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I
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N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
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4
,
No
.
1
,
A
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r
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20
1
5
:
29
–
3
7
30
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u
e
co
llect
s
u
n
iq
u
e
s
y
m
b
o
ls
f
r
o
m
t
h
e
s
o
u
r
ce
i
m
a
g
e
a
n
d
ca
l
cu
lates
it
s
p
r
o
b
a
b
ilit
y
v
alu
e
f
o
r
ea
ch
s
y
m
b
o
l
a
n
d
s
o
r
ts
th
e
s
y
m
b
o
ls
b
ased
o
n
its
p
r
o
b
ab
ilit
y
v
al
u
e.
Fu
r
t
h
er
,
f
r
o
m
th
e
lo
w
es
t
p
r
o
b
ab
ilit
y
v
al
u
e
s
y
m
b
o
l
to
th
e
h
ig
h
es
t
p
r
o
b
ab
ilit
y
v
alu
e
s
y
m
b
o
l,
t
w
o
s
y
m
b
o
ls
co
m
b
in
ed
a
t
a
ti
m
e
to
f
o
r
m
a
b
in
ar
y
tr
ee
.
Mo
r
eo
v
er
,
allo
ca
tes
ze
r
o
to
t
h
e
le
f
t
n
o
d
e
an
d
o
n
e
to
th
e
r
ig
h
t
n
o
d
e
s
t
ar
tin
g
f
r
o
m
t
h
e
r
o
o
t
o
f
th
e
tr
ee
.
T
o
o
b
tain
Hu
f
f
m
a
n
co
d
e
f
o
r
a
p
ar
ticu
lar
s
y
m
b
o
l,
all
ze
r
o
an
d
o
n
e
co
llected
f
r
o
m
t
h
e
r
o
o
t
to
th
at
p
ar
ticu
lar
n
o
d
e
in
th
e
s
a
m
e
o
r
d
er
.
T
h
e
m
ai
n
o
b
j
ec
tiv
e
o
f
th
i
s
p
ap
er
is
to
co
m
p
r
ess
i
m
ag
e
s
b
y
r
ed
u
ci
n
g
n
u
m
b
er
o
f
b
it
s
p
er
p
ix
el
r
eq
u
ir
ed
to
r
ep
r
esen
t
it
an
d
to
d
ec
r
ea
s
e
th
e
tr
an
s
m
is
s
i
o
n
ti
m
e
f
o
r
tr
a
n
s
m
is
s
io
n
o
f
i
m
a
g
es
a
n
d
t
h
en
r
ec
o
n
s
tr
u
cti
n
g
b
ac
k
b
y
d
ec
o
d
i
n
g
t
h
e
H
u
f
f
m
a
n
co
d
es.
T
h
e
e
n
tire
p
ap
er
is
o
r
g
a
n
ized
i
n
t
h
e
f
o
llo
w
i
n
g
s
eq
u
e
n
ce
.
Firstl
y
w
e
n
ee
d
f
o
r
th
e
co
m
p
r
ess
io
n
is
s
tated
,
s
ec
o
n
d
d
is
cr
i
b
es
v
ar
io
u
s
t
y
p
e
s
o
f
d
ata
r
ed
u
n
d
a
n
cies,
t
h
e
n
t
h
e
Me
th
o
d
s
\
tec
h
o
lo
g
y
o
f
co
m
p
r
e
s
s
io
n
s
ar
e
e
x
p
lai
n
ed
,
f
u
r
t
h
e
r
l
y
t
h
e
i
m
p
le
m
e
n
tatio
n
o
f
l
o
s
s
les
s
m
et
h
o
d
o
f
co
m
p
r
es
s
io
n
a
n
d
d
ec
o
m
p
r
ess
io
n
(
i.e
.
Hu
f
f
m
a
n
C
o
d
in
g
&
Dec
o
d
in
g
)
is
d
o
n
e
an
d
f
i
n
all
y
t
he
alg
o
r
it
h
m
is
d
ev
elo
p
ed
an
d
in
th
e
r
es
u
lts
wer
e
p
r
esen
ted
w
it
h
ex
p
la
n
atio
n
an
d
p
ap
er
co
n
clu
d
es
w
it
h
R
ef
er
en
ce
s
.
2.
NE
E
D
F
O
R
CO
M
P
RE
SS
I
O
N
T
h
e
f
o
llo
w
i
n
g
e
x
a
m
p
le
ill
u
s
tr
ates th
e
n
ee
d
f
o
r
co
m
p
r
ess
io
n
o
f
d
ig
ital i
m
a
g
es [
3
]
.
1
.
T
o
s
to
r
e
a
co
lo
u
r
im
a
g
e
o
f
a
m
o
d
er
ate
s
ize,
e.
g
.
