Xử lý ảnh số - Nén dữ liệu ảnh part 2 potx

1. sai sˆo
´
gi˜u
.
aa
˙’
nh v`ao v`a a
˙’
nh ra; v`a
2. u
.
´o
.
clu
.
o
.
.
ng sai sˆo
´
gi˜u
.
aa
˙’
nh ra v`a nhiˆe
˜
u.
X´et a
˙’
nh f(x, y),x =0, 1, ,M − 1,y =0, 1, ,N − 1. D
-

ˆe
˙’
lu
.
ua
˙’
nh f ta cˆa
`
n
M × N × m bit v´o
.
i m l`a sˆo
´
bit biˆe
˙’
udiˆe
˜
n gi´a tri
.
x´am hay mˆo
.
tt`u
.
m˜a. Viˆe
.
c n´en l`am
gia
˙’
msˆo
´

bit lu
.
utr˜u
.
(nho
˙’
ho
.
n M ×N ×m bit). Ngu
.
`o
.
i gia
˙’
i m˜a xu
.
˙’
l´y nh˜u
.
ng bit n`ay v`a
xˆay du
.
.
ng la
.
ia
˙’
nh ra g(x, y) c´o k´ıch thu
.
´o

.
c M ×N trong d¯´o mˆo
˜
i pixel tu
.
o
.
ng ´u
.
ng t `u
.
m˜a
c´o d¯ˆo
.
d`ai m bit.
Khi d¯´o lˆo
˜
ixa
˙’
y ra gi˜u
.
a c´ac pixel cu
˙’
aa
˙’
nh v`ao v`a a
˙’
nh ra l`a
e(x, y):=g(x, y) − f(x, y)
v`a sai sˆo

´
to`an bˆo
.
e
rms
:=

1
MN
M−1

x=0
N−1

y=0
e
2
(x, y)

1/2
=

1
MN
M−1

x=0
N−1

y=0

[g(x, y) −f(x, y)]
2

1/2
.
U
.
´o
.
clu
.
o
.
.
ng sai sˆo
´
cu
˙’
aa
˙’
nh ra v`a nhiˆe
˜
u x´ac d¯i
.
nh bo
.
˙’
i
(SNR)
rms

:=


M−1
x=0

N−1
y=0
g
2
(x, y)

M−1
x=0

N−1
y=0
e
2
(x, y)

1/2
.
Tiˆeu chuˆa
˙’
n chu
˙’
quan
Tiˆeu chuˆa
˙’

n d¯´anh gi´a kh´ach quan cung cˆa
´
pmˆo
.
tco
.
chˆe
´
thuˆa
.
ntiˆe
.
nv`ad¯o
.
n gia
˙’
nd¯ˆe
˙’
x´ac
d¯ i
.
nh thˆong tin mˆa
´
t. Tuy nhiˆen, hˆa
`
uhˆe
´
t c´ac a
˙’
nh gia

˙’
in´end¯ˆe
`
ud¯u
.
o
.
.
c quan s´at bo
.
˙’
i con
ngu
.
`o
.
i. Do d¯´o, s˜e thuˆa
.
ntiˆe
.
nho
.
nnˆe
´
u d¯´anh gi´a chˆa
´
tlu
.
o
.

.
ng h`ınh a
˙’
nh du
.
.
a v`ao ngu
.
`o
.
i
quan s´at.
T`uy thuˆo
.
c v`ao c´ach nh`ın cu
˙’
a con ngu
.
`o
.
i, c´o thˆe
˙’
hai a
˙’
nh c´o c`ung lˆo
˜
i ph´at sinh
nhu
.
ng quan s´at ta thˆa

´
ychˆa
´
tlu
.
o
.
.
ng hai a
˙’
nh ho`an to`an kh´ac nhau: d¯´o l`a do t´ınh chu
˙’
quan cu
˙’
a con ngu
.
`o
.
i. A
˙’
nh c´o lˆo
˜
i xuˆa
´
thiˆe
.
no
.
˙’
biˆen th`ı c´o chˆa

´
tlu
.
o
.
.
ng tˆo
´
tho
.
nlˆo
˜
i xuˆa
´
t
hiˆe
.
no
.
˙’
v`ung trung tˆam a
˙’
nh. Chˆa
´
tlu
.
o
.
.
ng cu

