M ha trn knh truynMc ch ca l thuytM ha trn knh truyn(channel
encoding theory) l tm nhng m c th truyn thng nhanh chng, cha ng
nhiu m k (code word) hp l v c th sa li (error correction) hoc t nht
pht hin cc li xy ra (error detection). Cc mc ch trn khng ph thuc vo
nhau, v mi loi m c cng dng ti u cho mt ng dng ring bit. Nhng c tnh
m mi loi m ny cn cn tu thuc nhiu vo xc sut li xy ra trong qu trnh
truyn thng. i vi mt a CD thng thng, li trong m thanh xy ra ch yu l
do bi v nhng vt xc trn mt a. V th, cc m c lng vo vi nhau. D liu c
phn b trn ton b mt a. Tuy khng c tt cho lm, song mt m ti din n gin
c th c dng lm mt v d d hiu. Chng hn, chng ta ly mt khi s liu bit (i
din cho m thanh) v truyn gi chng ba ln lin. Bn my thu, chng ta kim
tra c ba phn lp li trn, tng bit tng bit mt, ri ly ci no c s bu cao
nht. im tri khoy y l, chng ta khng ch truyn gi cc bit theo th t.
Chng ta lng n vo vi nhau. Khi d liu ny, trc tin, c chia ra lm 4 khi
nh. Sau chng ta gi mt bit khi u tin, tip theo mt bit khi th hai v.v
tun t qua cc khi. Vic ny c lp i lp li ba ln phn b s liu ra trn b mt
a. Trong ng cnh ca m ti din n gin trn, vic lm ny hnh nh khng c hiu
qu cho lm. Song hin nay c nhng m c hiu ng cao, rt ph hp vi vic sa
li xy ra t ngt do mt vt xc hay mt vt bi, khi dng k thut lng s liu
ni trn.Mi m thng ch thch hp cho mt ng dng nht nh. Vin thng trong v
tr (deep space) b gii hn bi nhiu nhit (thermal noise) trong thit b
thu. Hin trng ny khng xy ra mt cch t pht bt thng, song xy ra theo
mt chu trnh tip din. Tng t nh vy, modem vi di tn hp b hn ch v nhiu
m tn ti trong mng li in thoi. Nhng nhiu m ny c th c biu hin r hn
bng mt m hnh m tp tip din. in thoi di ng "Cell phones" hay c vn do
s suy sng nhanh chng xy ra. Tn s cao c dng c th gy ra s suy sng tn
hiu mt cch nhanh chng (rapid fading), ngay c khi my nhn ch di ch vi
phn Anh (inches)1. Mt ln na, ngi ta hin c mt loi thuc hng M ha trn
knh truyn c thit k i u vi tnh trng suy sng.T "L thuyt m ha i s" m
ch mt chi nhnh ca l thuyt m ha trn knh truyn, trong c tnh ca m c
biu hin bng cc i s v da vo m nghin cu su hn.L thuyt m ha i s c chia
ra lm 2 loi m chnh1. M khi tuyn tnh (Linear block codes)2. M kt hp
(Convolutional codes)Chng phn tch ba c tnh sau ca m -- ni chung l:
Chiu di ca m (code word length) Tng s cc m k hp l (total number of
valid code words) Khong cch Hamming ti thiu gia hai m k hp l (the
minimum Hamming distance between two valid code words)M khi tuyn
tnhM khi tuyn tnh mang tnh nng tuyn tnh (linearity), chng hn tng ca
hai m k no y li chnh l mt m k; v chng c ng dng vo cc bit ca ngun
trn tng khi mt; ci tn m khi tuyn tnh l v vy (linear block codes). C
nhng khi m bt tuyn tnh, song kh m chng minh c rng mt m no l mt m tt
nu m y khng c c tnh ny.Bt c m khi tuyn tnh no cng c i din l
(n,m,dmin), trong 1. n, l chiu di ca m k, trong k hiu (symbols),2.