5
1
2
×5
1
2
p
ix
els,
o
n
e
n
ee
d
s
0
.
7
5
MB
o
f
d
is
k
s
p
ac
e.
2
.
A
3
5
m
m
d
i
g
ital s
lid
e
w
ith
a
r
eso
lu
tio
n
o
f
1
2
μ
m
r
eq
u
ir
es 1
8
MB
.
3
.
On
e
s
ec
o
n
d
o
f
d
ig
ital P
AL
(
P
h
ase
A
l
ter
n
atio
n
L
i
n
e)
v
id
eo
r
eq
u
ir
es 2
7
MB.
A
h
i
g
h
-
q
u
alit
y
i
m
a
g
e
m
a
y
r
e
q
u
ir
e
1
0
to
1
0
0
m
illi
o
n
b
its
f
o
r
r
ep
r
esen
tatio
n
.
Fo
r
e
x
a
m
p
l
e,
a
clea
n
p
h
o
to
g
r
ap
h
ic
i
m
a
g
e
r
eq
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ir
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s
a
p
p
r
o
x
im
a
tel
y
1
,
2
8
0
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o
w
s
o
f
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0
0
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ix
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h
,
w
i
th
2
4
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its
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f
co
lo
r
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n
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o
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m
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er
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ix
el;
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at
is
,
a
to
tal
o
f
2
4
,
5
7
6
,
0
0
0
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its
,
o
r
3
,
0
7
2
,
0
0
0
b
y
te
s
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T
h
e
lar
g
e
d
ata
f
ile
s
as
s
o
ciate
d
w
it
h
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m
a
g
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th
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s
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ex
tr
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el
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ig
h
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m
p
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io
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s
to
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k
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e
p
r
ac
tical.
to
s
to
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ab
o
u
t
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0
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p
ictu
r
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t
h
at
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o
v
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t
th
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4
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r
a
m
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er
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o
n
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ate
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m
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tio
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r
e,
ab
o
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t
8
s
ec
o
n
d
s
W
ith
o
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t
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m
p
r
es
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n
,
a
CD
w
i
th
a
s
t
o
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ag
e
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p
ac
ity
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p
r
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m
at
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y
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il
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te
s
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ld
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a
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v
ie.
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o
s
to
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e
th
ese
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m
ag
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,
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d
m
ak
e
t
h
e
m
a
v
ailab
le
o
v
er
n
et
w
o
r
k
(
e.
g
.
t
h
e
in
ter
n
et)
,
co
m
p
r
e
s
s
io
n
tech
n
iq
u
es
ar
e
n
ee
d
ed
.
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m
ag
e
co
m
p
r
es
s
io
n
ad
d
r
ess
es
t
h
e
p
r
o
b
lem
o
f
r
ed
u
ci
n
g
th
e
a
m
o
u
n
t
o
f
d
ata
r
eq
u
ir
ed
t
o
r
ep
r
esen
t
a
d
ig
ital
i
m
a
g
e.
T
h
e
u
n
d
er
l
y
in
g
b
asi
s
o
f
t
h
e
r
ed
u
ctio
n
p
r
o
ce
s
s
i
s
t
h
e
r
e
m
o
v
al
o
f
r
ed
u
n
d
a
n
t
d
ata.
A
cc
o
r
d
i
n
g
to
m
at
h
e
m
atica
l
p
o
in
t
o
f
v
ie
w
,
t
h
is
a
m
o
u
n
t
s
to
tr
an
s
f
o
r
m
i
n
g
a
t
w
o
-
d
i
m
en
s
io
n
a
l
p
ix
el
ar
r
a
y
in
to
a
s
tatis
t
icall
y
u
n
co
r
r
elate
d
d
ata
s
et.
T
h
e
tr
an
s
f
o
r
m
atio
n
is
ap
p
lied
p
r
io
r
to
s
to
r
ag
e
o
r
tr
an
s
m
i
s
s
io
n
o
f
t
h
e
i
m
a
g
e.
A
t
r
ec
eiv
er
,
t
h
e
co
m
p
r
es
s
ed
i
m
ag
e
is
d
ec
o
m
p
r
ess
ed
to
r
ec
o
n
s
tr
u
ct
t
h
e
o
r
ig
in
al
i
m
ag
e
o
r
an
ap
p
r
o
x
i
m
a
tio
n
to
it.
T
h
e
ex
a
m
p
le
b
elo
w
clea
r
l
y
s
h
o
w
s
t
h
e
i
m
p
o
r
tan
ce
o
f
co
m
p
r
e
s
s
io
n
.