˙’
amˆo
.
ta
˙’
nh c´o thˆe
˙’
d¯ u
.
o
.
.
c d¯´anh gi´a chu
˙’
quan
qua quan s´at cu
˙’
a nhiˆe
`
u ngu
.
`o
.
i. C´ac d¯´anh gi´a du
.
.
a trˆen ba
˙’
ng phˆan loa
.

i hoˇa
.
cbˇa
`
ng c´ach
d¯ ˆo
´
i s´anh hai a
˙’
nh f(x, y)v`a
ˆ
f(x, y). Sau d¯ˆay l`a c´ach phˆan loa
.
icu
˙’
atˆo
˙’
ch´u
.
c TASO (viˆe
´
t
tˇa
´
tt`u
.
Television Allocation Study Organization):
147
1. Tuyˆe
.

tv`o
.
i:a
˙’
nh c´o chˆa
´
tlu
.
o
.
.
ng rˆa
´
t cao.
2. Tˆo
´
t:a
˙’
nh c´o chˆa
´
tlu
.
o
.
.
ng cao. Nhiˆe
˜
u khˆong d¯´ang kˆe
˙’
.

3. Kh´a:a
˙’
nh c´o chˆa
´
tlu
.
o
.
.
ng chˆa
´
p nhˆa
.
nd¯u
.
o
.
.
c. Nhiˆe
˜
u khˆong d¯´ang kˆe
˙’
.
4. Trung b`ınh:a
˙’
nh c´o chˆa
´
tlu
.
o

.
.
ng thˆa
´
p; cˆa
`
nca
˙’
i thiˆe
.
n. Nhiˆe
˜
uc´othˆe
˙’
gˆay kh´o chi
.
u.
5. K´em:a
˙’
nh c´o chˆa
´
tlu
.
o
.
.
ng rˆa
´
t thˆa
´

p. Nhiˆe
˜
u xuˆa
´
thiˆe
.
n nhiˆe
`
u.
6. Rˆa
´
tk´em:a
˙’
nh khˆong thˆe
˙’
xem d¯u
.
o
.
.
c.
Viˆe
.
c so s´anh chˆa
´
tlu
.
o
.
.

ng gi˜u
.
a c´ac a
˙’
nh f(x, y)v`a
ˆ
f(x, y) c´o thˆe
˙’
´ap du
.
ng thang d¯ˆo
.
{−3, −2, −1, 0, 1, 2, 3}
d¯ ˆe
˙’
biˆe
˙’
udiˆe
˜
n c´ac d¯´anh gi´a chu
˙’
quan {rˆa
´
txˆa
´
u, xˆa
´
u, tu
.
o

.
ng d¯ˆo
´
ixˆa
´
u, trung b`ınh, tu
.
o
.
ng
d¯ ˆo
´
i kh´a, kh´a, tˆo
´
t}.
6.2 C´ac mˆo h`ınh n´en a
˙’
nh
Trong Phˆa
`
n 6.1 ch´ung ta d¯˜a d¯ˆe
`
cˆa
.
p riˆeng r˜e ba phu
.
o
.
ng ph´ap d¯ˆe
˙’

gia
˙’
md¯ˆo
.
du
.
th `u
.
ad˜u
.
liˆe
.
uhayn´end˜u
.
liˆe
.
ua
˙’
nh. Tuy nhiˆen, c´ac phu
.
o
.
ng ph´ap n`ay thu
.
`o
.
ng d¯u
.
o
.

.
ctˆo
˙’
ho
.
.
pla
.
i
d¯ ˆe
˙’
ta
.
o th`anh mˆo
.
thˆe
.
thˆo
´
ng n´en d˜u
.
liˆe
.
ua
˙’
nh. Trong phˆa
`
n n`ay ch´ung ta nghiˆen c´u
.
u c´ac

d¯ ˇa
.
c tru
.
ng chung cu
˙’
anh˜u
.
ng hˆe
.
thˆo
´
ng n`ay v`a tr`ınh b`ay mˆo
.
t mˆo h`ınh tˆo
˙’
ng qu´at d¯ˆe
˙’
biˆe
˙’
u
diˆe
˜
nch´ung.
Nhu
.
trong H`ınh 6.2, mˆo
.
thˆe
.

