c th c l 2n-k v tng ng s c 2n-k Coset c th c
(trong chc mt Coset l tng ng vi b t m c s dng). * i vi vect y thu
c, tnh Syndrome s = yHT * Trong tp Coset c c trng bi Syndrome trn
chn tamuli c xc sut ln nht. Gi n v e0. PDF created with FinePrint
pdfFactory Pro trial version http://www.fineprint.comChng 4. M ho
knh kim sot li trong truyn dn v tuyn s 98 * Tnh vect m cho u ra: 0e
y+ ' cLu rng s hc mun 2 th tr cng ging nh cng. Trng lng Hamming cc
tiu TheonhnghathtrnglngHammingcamttmltngsccvtrbit
khckhngtrongtmny.Tacngcthcoitrnglngnylkhongcch
Hamminggiamttmkhckhngvitmtonkhng.Dothuctnhcam khi tuyn tnh l tng
(hoc hiu) hai t mbt klun lun bng mt t m th ba cu m, nn c th ni rng
trng lng Hamming cc tiu ca cc t m khc khng ca m khi tuyn tnh chnh
bng khong cch Hamming cc tiu. kt thc phn ny ta xt th d v m Hamming.
Th d 4.1 Ta xt mt h m c gi l m Hamming c cc thng s sau y: di t m n=
2m -1 S cc bit bn tink = 2m - m -1 S cc bit chn l n - k = m trong
m3 lm th d ta xt m Hamming (7,4)c n=7 v k=4 tng ng vi m=3. Ma trn
to m ca m ny phi c cu trc ph hp vi phng trnh (3.13) v c dng nh sau:
43 4 2 1 3 2 1MMMMk1 0 0 00 1 0 00 0 1 00 0 0 11 0 11 1 11 1 00 1
1I PG1111]1
(4.17) Ma trn kim tra chn l tng ng c dng sau: 3 2 1 3 2 1MMTk
n011111101011001010100P IH111]1
(4.18) PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 99 Cc t m c tnh theo phng trnh (4.14) v c cho bng 4.1. Bng
4.1 Cc t ca m Hamming (7,4) Bn tin T mTrng lng Bn tinT mTrng lng
0000 0001 0010 0011 0100 0101 0110 0111 0000000 1010001 1110010
0100011 0110100 1100101 1000110 0010111 0 3 4 3 3 4 3 4 1000 1001
1010 1011 1100 1101 1110 1111 1101000 0111001 0011010 1001011
1011100 0001101 0101110 1111111 3 4 3 4 4 3 4 7
Tbng4.1tathytrnglngnhnhtcacctmkhckhngl3,vy khong cch Hamming cc tiu
dmin = 3. Tt nhin cc m Hamming c thuc tnh l khong cch Hamming cc
tiu lun lun bng 3 khng ph thuc vo m. Do dmin = 3 nn t cc phng trnh
(4.1) v (4.2) ta thy cc m ny ch c th sa c mt li vpht hin c hai li.
Quan h ny cho m Hamming (7,4) c cho bng 4.2. Bng 4.2. Bng gii m cho
m Hamming (7,4) Syndrome Mu li 000 100 010 001 110 011 111 101
0000000 1000000 0100000 0010000 0001000 0000100 0000010 0000001
4.4.2. a thc to m PDF created with FinePrint pdfFactory Pro trial
version http://www.fineprint.comChng 4. M ho knh kim sot li trong
truyn dn v tuyn s 100Trong phn ny ta xt vic s dng a thc to m xy dng
cc b to m vng. M vng l mt tp con ca m tuyn tnh. Cc m ny c xy dng
trn c s cc thanh ghi dch c hi tip. Mt m c gi l m vng khi n th hin
hai thuc tnh c bn sau: 1. Thuc tnh tuyn tnh: tng ca hai t m cng l
mt t m. 2. Thuc tnh vng:Mi s dch vng mt t m s cng l mt t m. Ta c th
biu din t m l mt vect n-1 thnh phn nh sau: c = (c0, c1 , . . . . ,
cn-1)(4.19) Hay dng a thc bc (n-1) sau y: c = c0 + c1 x+ c2x2 + . .
. . + cn-1 xn-1 ( 4.20) trong cc h s ci = 0/1, v mi lu tha ca x tng
ng vi dch vng mt bit theo thi gian. V thkhi ta nhn a thc (4.20) vi
x c ngha l dch vng mt bit
sangphi,vvyxnphibng1vbitngoicngbnphichuynthnhbitngoi cng bn tri. Qu
trnh nhn v dch vng nh vy thng c biu din nh sau: xc(x) mod (xn - 1)
= cn-1 +c0 x + . . . . + cn-2 xn-1(4.21) trong mod c ngha l chia ch
ly phn d. Tng t nu nhn biu thc (4.21) vi x2 , ta cdch vng hai bit
sang ph nh sau: x2 c(x) mod (xn - 1) = cn-2 + cn-1 x + . . . . . +
cn-3xn-1(4.22) Mt m vng (n,k) c c t bi tp y cc a thc bc (n-1) hay
thp hn v nhn mt a thc bc thp nht (n-k) lm tha s. Tha s c bit ny ck
hiu l g(x) vc gi la thc tom cam ny. a thc tomg(x) tng ng vi ma trn
to mG m ta xt phn trc. a thc to m ca m vng c cc thuc tnh sau. Thuc
tnh 1: a thc to m ca mt m vng (n,k) l n nht ngha rngn l a thc t m
bc (n-k) cc tiu duy nht. Thuc tnh 2: Mi bi s ca a thc to m g(x) l
mt a thc t m mi, xc nh nh sau: c(x) = a(x)g(x)mod(xn-1) PDF created
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http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 101trong a(x) l mt a thc ca x. Hay: Mt a thc bc n-1 hay
thp hn l mt a thc t m ch v ch khi n l bi s ca g(x). g(x) l a thc to
m c biu din nh sau: g(x) = g0 + g1x + g2x2 + . . . . .+ gn-kxn-k
(4.23) trong gi={0,1} Cnm(x) l a thc ca khi bn tink bit c biu din
nh sau: m(x) = m0 + m1x + m2x2 + . . . . . . . + mk-1xk-1(4.24) Gi
s ta c cho mt a thc to m g(x) v phi m ho mt khi bn tin (m0, m1, . .