m, l s k hiu ngun (source symbols) c dng m ha tc thi,3. dmin, l
khong cch hamming ti thiu ca m (the minimum hamming distance for
the code)C nhiu loi m khi tuyn tnh, nh1. M tun hon (Cyclic codes)
(M Hamming l mt b phn nh (subset) ca m tun hon)2. M ti din
(Repetition codes)3. M chn l (Parity codes)4. M Reed-Solomon (Reed
Solomon codes)5. M BCH (BCH code)6. M Reed-Muller7. M hon ho
(Perfect codes)M khi c gn lin vi bi ton "ng gi ng xu" l bi ton gy
mt s ch trong nhiu nm qua. Trn b din hai chiu, chng ta c th hnh
dung c vn mt cch d dng. Ly mt nm ng xu, nm trn mt bn, ri dn chng li
gn vi nhau. Kt qu cho chng ta mt mu hnh lc gic tng t nh hnh t ong.
Cc m khi cn da vo nhiu chiu khc na, khng d g m hnh dung c. M
Golay2c hiu ng cao, dng trong truyn thng qua khong khng v tr, s dng
nhng 24 chiu. Nu c dng l m nh phn (thng thy), cc chiu m ch n chiu
di ca m k nh nh ngha trn.L thuyt v m s dng m hnh hnh cu vi s chiu
"N". Ly v d, bao nhiu ng xu phi cn ph kn mt mt bn, hay trong khong
khng 3 chiu, bao nhiu hn bi phi cn nhi kn mt hnh cu. Nhng cn nhc
khc bao gm vic chn la m. Ly v d, do nhi nhmg hnh lc lng vo trong mt
ci hp hnh ch nht, chng ta li nhng khong trng cc gc. Khi cc chiu ca
hp c tng ln, t l phn trm so snh ca cc khong trng nh i, cho n mt c
no y, nhng phn nhi chim ht cc khong khng v m ny c gi m hon ho. S m
kiu ny tng i him (Hamming [n,k,3], Golay
[24,12,8],[23,12,7],[12,6,6])Mt iu thng b b qua l s lng nhng hng xm
k cn (neighbors) m mt m k c th c. Chng ta c th dng li v d cc ng xu
y. u tin, chng ta gp cc ng xu li theo cc hng hnh ch nht. Mi mt ng
xu c 4 ng k cn (v 4 ci bn gc xa hn). Trong b cc ca hnh lc gic, mi
ng xu c 6 ng k cn. Khi chng ta tng s chiu ln, s lng cc ng k cn tng
ln mt cch nhanh trng.Kt qu l s lng cc m tp, bn cch cc m chnh, m my
thu c th chn, cng tng ln, v do m gy ra li. y chnh l khuyt im cn bn
ca m khi, v cng l khuyt im ca tt c cc loi m. C th vic gy li tr nn
kh khn hn, nu ch c mt hng xm k cn m thi, song con s cc hng xm k cn
c th ln n lm cho chnh tng xc sut li b nh hng (total error
probability actually suffers).M kt hpM kt hp (Convolutional codes)
c s dng trong cc modem di tn m (voiceband modems) (V.32, V.17,
V.34) v trong cc in thoi di ng GSM3, cng nh trong cc thit b truyn
thng ca qun i v trang v trong cc thit b truyn thng vi v tinh. nh y
l lm cho tt c cc k hiu m k (codeword symbol) tr thnh tng trng s
(weighted sum) ca nhiu loi k hiu thng ip trong nhp liu (various
input message symbols). N tng t nh ton kt hp c dng trong cc h tuyn
tnh bt bin (linear time invariant systems) dng tm xut liu (output)
ca mt h thng, khi chng ta bit nhp liu (input) v cc p ng xung
(impulse response).Ni chung chng ta tm xut liu ca b m ha kt hp h
(system convolutional encoder), tc s kt hp ca nhp liu bit, i chiu
vi trng thi ca b m ha kt hp (convolution encoder), hoc trng thi ca
cc thanh bin (registers).V c bn m ni, m kt hp khng gip thm g trong
vic chng nhiu hn mt m khi tng ng. Trong nhiu trng hp, chng ni chung
cho chng ta mt phng php thc thi n gin hn, hn hn mt m khi c hiu qu
tng ng (a block code of equal power). B m ha thng l mt mch in n