thˆo
´
ng n´en a
˙’
nh bao gˆo
`
m hai khˆo
´
icˆa
´
utr´uc: khˆo
´
im˜a
ho´a v`a khˆo
´
i gia
˙’
i m˜a.
2
A
˙’
nh f(x, y)d¯u
.
o
.
.
cd¯u
.
a v`ao bˆo
.

m˜a ho´a. Bˆo
.
n`ay s˜e ta
.
o ra mˆo
.
t
tˆa
.
p c´ac k´yhiˆe
.
ut`u
.
d˜u
.
liˆe
.
u nhˆa
.
p. Sau d¯´o tˆa
.
p n`ay d¯u
.
o
.
.
c chuyˆe
˙’
n qua mˆo
.

t kˆenh truyˆe
`
n
dˆa
˜
nd¯ˆe
´
nbˆo
.
gia
˙’
i m˜a. Bˆo
.
gia
˙’
i m˜a thu
.
.
chiˆe
.
ntiˆe
´
n tr`ınh gia
˙’
i m˜a v`a ta d¯u
.
o
.
.
ca

˙’
nh
ˆ
f(x, y).
N´oi chung, a
˙’
nh
ˆ
f(x, y) c´o thˆe
˙’
tr `ung hoˇa
.
c khˆong v´o
.
ia
˙’
nh f(x, y) ban d¯ˆa
`
u. Nˆe
´
u hai a
˙’
nh
tr `ung nhau, hˆe
.
thˆo
´
ng truyˆe
`
n khˆong c´o lˆo

˜
i hoˇa
.
c thˆong tin d¯u
.
o
.
.
cba
˙’
o to`an; ngu
.
o
.
.
cla
.
i,
a
˙’
nh d¯u
.
o
.
.
c xˆay du
.
.
ng la
.

ibi
.
suy biˆe
´
n.
Ca
˙’
hai khˆo
´
i m˜a ho´a v`a gia
˙’
i m˜a trong H`ınh 6.2 gˆo
`
m hai bˆo
.
phˆa
.
ntu
.
o
.
ng d¯ˆo
´
id¯ˆo
.
c
lˆa
.
p. Bˆo
.

m˜a ho´a gˆo
`
m m˜a ho´a nguˆo
`
n nhˇa
`
m loa
.
ibo
˙’
du
.
th `u
.
a trong d˜u
.
liˆe
.
u v`ao, v`a m˜a
2
C´ac khˆo
´
i n`ay c`on go
.
il`akhˆo
´
in´env`a khˆo
´
i gia
˙’

i n´en. Thuˆa
.
tng˜u
.
khˆo
´
i m˜a ho´a v`a khˆo
´
i gia
˙’
im˜apha
˙’
n
´anh a
˙’
nh hu
.
o
.
˙’
ng cu
˙’
a l´y thuyˆe
´
t thˆong tin d¯ˆo
´
iv´o
.
i l˜anh vu
.

.
cn´ena
˙’
nh.
148
ho´a kˆenh thu
.
.
chiˆe
.
n gia
˙’
m sai (nˆe
´
u c´o) khi truyˆe
`
nd˜u
.
liˆe
.
u qua kˆenh. Tu
.
o
.
ng tu
.
.
,bˆo
.
gia

˙’
i
m˜a gˆo
`
m gia
˙’
i m˜a kˆenh v`a sau d¯´o l`a bˆo
.
gia
˙’
i m˜a nguˆo
`
n. Nˆe
´
u kˆenh truyˆe
`
ngi˜u
.
a c´ac bˆo
.
m˜a
ho´a v`a gia
˙’
i m˜a khˆong c´o nhiˆe
˜
u th`ı m˜a ho´a kˆenh v`a gia
˙’
i m˜a kˆenh d¯u
.
o

.
.
cbo
˙’
qua.
f(x, y)

.