. . , mk-1)vo mt m vngh thng vo dng sau:
,_
4 4 3 4 4 2 1 4 4 3 4 4 2 11 k 1 0 1 k n 1 0m , . . . . . , m ,
m , b ., . . . . , b , b (4.25) n-k bit chn l k bit bn tin Ta c th
vit a thc t m nh sau: c= b0+b1x++bn-k-1xn-k-1+ m0xn-k++ mn-1xn-1
=b(x)+ xn-km(x)(4.26) trong : b(x)= b0+b1x++bn-k-1xn-k-1
xn-km(x)=m0xn-k++ mn-1xn-1 l a thc t m c dch vng n-k Ta chiaa thc
xn-km(x) cho a thc tomg(x) v nhn c thng a(x) v phn db(x) nh
sau:
x n k( x )( x )( x )( x )( x ) +mgabg (4.27) hay : xn-k m(x) =
a(x)g(x) + b(x) (4.28) trong : a(x) = a0 + a1 x + . . . . . + ak-1
xk-1(4.29) PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 102v: b(x) = b0 + b1 x + . . . . . + bn-k-1 xn-k-1 (4.30)
Trongshcmun2b(x)=-b(x),nntacthvitliphngtrnh(4.26)nh sau: c(x)= b(x)
+ xn-k m(x) = a(x)g(x)(4.31) Bc ca phn db(x) lun lun nh hn bc ca s
chia: n-k. Cc h s ca phn db(x) chnh l cc bit chn l.T phn tch trn ta
c th tng kt cc bc trong qu trnh thc hin m ho cho mt m vng (n,k) nh
sau: 1. Nhn a thc bn tin m(x) vi xn-k. 2. Chia xn-k m(x) cho g(x) c
phn d b(x). 3. Cng b(x) vi xn-km(x) nhn c a thc t m c(x). a thc to
m g(x) v a thc kim tra chn l h(x) l cc tha s ca a thc 1 + xn nh
sau: h(x) g(x) = 1 + xn(4.32) trong h(x) l mt a thc chn l dnh ngha
nh sau: h(x)g(x)mod(xn-1) = 0 (4.33) hay t phng trnh (4.31), ta c:
h(x)c(x)mod(xn-1) = 0(4.34)
Thuctnhnycungcpchotacschnathctomhayathckimtra chn l. Chng hn ta c
th pht biu rng nu a thcg(x) l mt a thc bc n-k v
ngthilmtthasca1+xnthnlmtathctomcamtmvng (n,k). Tng t ta c th pht
biu rng nu h(x) l mt a thc bc k v ng thi l
thasca1+xnthnlmtathckimtrachnlcamvng(tunhon) (n,k).
Mithasca1+xncbc(n-k)(sccbitchnl)ucthcsdng nh mt a thc to m. Khi gi
tr n ln, a thc 1 + xn c th c nhiu tha s bc n-k. Mt s trong s ny to
ra cc m vng tt cn mt s khc li to ra cc m vng
tihn.Vntmracchchnmvngttlmtvnrtkhmccnhbc hc mt nhiu cng nghin cu.PDF
created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 103Th d 4.2Cc m Hamming minh ho cc vn lin quan n vic trnh
by a thc chocc m vng ta kho st qu trnh to ra mt m vng (7,4) cho m
Hamming.Vi di t m n = 7, ta thc hin khai trin a thc 1 + x7 vo ba a
thc tha s ti gin nh sau: x7 + 1 = (1 + x)(1 + x2 + x3) (1 + x + x3
) athctiginlathckhngthphnchiathnhthasbngcchsdng ccathc c cchs lm c
s hai. Mt athc ti gin bcm c gi la
thcnguynthunutntiquanhn=2m-1,trongnlbccaathc1+xn chia ht cho a thc
nguyn thu. Vy th d ang xt ta ch c hai a thc nguyn thuy l (1 + x2 +
x3) v (1 + x + x3). Gi s ta chn: g(x) = 1 + x + x3 lm a thc to m vi
bc bng s cc bit chn l, th a thc kim tra chn ls l a thc sau: h(x) =
(1 + x) (1 + x2 + x3) =1 + x + x2 + x4 c bc bng s cc bit ca khi bn
tin.By gi ta s xt cc th tc to m cho mt khi bn tin 1001 bng cch s
dng a thc to m ni trn.Trc ht ta vit a thc khi bn tin nh sau: m(x) =
1 + x3 Nhn a thc bn tin vi xn-k = x3, ta c: x3 (1 + x3) = x3 + x6
Sau ta chia tch trn cho a thc to m nhn c phn d b(x). PDF created
with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 104+ ++++ ++ ++36 336 4 344 22x x 1x xx xx x xxx x xx x Ta
c th vit li kt qu chia trn nh sau:
x x1 x xx xx x1 x x3 63323++ + + +++ + Vy ta c a thc ca thng
vphn d l: a(x) = x + x3 b(x) = x + x2 Nh vy theo cng thc (4.31) ta
c a thc t mcn tm :
c(x) = b(x) + xn-k m(x) = x + x2 + x3 + x6 Kt qu ta c t m l:
0111001. Bn bit bn phi 1001 l cc bit ca khi bn tin. Ba bit bn tri l
cc bit kim tra chn l. Ta thy t m ny ging nh mt t m c trong bng 3.1
cho m Hamming (7,4).Ta c th tng qut ho kt qu ni trn bng cch pht biu
rng mi m vng c to ra bi mt a thc nguyn thu l mt m Hamming c khong
cch cc tiu bng 3. S b m ho vng Trong phn trc chng ta thy rng th tc
m ho vng (n,k) bao gm ba bc sau: 1. Nhn xn-k vi a thc bn tin m(x)
2. Chia tch trn cho a thc to m g(x). PDF created with FinePrint
pdfFactory Pro trial version http://www.fineprint.comChng 4. M ho
knh kim sot li trong truyn dn v tuyn s 1053, Cng phn d b(x) vi tch
xn-k m(x) c a thc t m cn tm. Ba bc ni trn c thc hin b lp m c cho
hnh 4.5 bao gm mt thanh ghi dch (n-k) tng c mch hi tip tuyn
tnh.1g2g1 n kg Hnh 4.5. B to m vng Thanh ghi ny bao gm cc Flip-Flop
hay cc phn t tr. Cc Flip-Flop ny c th nhn mt trong hai trng thi: 0
hay 1. Mt ng h ngoi (khng c hnh v) thc hin iu khin tt c cc
Flip-Flop. Ngoi cc Flip-Flop, b lp m li c mt tp hp
ccmchcngmun-2thchincngmun-2giauracaFlip-Flopvi mch hi tip. Cui cng
l cc b nhn nhn chng vi nhau. Chng hn nu gi = 1 th b nhn c ngha l
"ni trc tip", cn nu gi = 0 th b nhn c ngha l "khng ni". Mi ln c sn
tng ca xung ng h, ni dung ca thanh ghi dchli dch i mt v tr theo
chiu mi tn. Hot ng ca s hnh 4.5 nh sau: 1.u tin cc flip-flop c t vo
khng v kho chuyn mch CM1 pha trncasvtrngmch,vkhochuynmchphadivtr
di.kbitbntindchvoknhvbtomtora(n-k)bitchnltrong thanh ghi dch (nhc
la rng cc bit chn l ny c cng gi tr nh cc h s ca phn d b(x) ). 2.