gin, c mt b nh (state memory), mt vi bin php truyn thng tin phn hi
bo tnh hnh (some feedback logic), thng l cc cng loi tr XOR (XOR
gates). B m ha c th c thc thi trong phn mm hay phn sn
(firmware).Thut ton Viterbi (Viterbi algorithm) l mt thut ton ngn
gn nht (optimum algorithm) c dng gii m cc m kt hp. Hin c nhng phng
php gim c gip vo vic gim khi lng tnh ton phi lm. Nhng phng php ny
phn ln da vo vic tm tuyn ng c kh nng xy ra cao nht (most likely
paths). Tuy khng ngn gn, song trong mi trng nhiu thp hn, ngi ta
thng thy chng cho nhng kt qu kh quan. Cc b iu hnh vi x l hin i
(Modern microprocessors) c kh nng thc hin nhng thut ton tm gim c ni
trn vi t l trn 4000 m k trong mt giy.Cc ng dng ca l thuyt m haMt
quan tm khc ca l thuyt m ha l vic thit k cc m gip vo vic ng b ha
(synchronization). Mt m c th c thit k pht hin dch pha sng in (phase
shift) v sa li, ng thi cho php nhiu tn hiu (multiple signals) c
truyn gi trn cng mt knh. C mt hng loi ca nhng m m chng ta hng ngy
thng gp trong cc in thoi di ng ca mnh. Chng c gi l m a truy nhp phn
chia theo m (Code Division Multiple Access - vit tt l CDMA). Chi
tit v chng thuc phm vi bn ngoi cuc m lun y, song ni mt cch ngn gn,
mi ci in thoi c gn cho mt m k (codeword) ly ra t mt hng c bit
(special class) (ngnh i S). Trong khi truyn thng, m k c dng xo trn
cc bit i biu cho thng ip m thanh (voice message). Ti my thu, mt quy
trnh gii xo trn ("descrambling") c tin hnh gii m (decipher) thng
ip. c tnh ca hng m k ny cho php nhiu ngi dng (vi cc m khc nhau) s
dng cng mt knh truyn rai trong cng mt lc. My thu, dng chu trnh gii
xo trn, ch "nghe" thy nhng ngi gi khc nh "nhiu m" thp m thi.Mt hng
m ni ting khc na l m Yu cu lp li t ng (Automatic Repeat reQuest -
vit tt l ARQ). Trong hng ph qut (general class) ny, my pht cho thm
cc bit chn l kim tra (parity check bits) vo cc thng ip di hn bnh
thng. My thu kim tra bit chn l ca thng ip thu c v nu n pht hin ra
mt s bt ng, n s yu cu my pht truyn tin li thng ip. Hu ht cc mng din
rng (wide area networks) v cc giao thc, ngoi tr nhng ci ht sc n
gin, u s dng ti truyn thng ARQ. Nhng giao thc thng dng bao gm SDLC
(IBM), TCP (Internet), X.25 (Quc t) v nhiu ci khc na. Hin c nhiu
nghin cu trn phm vi rng trong lnh vc v ti ny do kh khn trong vic so
snh gia mt gi d liu b t b (rejected packet) vi mt gi d liu mi. Gi d
liu mi n ny l mt gi mi hay l mt gi c c truyn li? Thng th cc h thng
nh s c s dng, tuy nhin trong mt s mng truyn thng, gi d liu c th c
mt nh danh khc, hoc vn ny c dnh li cho tng cao hn (ca giao thc) n
yu cu truyn thng li. TCP/IP l mt giao thc in hnh s dng c hai k
thut. Trong bi cnh kt ni, TCP/IP dnh vic truyn thng li cho mng li
truyn thng, v v th n s dng m ha ARQ. Trong mng li v tuyn (wireless
network), ngi ta khng s dng ARQ. Thay vo , ngi ta dnh trch nhim ny
cho chng trnh ng dng kim nghim gi d liu v yu cu vic truyn thng li
khi cn. Vic ny c th nng cao ln n mc i hi ngi dng phi n nt "np li"
("refresh" button) trn mt trnh duyt web. Song, ngay c ci ny hin nay
vn trong hng ARQ ang c nghin cu; ngi dng bt buc phi can thip (the
user just has to become involved).