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ˆ
f(x, y)
M˜a ho´a
Gia
˙’
im˜a

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M˜a ho´a
nguˆo
`
n

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M˜a ho´a
kˆenh

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Kˆenh

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Gia
˙’
im˜a
kˆenh

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Gia
˙’
im˜a
nguˆo
`
n
H`ınh 6.2: Mˆo h`ınh mˆo
.
thˆe
.
thˆo
´
ng n´en d˜u
.
liˆe
.
utˆo
˙’
ng qu´at.
6.2.1 M˜a ho´a v`a gia
˙’
i m˜a nguˆo

`
n
M˜a ho´a nguˆo
`
nc´och´u
.
c nˇang gia
˙’
m hoˇa
.
ckhu
.
˙’
bo
˙’
du
.
th `u
.
a trong m˜a ho´a, trong quan hˆe
.
gi˜u
.
a c´ac pixel hay du
.
th `u
.
a trong tˆam sinh l´yt`u
.
a

˙’
nh d¯ˆa
`
u v`ao. Nhiˆe
`
u´u
.
ng du
.
ng d¯ˇa
.
c
biˆe
.
t v`a c´ac l˜anh vu
.
.
c liˆen quan d¯`oi ho
˙’
icˆa
`
n c´o nh˜u
.
ng c´ach m˜a ho´a tˆo
´
t nhˆa
´
t. Thˆong
thu
.

`o
.
ng, c´ach tiˆe
´
pcˆa
.
n n`ay c´o thˆe
˙’
mˆo h`ınh ho´a bo
.
˙’
i ba thao t´ac d¯ˆo
.
clˆa
.
p liˆen tiˆe
´
p nhau.
Nhu
.
trong H`ınh 6.3(a), mˆo
˜
i thao t´ac d¯u
.
o
.
.
c thiˆe
´
tkˆe

´
d¯ ˆe
˙’
thu
.
.
chiˆe
.
n gia
˙’
md¯ˆo
.
du
.
th `u
.
ad˜u
.
liˆe
.
ud¯u
.
o
.
.
cmˆota
˙’
trong Phˆa
`
n 6.1. H`ınh 6.3(b) l`a so

.
d¯ ˆo
`
tu
.
o
.
ng ´u
.
ng khˆo
´
i gia
˙’
i m˜a nguˆo
`
n.
f(x, y)




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M˜a ho´a nguˆo
`
n
(a)

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Biˆe
´
nd¯ˆo
˙’
i

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Lu
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o
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ng tu
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˙’
ho´a

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M˜a ho´a
k´yhiˆe
.
u
Kˆenh
Kˆenh




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Gia
˙’
i m˜a nguˆo
`
n
(b)

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Gia
˙’
im˜a
k´yhiˆe
.
u

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Biˆe
´
nd¯ˆo
˙’
i ngu
.
o

.
.
c
ˆ
f(x, y)
H`ınh 6.3: Mˆo h`ınh m˜a ho´a nguˆo
`
n (a) v`a gia
˙’
i m˜a nguˆo
`
n (b).
X´et a
˙’
nh f d¯ u
.
o
.
.
cbiˆe
˙’
udiˆe
˜
nbo
.
˙’
i d˜ay c´ac gi´a tri
.
x´am z
0

,z
1
, ,z
n−1
. M˜a ho´a a
˙’
nh f
d¯ u
.
o
.
.
c thu
.
.
chiˆe
.
n thˆong qua ba bu
.
´o
.
c:
149
1. Biˆe
´
nd¯ˆo
˙’
i c´ac phˆa
`
ntu

.
˙’
a
˙’
nh z
0
,z
1
, ,z
n−1
th`anh c´ac hˆe
.
sˆo
´
y
0
,y
1
, ,y
n−1
;
2. Lu
.
o
.
.
ng tu
.
˙’
ho´a c´ac hˆe

.
sˆo
´
y
0
,y
1
, ,y
n−1
v`a l`am tr`on th`anh ν
0
,ν
1
, ,ν
n−1
;
3. G´an m´u
.
clu
.
o
.
.
ng tu
.
˙’
ho´a ν
i
,i=0, 1, ,n− 1, v´o
.