Sau kho chuyn mch trn ngt v kho chuyn mch di chuyn vo v tr trn. Ni
dung ca thanh ghi dch c dch vo knh. Th d 4.3. B lp m vng Hamming
(7.4) Hnh 4.6 cho ta s ca b lp m to ra m vng Hamming (7,4) t b to m
sau: g(x) = 1 + x + x3. PDF created with FinePrint pdfFactory Pro
trial version http://www.fineprint.comChng 4. M ho knh kim sot li
trong truyn dn v tuyn s 106 Hnh 4.6. B to m vng (7,4) vi g(t) =
1+x+x2 m t hot ng ca b lp m ny ta xtchui bn tin u vo l (1001). Thay
inidungcathanhghidchsaumilndchvomtbitthngtinccho bng 4.3. Sau bn ln
dch ni dung ca thanh ghi dch v cc bit chn l tng ng l (011). Vy nu
gn cc bit ny vo cc bit bn tin ta c t m (0111001). Kt qu ny ging ht
th d 4.1. Bng 4.3. Ni dung thanh ghi dch th d 4.3 khi bn tin vo
(1001) DchBit voNi dung thanh ghi 1 2 3 4 1 0 0 1 000 (trng thi u)
110 011 111 011 Syndrome Gi thit t m c = (c0, c1, . . . . , cn-1) c
truyn trn mt knh c tp m. dn n thu c t m y = (y0, y1, . . . . .,
yn-1). Bc u tin gii m cho mt m khi tuyn tnh l phi tnh Syndrome cho
t m thu. Nu Syndrome bng khng th t thu khng b li, ngc li nu
Syndrome khc khng th t ny b mc li v cn sa n. i vi m vng dng h thng
th c th tnh ton Syndrome d dng. Gi thit t thu c trnh by dng a thc
sau y: y = y0 + y1 x + . . . . . + yn-1 xn-1(4.35) tnh Syndrome ta
chia a thc y(x) cho a thc to m g(x). Gi s a(x) l thng cn s(x) l phn
d ca kt qu chia, ta c th biu din y(x) nh sau: PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 107 y(x) = a(x) g(x)
+ s(x)(4.36) Phn ds(x) l mt a thc bc n-k-1 hay thp hn. a thc ny c
gi l a thc Syndrome.Nu a thc Syndromes(x) khckhng, th c nghi lpht
hin thy s c mt ca li truyn dn t m thu c. B tnh ton Syndrome c s
ging nh b to m ch khc ch cc bit ca t
mthuccavo(n-k)tngcathanhghidchchitiptphabntri (xem hnh 4.7). Sau
khi cc bit cu t m thu dch ht vo thanh ghi dch, ni dung ca thanh ghi
ny s xc nh syndrome s. Bit c s ta c th xc nh c mu li v a ra c quyt
nh sa nh xt phn trc. 1g2g1 n kg
Hnh 4.7. B tnh syndrrome Th d 4.4B tnh syndrome cho m Hamming
vng (7,4) ivimHammingvngctobibtomg(x)=1+x+x3,stnh syndrome c cho
hnh 4.8. Hnh 4.8. B tnh syndrom cho m vng (7.4) vi a thc
g(x)=1+x+x2 Ga s t m pht l (0111001) v t m thu l (0110001); ngha l
bit gia b sai. Ni dung thanh ghi dch ca b tnh syndrome trong trng
hp ny c cho bng 4.4. PDF created with FinePrint pdfFactory Pro
trial version http://www.fineprint.comChng 4. M ho knh kim sot li
trong truyn dn v tuyn s 108 Bng 4.4. Ni dung b tnh syndrome hnh 4.8
khi t m thu (0110001) DchBit voNi dung thanh ghi 1 2 3 4 5 6 7 1 0
0 0 1 1 0 000 (trng thi u) 100 010 001 110 111 001 110 Sau by ln
dch syndrome c xcnh bng 110. V syndromekhc khng tm nhn c b mc li. T
bng 4.4 ta c mu li tng ng l 0001000, ngha l bit gia ca t m b li.
4.4.3. ki m ha li m ha c nh ngha l vic s dng m ha knh sa li cho php
gim t s Eb/N0 i bao nhiu ln m vn gi nguyn xc sut li bit. li m ha G
c biu din dB nh sau: G(dB)= b b0 0u cE E[dB] -[dB]N N _ _ , ,
trong ch s "u" v "c" k hiu cho khng m ha v m ha tng ng. 4.5. M
XON 4.5.1 M u Mtmkhituyntnhcxtccphntrccctrngbihais nguyn, n v k, v
mt ma trnhay a thc to m. S nguyn k l s bit hay k hiu ca khi bn tin
du vo ca b lp m, cn s nguynn l tng s bit hay k hiu cu t m u ra ca b
lpm. r= k/nc gi l t lm, l s o nh gi lng d c b sung. M xon c trnh by
bi ba s nguyn: n, k v K, trong r = k/n cng c gi l t l m nh trng hp
hp m khi.S nguyn K c gi l di hn ch ; n th hin s ln dch cc i ca mt
nhm k bit bn tin m trong nhm k bit ny vn cn gynh hng u ra b to m.