imˆo
.
tt`u
.
m˜a c
i
.
Biˆe
´
nd¯ˆo
˙’
i
Giai d¯oa
.
nd¯ˆa
`
utiˆen cu
˙’
a qu´a tr`ınh m˜a ho´a nguˆo
`
n, bˆo
.
phˆa
.
n biˆe
´
nd¯ˆo
˙’
i c´o thˆe
˙’

xem nhu
.
mˆo
.
t ´anh xa
.
t`u
.
tˆa
.
p c´ac sˆo
´
(c´ac pixel) th`anh tˆa
.
p c´ac sˆo
´
kh´ac nhˇa
`
m gia
˙’
msu
.
.
du
.
th `u
.
a
trong quan hˆe
.

gi˜u
.
a c´ac pixel cu
˙’
aa
˙’
nh ban d¯ˆa
`
u. Ph´ep to´an n`ay n´oi chung l`a kha
˙’
nghi
.
ch
v`a c´o thˆe
˙’
hoˇa
.
c khˆong gia
˙’
m tru
.
.
ctiˆe
´
psˆo
´
lu
.
o
.

.
ng d˜u
.
liˆe
.
u d¯`oi ho
˙’
ibiˆe
˙’
udiˆe
˜
na
˙’
nh.
Trong m˜a ho´a run length, d˜ay c´ac phˆa
`
ntu
.
˙’
a
˙’
nh do
.
c theo mˆo
.
t d`ong qu´et z
0
,z
1
, ,z

m−1
d¯ u
.
o
.
.
cbiˆe
´
nd¯ˆo
˙’
i th`anh d˜ay c´ac cˇa
.
p
S := {(l
0
,g
0
), (l
1
,g
1
), ,(l
k−1
,g
k−1
)},
trong d¯´o l
i
l`a sˆo
´

lˆa
`
nlˇa
.
pcu
˙’
a gi´a tri
.
x´am g
i
. Ph´ep biˆe
´
nd¯ˆo
˙’
i n`ay kha
˙’
nghi
.
ch v`ı d˜ay c´ac
phˆa
`
ntu
.
˙’
a
˙’
nh c´o thˆe
˙’
xˆay du
.

.
ng la
.
it`u
.
d˜ay S.
Mˆo
.
tph´ep biˆe
´
nd¯ˆo
˙’
i kh´ac l`a
y = Az, (6.1)
trong d¯´o A l`a ma trˆa
.
n vuˆong cˆa
´
p n. Ph´ep biˆe
´
nd¯ˆo
˙’
i n`ay c´o thˆe
˙’
kha
˙’
nghi
.
ch hoˇa
.

c khˆong
t`uy theo ma trˆa
.
n A. V´o
.
itˆa
.
p c´ac vector z v`a ma trˆa
.
n A n`ao d¯´o, ta c´o thˆe
˙’
lu
.
utr˜u
.
vector y v´o
.
isˆo
´
bit ´ıt ho
.
nlu
.
utr˜u
.
z.
Chˇa
˙’
ng ha
.

n, ph´ep biˆe
´
nd¯ˆo
˙’
i sai phˆan x´ac d¯i
.
nh bo
.
˙’
i ma trˆa
.
n
A :=











100000
1 −10000
01−10 0 0
00 1−10 0
0001−10
00001−1












.
Ta c´o



y
0
= z
0
,
y
i
= z
i−1
−z
i
,i=1, 2, ,n− 1.
(6.2)
150

Nˆe
´
u c´ac pixel kˆe
`
nhau c´o m´u
.
c x´am tu
.
o
.
ng tu
.
.
th`ı hiˆe
.
u y
i
= z
i−1
− z
i
, vˆe
`
trung b`ınh,
nho
˙’
ho
.
nc´acm´u
.

c x´am v`a do d¯´o d¯`oi ho
˙’
i ´ıt bit ho
.
nd¯ˆe
˙’
lu
.
utr˜u
.
. Ph´ep biˆe
´
nd¯ˆo
˙’
i n`ay l`a
kha
˙’
nghi
.
ch.
Lu
.
o
.
.
ng tu
.
˙’
ho´a
X´et ph´ep biˆe

´
nd¯ˆo
˙’
i (6.1), nˆe
´
umˆo
˜
i phˆa
`
ntu
.
˙’
z
i
c´o thˆe
˙’
lˆa
´
y2
m
gi´a tri
.
kh´ac nhau th`ı y
j
c´o thˆe
˙’
lˆa
´
y(2
m

)
n
=2
mn
gi´a tri
.
kh´ac nhau. N´oi c´ach kh´ac, cˆa
`
n c´ac t`u
.
m˜a c´o d¯ˆo
.
d`ai
mn−bit d¯ˆe
˙’
g´an mˆo
.
tt`u
.
m˜a cho mˆo
.
t gi´a tri
.
y
j
. Nhu
.
ng mˆo
˜
i gi´a tri

.
z
i
d¯ u
.
o
.
.
c g´an t`u
.
m˜a
c´o d¯ˆo
.
d`ai m v`a mu
.
c tiˆeu cu
˙’
ach´ung ta l`a su
.
˙’
du
.
ng ´ıt bit ho
.
nd¯ˆe
˙’
m˜a ho´a y
i
v`ıvˆa
.

yta
cˆa
`
nlu
.
o
.
.
ng tu
.
˙’
ho´a c´ac gi´a tri
.
n`ay.
Lu
.
o
.
.
ng tu
.
˙’
ho´a l`a ´anh xa
.
biˆe
´
nmˆo
.
ttˆa
.

p Y gˆo
`
m nhiˆe
`
u phˆa
`
ntu
.
˙’
(c´o thˆe
˙’
vˆo ha
.
n)
th`anh tˆa
.
p V c´o ´ıt phˆa
`
ntu
.
˙’
ho
.
n: ta phˆan hoa
.
ch da
˙’
id¯ˆo
.
ng cu

˙’
atˆa
.
p Y bo
.
˙’
i c´ac m´u
.
c
l
0
,l
1
, ,l
t−1
. Nˆe
´
u gi´a tri
.
nˇa
`
m trong khoa
˙’
ng (l
i
,l
i+1
] th`ı ta s˜e g´an n´o c´o gi´a tri
.
ν

i
(c´o
thˆe
˙’
cho
.
n l`a tˆam cu
˙’
a khoa
˙’
ng n`ay). Lu
.
o
.
.
ng tu
.
˙’
ho´a d¯ˆe
`
u l`a ph´ep phˆan hoa
.
ch d¯ˆe
`
u; ngu
.
o
.
.
c

la
.
il`akhˆong d¯ˆe
`
u. Qu´a tr`ınh lu
.
o
.
.
ng tu
.
˙’
ho´a nhˇa
`
m gia
˙’
msu
.
.
du
.
th `u
.
a trong tˆam sinh l´y.
Nhu
.
d¯˜a n´oi tru
.
´o
.

c, thao t´ac n`ay khˆong kha
˙’
nghi
.
ch. Do d¯´o, lu
.
o
.
.
ng tu
.
˙’
ho´a khˆong d¯u
.
o
.
.
c
su
.
˙’
du
.
ng trong nh˜u
.
ng ´u
.
ng du
.
ng d¯`oi ho

˙’
i n´en ba
˙’
o to´an thˆong tin.
Gia
˙’
su
.
˙’
p(y) l`a h`am mˆa
.
td¯ˆo
.
x´ac suˆa
´
tcu
˙’
a y v`a ν l`a m ´u
.
clu
.
o
.
.
ng tu
.
˙’
ho´a cu
˙’
a y. Khi

d¯´o sai sˆo
´
cu
˙’
a ph´ep lu
.
o
.
.
ng tu
.
˙’
ho´a l`a
e
2
q
:=

+∞
−∞
(ν − y)
2
p(y)dy,
v`a u
.
´o
.
clu
.
o

.
.
ng sai sˆo
´
t`u
.
t´ın hiˆe
.
u sang lu
.
o
.
.
ng tu
.
˙’
ho´a d¯i
.
nh ngh˜ıa b o
.
˙’
i
Q
SN R
:=


+∞
−∞
y

2
p(y)dy/e
2
q
.
M˜a ho´a
X´et vector v := (ν
0
,ν
1
, ,ν
n−1
) trong d¯´o mˆo
˜
i gi´a tri
.
ν
i
c´o thˆe
˙’
lˆa
´
ymˆo
.
t trong L gi´a
tri
.
a
i
,i =0, 1, ,L − 1. Tiˆe