Mt c tnh quan trng PDF created with FinePrint pdfFactory Pro trial
version http://www.fineprint.comChng 4. M ho knh kim sot li trong
truyn dn v tuyn s 109ca cc m xonkhc bit so vi cc m khi l b to m ca
chng c b nh, nn qu trnh to ra n phn t u ra ca cc b lp m ny khng ch
ph thucvo k bit u vo m cn ph thuc v (K-1) tp hp k bit u vo trc .
4.5.2. To m xon S tng qut ca mt b lp m xon c cho hnh 4.9.1 2..k...1
2..k...1 2..k...M b nh(thanh ghidch) v i k phn t mib nhChuivo k bi
t(mil n dch k bi t)n b cng modul -2Chuit mra Hn 4.9. S tng qut ca b
to m xon t l m k/n Mxonctorabngcchchomtchuibitthngtiniquacctngnh
(thng l cc thanh ghi dch tuyn tnh tuyn tnh trng thi hn ch). Tng qut
cc b nhtrong b m ho xon bao gm M tng (k bit mi tng) v n b to hm i s
tuyn tnh dng cng modul-2 nh hnh 4.9. Cc bit s liu u vo ca b m ho c
dch vo b nh mi ln k bit. S cc bit u ra ca b lp m cho mi ln dch k
bit u vo l n bit, trong kP(v,c)2,thtrnhnh4.16taloibngdn lin tc v ch
xt tip ng dn t nt. ng dn c duy tr c gi l ng dn sng st. i vi quyt nh
cng, s o ng dn c th tnh theo cng thc sau: PM(v,c) =Iii =1d (4.48)
trongdilkhongcchHamminggiacckhiuthuvcckhiucatm c(m) c xt ti nhnh i
hay cn c gi l s o nhnh.. Thay v chn PM(v,c) ln nht theo phng trnh
(4.48) ta c th chn PM(v,c) nh nht khi thay du "-" trong phng trnh
ny thnh du "+"nh sau: PM(v,c) = min _ ,Iii =1d (4.49) Phng trnh
(4.48) ch ra rng ta phi chn ng dn c tng khong cch Hamming ca cc
nhnh so vi chui thu l nh nht.
DiytastrnhbygiimquytnhcngtheoViterbichosmha c xt trong trn hnh 4.11
v th d hnh 4.15, trong chui k hiu thuc chuyn thnh 0 v 1 nh trn hnh
4.16. Lu rng trn hnh ny cc nhnh c nh nhn bng khong cch Hamming gia
cc k hiu thu v cc k hiu m c xt. S0=002S1=10S2=01S3=11Chui bit c
pht: 1 1 01 1t1 t2 t3 t4t5t6T m c pht: 11 01 11 11 10Chui k hiu
thu11 01 01 10 1001102111102201111200211112002S o nhnh PDF created
with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 120Hnh 4.16. Biu li ca b gi m cho th d trn hnh 4.15.
Hnh4.17mtchnngdnsngsttithiimt4chocholitrnhnh
4.16khigiimxon.Trnhnh4.17,tronghaingdnhinhpvocngmt trng thi ti thi
im t4, b gii m chn ng sng st cho ng c s o tch ly
theokhongcchHammingnhhnvluktqunyvobnhsdngcho vic chn ng dn sng st
ti thi im t5 tip theo. Hnh 4.17. Chn ng dn sng st ti thi im t4 cho
gii m Viterbi PDF created with FinePrint pdfFactory Pro trial
version http://www.fineprint.comChng 4. M ho knh kim sot li trong
truyn dn v tuyn s 1214.6. M TURBO 4.6.1. M u
Ccmturbolnutinctrnhbytihinghthngtinquctvonm 1993. Trc mi ngi u tin
tng rng t c hiu nng gn vi gii hn Shannon, cn thc hin b gii m c phc
tp v tn hoc gn nh v tn. M turbo c xy dng trn c s m PCCC (Parallel
Concatened Convolutional Code: m xon mc ni song song). M ny bao gm
nhiu b m ho thnh phn. t c hiu nng tt, cc m thnh phn phi l cc m hi
quynhng khng nht thit phi l cc m h thng. Tuy nhin n gin cc m thnh
phn thng c sdnglccmhthngvvthccmRSC(RecursiveSystematic
Convolutional: M xon hi quy h thng) thng c s dng. i vi b m ha RSC t
l m 1/n vi b nhM, khong cch t dohiu dng gii hn trn c xc nh nh sau:
( )1ee2 ( 1) 2 2Mfrd n + + (4.50) Ngoi ra du bng trong cng thc trn
t c khi m trn to m c dng sau: 1 1( ) ( )( ) 1, ,....,( ) ( )ng x g
xg xQ x Q x 11 ] (4.51) Trong Q(x) lmta thc nguyn thytrn GF(2) bc
M, g1(x), gn-1(x) lcca
thckhcQ(x)cdng(1+.+gixp++xM),p=1,,M;gi(0,1);xltonttrv thng k hiu D
c s dng thay cho n. PCCC c xy dng trn c s ba tng sau: Chuyn i cc m
xon khng h thng vo cc m xon h thng
Sdnggiimvommramm.Thayvsdngccquytnhcng,b gii m s s dng cc xc sut v s
liu thu to ra u ra mm. u ra ny cng cha thng tin v mc chc chn ca cc
bit u ra Cc b m ha v gii m hot ng hot ng trn cc phin bn c hon v ca
cng mt thng tin. iu ny t c bng cch s dng b an xen. Gii thut gii m
lp da trn hai khi nim sau cng ni trn s tinh lc u ra sau mi bc lp
ging nh u my turbo trong my bay. Chnh v th m ny c gi l m turbo. Di
y ta s xt nguyn l xy dng PCCC cho m turbo PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 122 4.6.2. Cc m xon
h thng M xon c coi l m xon h thng (SC: Systematic Convolutional)
khi cc bit thng tin c atrc tip ra u ra. Trng hp ngc li m xon c coi
l phi hthng.TronghccmSC,ccmhiquyccbitquantmvchngc hiu nng tt hn cc
m phi h thng khi t s tn hiu trn tp m thp. Li l c tm quan trng trong