´
n tr`ınh m˜a ho´a nhˇa
`
m xˆay du
.
.
ng c´ac t`u
.
m˜a nhi
.
phˆan
c
i
,i=0, 1, ,L− 1, tu
.
o
.
ng ´u
.
ng mˆo
.
t-mˆo
.
tv´o
.
imˆo
˜
i gi´a tri
.
a

i
. Mu
.
cd¯´ıch cu
˙’
a m˜a ho´a l`a
thiˆe
´
tkˆe
´
bˆo
.
m˜a sao cho su
.
˙’
du
.
ng sˆo
´
bit ´ıt nhˆa
´
t c´o thˆe
˙’
.V´o
.
im˜ac´od¯ˆo
.
d`ai khˆong d¯ˆo
˙’
i, ta

d`ung b = log
2
L bit d¯ˆe
˙’
biˆe
˙’
udiˆe
˜
ntˆa
´
tca
˙’
L kha
˙’
nˇang. M˜a n`ay tˆo
´
iu
.
u trong tru
.
`o
.
ng ho
.
.
p
x´ac suˆa
´
t xuˆa
´

thiˆe
.
ncu
˙’
a c´ac m´u
.
c a
0
,a
1
, ,a
L−1
bˇa
`
ng nhau.
151
Trong tru
.
`o
.
ng ho
.
.
ptˆo
˙’
ng qu´at, ta thu
.
`o
.
ng d`ung m˜a c´o d¯ˆo

.
d`ai thay d¯ˆo
˙’
id¯ˆe
˙’
g´an c´ac
t`u
.
m˜a c´o d¯ˆo
.
d`ai ngˇa
´
ntu
.
o
.
ng ´u
.
ng gi´a tri
.
thu
.
`o
.
ng xuyˆen xuˆa
´
thiˆe
.
n v`a ngu
.

o
.
.
cla
.
i. Ta
c´o b`ai to´an: cho c´ac gi´a tri
.
a
0
,a
1
, ,a
L−1
v´o
.
i c´ac x´ac suˆa
´
t xuˆa
´
thiˆe
.
n p
0
,p
1
, ,p
L−1
tu
.

o
.
ng ´u
.
ng. X´ac d¯i
.
nh sˆo
´
bit tˆo
´
i thiˆe
˙’
ud¯ˆe
˙’
m˜a ho´a c´ac gi´a tri
.
n`ay v`a thiˆe
´
tkˆe
´
bˆo
.
m˜a
tu
.
o
.
ng ´u
.
ng.

H`ınh 6.3(a) chı
˙’
ra tiˆe
´
n tr`ınh m˜a ho´a nguˆo
`
ngˆo
`
m ba thao t´ac liˆen tiˆe
´
p, nhu
.
ng tˆa
´
t
ca
˙’
c´ac thao t´ac n`ay khˆong nhˆa
´
t thiˆe
´
td¯u
.
o
.
.
csu
.
˙’
du

.
ng trong tˆa
´
tca
˙’
c´ac hˆe
.
thˆo
´
ng n´en d˜u
.
liˆe
.
u. Nhˇa
´
cla
.
i, chˇa
˙’
ng ha
.
n, lu
.
o
.
.
ng tu
.
˙’
ho´a c´o thˆe

˙’
bo
˙’
qua khi n´en ´ap du
.
ng trong hˆe
.
thˆo
´
ng
ba
˙’
o to`an thˆong tin. Ngo`ai ra, mˆo
.
tsˆo
´
k˜y thuˆa
.
tn´en thu
.
`o
.
ng d¯u
.
o
.
.
c mˆo h`ınh ho´a bˇa
`
ng

c´ach ho
.
.
p nhˆa
´
t c´ac khˆo
´
id¯u
.
o
.
.
c phˆan t´ach vˆa
.
tl´y trong H`ınh 6.3(a). Chˇa
˙’
ng ha
.
n, trong
c´ac hˆe
.
thˆo
´
ng n´en d˜u
.
liˆe
.
u theo phu
.
o

.
ng ph´ap du
.
.
b´ao, c´ac khˆo
´
ibiˆe
´
nd¯ˆo
˙’
iv`alu
.
o
.
.
ng tu
.
˙’
ho´a
thu
.
`o
.
ng d¯u
.
o
.
.
cbiˆe
˙’

udiˆe
˜
nbo
.
˙’
imˆo
.
t khˆo
´
i m`a thu
.
.
chiˆe
.
nd¯ˆo
`
ng th`o
.
i hai tiˆe
´
n tr`ınh n`ay.
Bˆo
.
gia
˙’
i m˜a nguˆo
`
nd¯u
.
o