vic th hin gii thut MAP. Li m t hai tnh cht ca mt b m ha khi chuyn
t mt trng thi ny sang trng thi khc. Ta xt mt m xon hi quy h thng
(RSC) c bn trng thi trn hnh 4.18. dkck0kS1kS Hnh 4.18. M xon hi quy
h thng t l y l mt m xon c t l m do c mt u v v hai u ra. di b nh ca
n bng 2 (c hai phn t nh) v di hn ch l 3. Ta thy rng Q=1112=78 v
g1=1012=58. Vy y l b m ha c nh ngha bi a thc 5/7. Ma trn to m trong
trng hp ny c xc nh theo phng trnh sau: _
,1( )( ) 1,( )g xgxQx _+
+ + ,2211,1xx x(4.52) Ti u ra ca b m ha ta nhn c chui m:
C1,N=(c1, c2,ck.., cN)(4.53)
TrongCk=(dk,ck),dklbituvobmhatithiimkvcklbit c m ha ti thi im k,
k=1,2,..,N. PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 123Ta s m t cu trc li cu b m ha ny trn hnh 4.19. Trn hnh
ny, ta c tt cccchuynitrngthicthccabmha.Minhnhcalicungcp
chotabathngtin.l:cctrngthicunhnh(trngthihintivtrngthi
tiptheo),uracmhacabmha(ck)vbitsliukhngmhaca chuyn i (dk). k k(d c
)kd 0 kd 1 0 1k ks s Hnh 4.19. Li ca RSC Nu ta chn ng t nt m ca li
trn hnh v, ta c th thy rng bm ha i t trng thi 00 n 10 khi bit ti u
vo b m ha l 1. Ngoi ra s liu c m ha ti u ra ca b m ha s l 1 (ck=1)
v cp bit u ra ca b m ha s l 11 (dk=1, ck=1).Khi bit c chui bit thu
c t knh tp m, mt cch gii m chui pht l
tmmtngdncxcsutlnnhttrongsttcccngdncthcca li. iu ny c th thc hin c
bng gii thut Viterbi. Ta s khng s dng gii thut Viterbi v cc u ra ca
n ch c cc quyt nh cng. Thay vo ta s dng gii thut MAP cho php cc u
ra mm. Gii thut ny da trn vic tm kim bit c xc sut ln nht, khi bit
chui bit b tp m. 4.6.3. S b to m turbo Hnh 4.20 cho thy s b to m
turbo dc xy dnng trn hai b to m RSC trn hnh 4.18. PDF created with
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4. M ho knh kim sot li trong truyn dn v tuyn s 124(1)kc(2)kc Hnh
4.20. B to m turbo da trn b to m RSC hnh 4.18. Nguyn l hot ng ca b
tom turbo nh sau. Khi u cc trng thithanh ghi dch trong cc m m ha
RSC thnh phn c t vo 0. Sau N bit ca chui
sliumtmtcaratrctip,mtkhccdchvoccbmhathnh phn theo v tr trn ca chuyn
mch trn hnh v. u ra ca b to m ta c N t
hphaibithocbabittythucvosbitcmhacgiicngvimibit khng m ha, nh vy t l
m c th l r=1/2 hoc 1/3 (xem hnh 4.21). _ ,1(1)1dc _ ,2(2)2dc _
,3(1)3dc _ ,4(2)4dc _ ,(2)1 2 1(1) (2) (1)2 2 1c d dc c c _ ,(2)3 4
3(1) (2) (1)4 4 3c d dc c c Hnh 4.21. u ra b to m cho cc t l m khc
nhau PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 125SaukhiaraNbitthngtincngviccbitcmhatngng.Kha chuyn mch c
chuyn xung v tr di a cc b m ha vo trng thi "0" v to ra cc k hiu ui
kt cui chui k hiu m u ra cho N bit s liu u vo. Hiu nng ca cc m
turbo s dng b an xen ph thuc vo kiu v su ca
banxencsdng.Ldovcutrcbanxennhhnglntnhcht khong cch ca m turbo. Qua
trnh an xen c thc hin bng cch ta vit chui s liu u vo theo th t thng
thng v c s liu ra theo mt quy tc no c khong cc ln nht gia cc k hiu
cnh nhau u vo. Di y ta xt gii thut an xen tng qut. Gi s dk,
k{1,2,.,N} l ton b s liu m ta cn an xen. Khi vit s liu ny vo b nh
theo trnh t thng thng (lgn lt theo tng dng chng hn) c th coi y l mt
mnggm hai bin s. Tt c s liu c lu, v th nu ta an xen N s liu, ta s c
N s liu trong mng c an xen. an xen ta cn xy dng mt mng khc, ta gi l
mng ch s. Trong mi ca mng ny s c mt trong s cc s t 1 n N. Cc s ny
tng ng vi cc a ch c ngu nhin ha.Gi s int[]l mng ch s, data[] l mng
s liu v intdata[] l mng s liu sau an xen. S dng chng trnh kiu
Pascal ta c: For I:=1toN Indata[int[I]:=dat[I] Hnh 4.22 cho thy th
d vi N=10. PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 126d1 d2 d3 d4 d5 d6 d7 d8 d9 d109 4 10 1 7 5 2 6 8 3Mi s
liu tng ng mt a chi mi ngu nhind4 d7 d10 d2 d6 d8 d5 d9 d1 d3Mng ch
s cha cc s ngu nhin gia 1 v NS liu c an xen1 2 3 4 5 6 7 8 9 10 Hnh
4.22. Gii thut an xen 4.6.4. Gii thut gii m MAP Khi s dng cc m
turbo, qu trnh gii m l qu trnh lp. Cc gii thut ny c hai khi gii m
vo mm ra mm (SISO) hot ng gn b vi nhau. C hai loi gii thut gii m
turbo chnh hin ang c s dng cho cc b gii m turbo SISO: gii
thutViterbyramm(VA/SOVA)vgiithutccihunh(MAP),giithut ny cng c bit n
nh l gii thut BCJT theo tn ca cc tc gi Bahl, Cocke, Jelinek v
Ravive. C hai gii thut u da trn li. Gii thut MAP l gii thut tt nht
trong s hai gii thut ni trn, v th trong ti liu ny ta ch xt MAP.
4.6.4. 1. Nguyn l MAP Ti u vo ca b gii m ta nhn c chui N bit m ha,
iu ch BPSK b tp m nh sau:R1,N = (R1, R2,.., RN)trong Rk=(xk, yk),
k=1,2,...,N
Gi s nk v mk l hai bin ngu nhin Gauss trung bnh khng c phng sai
2 v dk l bit u vo b m ha v ck bit c m ha m ha ti thi im k. Ta c:
PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 127 xk= ak+nk(4.54) yk=bk+mk(4.55) trong : ak= (1-2dk) l k
hiu ca bit khng m ha (thng tin h thng) bk= (1-2ck) l k hiu ca bit c
m ha (s liu kim tra chn l) k=1,2,..., N
McchcugiimMAPltmradkcxcsutcaonhtkhichotrcR1,N. iu ny t c bng cch
tnh log hm kh nng ging (LLR: Log likelihood ratio) k cho tng dk, hm
ny c nh ngha nh sau: _ ,1,1.( 1( ) l n( 0k Nkk NPdLdPdRR(4.56) Gi
tr ny c gi l u ra mm. Thc hin quyt nh cng cho u ra ny, ta c th xc
nh bit thng tin c kh nng ging bit pht nht: . < u ( ) 0 0u ( ) 0
1k kk kN Ld dN Ld d(4.57) Nu Sk l trng thi ca b gii m ti thi im k,
tac: ( ) ( ) 1, 1,0 0,k N k k NmP d P d S m R R (4.58) Tng t ( ) (
) 1, 1,1 1,k N k k NmP d P d S m R R (4.59) Ta t ( ) , 1,( ) ,k i k
k Nm P d i S mR vi i=0 hoc 1 v cng tt c cc trng thi c th c ca b gii
m, ta c: 1 1 1 1 1 1 ],0,1( )( ) l n( )kmkkmmLdm(4.60) PDF created
with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 128trong ( ) , 1,( ) ,k i k k Nm P d i S m Rl xc sut m ti
thi im k, trng thi cu b gii m l Sk , bit pht bng i khi cho trc chui
k hiu thu R1,N. Gi s: R1,N=[Rk-1,Rk,Rk+1], ta c th vit li , ( )k im
vo dng sau: { { { _ ,, k-1 k k+1B C D( ) , R RR144 2443k i k kAm P
d i S m (4.61) S dng quy tc Bayes sau y: P(A, B, C, D) P(B| A, C,
D)P(A, C, D)P(A| B, C, D)P(B, C, D) P(B, C, D) =P(B| A, C, D)P(D|
A, C)P(A, C)P(B, C, D) ta c th vit li (4.61) nh sau: ( ) ( ) + + ,
1 k 1 1( ) d , , , , ,N Nk i k k k k k k k km P R i S mR R P R d i
S mR ( ) k 1,d , , / ( )k k NP i S mR PR (4.62) trong +1NkRk hiu
cho chui k hiu t k n N.
DoRk-1chlinquanntrngthimmngyravkhngththucvoph thuc vo dk cng nh
Rk+1 (l cc s kin xy ra sau ), nn ta c th vit li thnh phn th nht
trong t s ca phng trnh (4.61) v k hiu n nh sau: ( ) ( ) + 1 k 1 1d
, , , ( )k k k k k k kP R i S mR R P R S m m (4.63) ( )km c gi l s
o trng thi thun (Forward State Metric). N biu din xc sut chui k hiu
thu trc thi im k v chph thuc vo trng thi m hin thi ti thi im k.S
dng cc phng trnhTa c th biu din thnh phn th hai t s ca ca phng trnh
(4.61) v k hiu nh sau: ( ) ( ) + + + + 1 1 1 1, , ( , ) ( ( , ))N
Nk k k k k k kP R d i S mR P R S f i m f i m (4.64) +1( ( , ))kf i
m cgilsotrngthingc(BackwardStateMetric),trong biu th y l s o cho
trng thi sau m nhn c khi u vo l "i"cn( )km l s o trng thi ngc ti
thi im k, cng thc cho s o ny s c xt di y. N biu din xc sut chui k
hiu sau thi im k v chph thuc vo trng thi m cng nh bittrc (ti thi im
k).Ta c th biu din thnh phn th ba trong t s ca phng trnh (4.61) nh
sau: PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 129( ) k ,d , , ( )k k k iP i S mR m (4.65) , ( )k im c gi
l s o nhnh (Branch Metric). N biu din xc sut pht lin hip dk, thu k
hiu Rk ti trng thi m.S dng cc phng trnh (4.62)-(4.65) tac cc phng
trnh sau. +, 1,,1,( ) ( ) ( ( , ))( )( )k k i k ik iNm m f i mmP R
(4.66) ++ 1 1 1 1 1 1 ],0 1,0,1 1,1( ) ( ) ( (0, ))( ) l n( ) ( ) (
(1, ))k k kmkk k kmm m f mLdm m f m (4.67) 4.6.4.2. Tnh ton s o
nhnh , ( )k im Ta c th vit liphng trnh (4.65) nh sau: ( ) ( ) ( ) ,
k k k( ) d , , d , d ,k i k k k k km P i S mR P R i S mP i S m ( )
( ) ( ) k k kd , d dk k kP R i S mP S m i P i (4.68) Do nh hng ca
tp m ln s liu v bit chn l c vp vi nhau, nn trng thi ti thi im k