.
.
cchı
˙’
ra trong H`ınh 6.3(b) chı
˙’
gˆo
`
m hai th`anh phˆa
`
n: gia
˙’
i
m˜a k ´yhiˆe
.
u v`a biˆe
´
nd¯ˆo
˙’
i ngu
.
o
.
.
c. C´ac khˆo
´
i n`ay thu
.
.
chiˆe

.
n, theo th´u
.
tu
.
.
ngu
.
o
.
.
cla
.
iv´o
.
itiˆe
´
n
tr`ınh m˜a ho´a nguˆo
`
n: tru
.
´o
.
chˆe
´
t gia
˙’
i m˜a c´ac k´yhiˆe
.

ud¯u
.
o
.
.
c m˜a ho´a v`a sau d¯´o biˆe
´
nd¯ˆo
˙’
i
ngu
.
o
.
.
c. Do d˜u
.
liˆe
.
u sau khi lu
.
o
.
.
ng tu
.
˙’
ho´a s˜e l`am mˆa
´
t thˆong tin nˆen khˆo

´
ilu
.
o
.
.
ng tu
.
˙’
ho´a
ngu
.
o
.
.
c khˆong d¯u
.
o
.
.
csu
.
˙’
du
.
ng trong mˆo h`ınh gia
˙’
im˜anhu
.
chı

˙’
ra trong H`ınh 6.3(b).
6.2.2 M˜a ho´a v`a gia
˙’
i m˜a kˆenh
M˜a h´oa kˆenh v`a gia
˙’
im˜akˆenh d¯´ong vai tr`o quan tro
.
ng trong to`an bˆo
.
qu´a tr`ınh m˜a
h´oa-gia
˙’
i m˜a khi kˆenh truyˆe
`
n c´o nhiˆe
˜
u hoˇa
.
cc´olˆo
˜
i. Ch´ung d¯u
.
o
.
.
c thiˆe
´
tkˆe

´
d¯ ˆe
˙’
gia
˙’
m thiˆe
˙’
u
nhiˆe
˜
ucu
˙’
ad¯u
.
`o
.
ng truyˆe
`
nbˇa
`
ng c´ach ch`en mˆo
.
tbˆo
.
d¯ i ˆe
`
u khiˆe
˙’
n. Phu
.

o
.
ng ph´ap m˜a h´oa
kˆenh truyˆe
`
nhiˆe
.
u qua
˙’
nhˆa
´
td¯u
.
arabo
.
˙’
i Hamming [11] nˇam 1950. Phu
.
o
.
ng ph´ap n`ay du
.
.
a
trˆen viˆe
.
c thˆem c´ac bit v`ao d˜u
.
liˆe
.

ud¯u
.
o
.
.
c m˜a h´oa d¯ˆe
˙’
ba
˙’
od¯a
˙’
mnˆe
´
usˆo
´
lˆo
˜
i trong d¯u
.
`o
.
ng
truyˆe
`
n xuˆa
´
thiˆe
.
nd¯u
˙’

´ıt th`ı c´o thˆe
˙’
phu
.
chˆo
`
id¯u
.
o
.
.
cd˜u
.
liˆe
.
u ban d¯ˆa
`
u.
D
-
ˆe
˙’
gia
˙’
im˜ad˜u
.
liˆe
.
ud¯u
.

o
.
.
c m˜a h´oa bˇa
`
ng phu
.
o
.
ng ph´ap Hamming, bˆo
.
gia
˙’
i m˜a kˆenh
kiˆe
˙’
m tra t´ınh ho
.
.
plˆe
.
(v`a su
.
˙’
asainˆe
´
u c´o) cu
˙’
ad˜u
.

liˆe
.
ud¯u
.
o
.
.
cgu
.
˙’
i. Sau d¯´o, loa
.
ibo
˙’
nh˜u
.
ng
bit thˆem v`ao trong d˜u
.
liˆe
.
u ban d¯ˆa
`
u.
152