khng ph thuc vo s liu u vo. V vy: ( ) k1d2kMP S m i (4.69) K hiu
P(dk=i)=k,i. Ta c th vit li phng trnh (4.68) nh sau: 1 _ 1 1 , ]2,
,,1( ) exp -22 2k i k k ik i kMx am dx
1 _ 1 1 , ]2, ( ) 1 1exp -2 2k k iky b mdy (4.70)
Luchbk,ilphthucvotrngthim.nginhaphngtrnh(4.70)bng cch loi b cc tha
s chung cho mu v t trong phng trnh (4.70), ta c: ( ) 1 + 1 ], , ,
,21( ) exp ( )k i k i k k i k k im x a yb m (4.71) Hnh 4.23 th hin
, ( )k im trn biu li. PDF created with FinePrint pdfFactory Pro
trial version http://www.fineprint.comChng 4. M ho knh kim sot li
trong truyn dn v tuyn s 130 2,0(00) 3,1(10) 2,1(01) 3,1(01) 2,0(01)
2,0(10) 3,1(11) ( )2 2x y ( )3 3x y Hnh 4.23.Th hin , ( )k im trn
li
Nu ta xt th d cho hai nhnh trn hnh 4.23, s dng phng trnh (4.71)
vi coi rng k,i=1/2 ta c: + ' ; 2,0 2 221 1(01) exp ( 1 1)2x y + ' ;
3,1 3 321 1(01) exp ( 1 1)2x y 4.6.4. 3.Tnh ton s o trng thi thun(
)km Biu thc( )km c gi l s o trng thi thun v n biu din s o trng thi
chochuynittrngthimsangtrngthitiptheo,tithiimk.Tphng trnh (4.63) ta
c th biu din ( )km l tng tt c xc sut chuyn i trng thi c th xy ra nh
sau: ( ) 11 1 1' 0( ) , ' ,k k k k km jm P d j S m R S m (4.72) Biu
din Rk-1 thng qua [ Rk-2 , Rk-1] v s dng quy tc Bayes ta c th vit
li phng trnh (4.72) nh sau: ( ) 12 1 1 1' 0( ) , , ' ,k k k k k km
jm P R S md j S m R
( ) 1 1 1, ' ,k k k kP d j S m R S mPDF created with FinePrint
pdfFactory Pro trial version http://www.fineprint.comChng 4. M ho
knh kim sot li trong truyn dn v tuyn s 131( ) ( ) 12 1 1 1 10( ) (
) , ( ),k k k j k k j kjm P R S b m P d j S b m R (4.73) trong
bj(m) biu th cho trng thi trc k chuyn n trng thi m khi bit u vo l
j. Sdngccphngtrnh(4.63)v(4.64)tacthvitliphngtrnh(4.73)nh sau: 11 j
, j0( ) (b( )) (b( ))k k kjjm m m (4.74) Ta s s dng litrn hnh 4.24
gii thch cng thc (4.74). 1 + ] 1 1,0 1 1,0(00) (00) (00) (10) (10)k
k k k k + 1 + ] 1 ,1 ,1(10) ( 00) (00) (01) (01)k k k k k Hnh
4.24.Trnh by( )km trn li Tt c cc( )km c th c tnh theo (4.72) trong
iu kin chng c khi u ng, Ta khi u chng nh sau: 1 1(00) 1 ( 0) 0 v m
(4.75) lm th du ta xt iu kin khi u (4.64) cho cc th d trn hnh 4.24
khi k=2: 2 2 2,0 2 2,0 2,0(00) (00) (00) (01) (01) (00)1 + ] 4.6.4.
4. Tnh ton s o trng thi ngc k(m) Biu thc k(m) rt ging vi biu thc
k(m). Thay v tnh tt c thun theo thi gian, ta tnh ton chng ngc theo
thi gian. Chnh v th chng c gi l cc s o trng thi ngc.T phng trnh
(4.64) ta c: ( )+ + + 1 1 1( ( , )) ( , )k k kf i m P R S f i m ,
vy: PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 132 ( ) ( )k k km P R S m =( ) +1,Nk k kP R R S m (4.76)
Ta c th biu din k(m) nh l tng tt c cc xc sut chuyn i trng thi c th
c n thi im k+1 nh sau: ( ) + + 11 1' 0( ) , ' , ,Nk k k k k km jm P
d j S m R R S m (4.77) p dng quy tc Bayes, ta c: ( ) + + 11 1' 0( )
, , 'Nk k k k km jm P R S md j S m ( )+ 1, ' ,k k k kP d j S m R S
m (4.78) Sk=m,dk=jhontonxcnhtrngthidnnSk+1=m'=f(j,m),(trngthitipm)
khi cho trc u vo j v m nn trong thnh phn th hai ca phng trnh (4.77)
ta c th thay Sk+1 =m' bng Sk=m v vit li phng trnh (4.77) nh sau: (
)( )+ + 11 10( ) ( , ) , ,Nk k k k k kjm P R S f i m P d j S mR +1,
10( ) ( ( , ))kj kjm f j m (4.79) Ta s s dng li trn hnh 4.25 gii
thch k,i(m) + + +1,0 ,0 1,1 ,1(01) (00) (01) (10) (01)k k k k k Hnh
4.25. Trnh by k,i(m) trn li
Ttcccgitrctnhtheo(4.78)trongiukinlchngckhiu ngc ng. Hi quy ngc c
khi u bng cch buc trng thi cui cng tr v 0 v t: + , N+ M,i(00) 1 (
0) 0N Miv m (4.80) trong N l s bit vo b m ha, M l s b nh ca b m ha.
PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 133Diytaxtthdtnhtonk,i(01)ti k=N+M-1visdngiukinkhi u ngc
theo (4.79): j=1
1,1 ,1 1,0 1,0(01) (00) (01) (01)+ + N M N M N M N M j=0
1,0 ,0 ,0(01) (10) (01) 0+ + + N M N M N M Sau tt c cc nh ngha
trn ta c th i n xt gii thut c th. 4.6.5. Gii m turbo B gii m turbo
trn c s b gii m SISO (Soft in soft out) c cho trn hnh4.26.kxky(
)kd( )a kd Hnh 4.26. B gii m SISO Cc b gii m SISOtnh ton u ra mm
(Soft Output) LLR( )kL dba thng tin u vo: Thng tin tin nh( )a kL dl
xc sut tin nh bit dk K hiu thu khng m ha kx v k hiu thu c m ha) ky
tnh ton thng tin mm u ra b gii m SISO s dng gii thut
MAPTacthtnhLLRtiuracaSISOchobitthngtindktrongiukincho trc ton b
chui k hiu thu theo phng trnh (4.56) nh sau: _ ,1,1,( 1( ) l n( 0k
Nkk NPdLdPdRR + + ( ) ( )c k a k e kL x L d L d (4.81) PDF created
with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 134( )e jL d lthngtinngoilaicrtratttc ' ky , ' kx , '( )a
kL d ;k'khckv Lc=4Es/N0, thng tin ny khng ph thuc vo cc u vo hin
thi cu bgii m. Ta c th coi( )e jL dl thnh phn hiu chnh do b gii m
to ra hiu chnh mi sai li trong knh. tng cng hiu qu gii m, ngi ta s
dng hai b gii m SISO ni trn mc ni tip nhau, trong hiu s gia thng
tin mm u ra (( )kL d ) vi thng tin mm u vo ca b gii m th nht (( )a
kL d )s c s dng lm u vo cho b gii m tip theo. Theo phng trnh (4.81)
ta c u vo cu b gii m th hai nh sau: + ( ) ( ) ( )k a k c k e kLd L
d Lx L d `(4.82) 4.6.6. Gii m Turbo lp tng hiu sut gii m, qu trnh
gii m turbo c thc hin theo mt qu trnh
lpnhtrnhnh4.27.TrongqutrnhnynhiubgiimMAPtheonguynl SISO ni trn c s
dng. Bgiimturbolptrnhnh4.27cxydngtrncscccpbgimthnh phn mc ni tip
nhau. Ti thi im k, c ba kiu u vo: thng tin h thng 1 2( , ,.....,
,..., )N N Mx x x x x+ ,thngtind 1 2( , ,....., ,..., )N N My y y y
y+ vthngtintin nh(thngtinngoilai)vbitthngtin { } 1 1 2 2 ( ), (
),....., ( ),..., ( )+ +e N N N M N ML L d L d L d L d .
ivibgiimMAP1naucalpkhngcthngtintinnhnn: La(jd )=0 (v th n khng gy
nh hng g ln cc ln gii m tip theo), v th ta c: +(1)1 ( ) ( )j c j e
jL d L x L d (4.83) Trong j=k-D, D l tr ca b gii m Trn hnh 4.27 ta
thy rng(1)( )a jL db loi tr khi 1( )jL d c ,+(1)( )c j e jL x L d .
SaubgiimMAP1lbanxen.Bnycnhimvphntnlicmbng cch dn cch cc k hiu lin k
trong chui pht.Sau an xen, s liu+(1)( )c i e jL x L dc a vo b gii m
MAP2.i vi b gii m MAP2 ,thng tin tin nh ca n l thng tin ngoi lai
nhn c t b gii m MAP1, nn nu t:(1) ( 2) ( ) ( )e i a iL d L d ,ta c:
PDF created with FinePrint pdfFactory Pro trial version
http://www.fineprint.comChng 4. M ho knh kim sot li trong truyn dn
v tuyn s 135 + +( 2) ( 2)2 ( ) ( ) ( )h c h a h e hL d Lx L d L d
(4.84) Trong h=i-D, D l tr gii m v (2)( )e hL dl thng tin ngoi lai
do b gii m MAP2 cung cp. V dh c an xen, n phi c gii an xen c kt qu
ng. V +(1)( )c i e iL x L dmc t li hn xi, nn b m ha th hai s hiu
chnh li tt hn khi s dng (2)ky . By gi ta c th s dng thng tin mi nhn
c t b gii m MAP2 v cp n chouvocabgiimMAP1.vytasdngthngtintinnht 2
2( ) L d . Trn hnh 4.27 ta tr n vi+( 2)( )c h a hL x L d c (2)( )e
hL d . Sau ta gii an xen n c (2) (1) ( ) ( ) e k a kL d L d , trong
l tng tr ca b gii m MAP1, b an xen, bgiimMAP2vbgiianxen.Khiny (1)(
) a kL d strthnhthngtintin nh cho b gii m 1 v qu trnh gii m li bt
u. By gi ( 2)( )e kL d tr thnh gi tr tin nh La(kd ) cho lnlp tip
theo v v.v... (1)( )a kL d +(1)( )c k a kL x L d(1)( )a jL d1( )jd
+(1)( )c j e jL x L d +( 2)( )c h a iL x L d 2( )hL d( )e kd( )e hL
d c kL x(1)c kLy( 2)c kLy1( )jd2( )hL dhd( )e hL dckL x(1)c kLy(2)c
kLy1( )iL d1( )hL dkd + (1)( )c i e iL x d 2( )e hL dhdkd+(1)( )c j
e jL x L d D l trca qu trnh gi m 1 v gii m 2 Tr l tr ca mt ln lp ca
qu trnh gii m PDF created with FinePrint pdfFactory Pro trial
version http://www.fineprint.comChng 4. M ho knh kim sot li trong
truyn dn v tuyn s 136(1/ 2)/( )a k iL dl thng tin tin nh ti u vo b
gii m th nht (hoc th 2) ca mt ln lp(1) ( 2) ( ) ( )e j a jL d L d
urathngtinngoilaidoGiim1toravbnguvo thng tintin nh cho Gii m 2 xk l
mu thng tin khng m ha thu c yk l mu thng tin m ha thu c 1/ 2 /( )j
hL dl LLR ti u ra ca Gii m 1 v 2( 2)( )e kL dthng tin ngoi lai ti u
ra ca gii m 2 ca mt ln lp tr Hnh 4.27. B gii m turbo lp
Tithiimbanu,ccgitrngoilaiclpthngkvlinhnct mi ln lp l cao. Tuy nhin
do cng mt thng tin c s dng, ci thin nhn c sau mt s ln lp tr nn rt
nh. Sau ln lp cui cng, quyt nh mm u ra s l tng cahai gi tr ngoi lai
cui cng cng vi Lcxk. Bgiims thc hin quyt nh cng bng cch so snh u ra
vi ngng bng khng: L(kd ) 0, th bitc gii m bng 0 L(kd )