An
i
m
a
g
e,
1
0
2
4
p
ix
el×
1
0
2
4
p
ix
el×
2
4
b
it,
w
it
h
o
u
t
co
m
p
r
es
s
io
n
,
w
o
u
ld
r
eq
u
ir
e
3
MB
o
f
s
to
r
ag
e
an
d
7
m
in
u
tes
f
o
r
tr
an
s
m
is
s
io
n
,
u
til
izin
g
a
h
ig
h
s
p
ee
d
,
6
4
Kb
its
/s
,
I
SD
N
lin
e.
I
f
th
e
i
m
ag
e
i
s
co
m
p
r
ess
ed
at
a
1
0
:1
co
m
p
r
ess
io
n
r
atio
,
th
e
s
to
r
ag
e
r
eq
u
ir
e
m
en
t is r
ed
u
ce
d
to
3
0
0
KB
an
d
th
e
tr
an
s
m
i
s
s
io
n
ti
m
e
d
r
o
p
t
o
less
th
a
n
6
s
ec
o
n
d
s
.
A
co
m
m
o
n
c
h
ar
ac
ter
i
s
tic
o
f
m
o
s
t
i
m
ag
e
s
is
th
at
t
h
e
n
ei
g
h
b
o
r
in
g
p
ix
els
ar
e
co
r
r
elate
d
a
n
d
th
er
ef
o
r
e
co
n
tain
r
ed
u
n
d
an
t in
f
o
r
m
a
tio
n
.
T
h
e
alti
m
ate
tas
k
i
s
t
h
en
,
i
s
t
o
f
in
d
le
s
s
co
r
r
elate
d
r
ep
r
esen
tatio
n
o
f
t
h
e
i
m
a
g
e.
T
w
o
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
e
n
t
s
o
f
co
m
p
r
ess
io
n
ar
e
r
ed
u
n
d
an
c
y
an
d
i
r
r
elev
a
n
c
y
r
ed
u
c
tio
n
.
R
ed
u
n
d
an
c
y
r
ed
u
ctio
n
ai
m
s
ar
e
r
em
o
v
i
n
g
d
u
p
licatio
n
f
r
o
m
t
h
e
s
i
g
n
a
l
s
o
u
r
ce
(
i
m
ag
e/v
id
eo
)
.
I
r
r
elev
an
c
y
r
ed
u
ctio
n
o
m
its
p
ar
ts
o
f
t
h
e
s
i
g
n
al
t
h
at
w
ill
n
o
t
b
e
n
o
ticed
b
y
th
e
s
i
g
n
a
l
r
ec
eiv
er
,
n
a
m
el
y
t
h
e
Hu
m
an
V
is
u
al
S
y
s
te
m
(
HVS)
.
I
n
g
en
er
al
,
t
h
r
ee
t
y
p
es o
f
r
ed
u
n
d
an
c
y
ca
n
b
e
id
en
ti
f
ied
.
3.
VARIO
US
T
YP
E
S O
F
RE
D
UNDA
NCY
I
n
d
ig
ital i
m
a
g
e
co
m
p
r
ess
io
n
,
th
r
ee
b
asic d
ata
r
ed
u
n
d
an
cie
s
ca
n
b
e
id
en
ti
f
ied
an
d
ex
p
lo
ite
d
:
1
.
C
o
d
in
g
r
ed
u
n
d
a
n
c
y
2
.
Sp
atial
R
ed
u
n
d
a
n
c
y
a
n
d
T
e
m
p
o
r
al
R
ed
u
n
d
a
n
c
y
3.
I
r
r
elev
an
t
I
n
f
o
r
m
a
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
C
o
mp
r
ess
io
n
Tech
n
iq
u
es V
s
Hu
ffma
n
C
o
d
in
g
(
V
ika
s
K
u
ma
r
)
31
Data
co
m
p
r
ess
io
n
i
s
ac
h
ie
v
ed
w
h
e
n
o
n
e
o
r
m
o
r
e
o
f
th
ese
r
ed
u
n
d
a
n
cies a
r
e
r
ed
u
ce
d
o
r
eli
m
i
n
ated
.
3
.
1
.
Co
din
g
Redund
a
ncy
A
co
d
e
is
a
s
y
s
te
m
o
f
s
y
m
b
o
ls
(
letter
s
,
n
u
m
b
er
s
,
b
it
s
,
a
n
d
th
e
l
ik
e)
u
s
ed
to
r
ep
r
esen
t
a
b
o
d
y
o
f
in
f
o
r
m
atio
n
o
r
s
et
o
f
ev
e
n
t
s
.
E
ac
h
p
iece
o
f
in
f
o
r
m
atio
n
o
r
ev
en
t
s
is
as
s
i
g
n
ed
a
s
eq
u
e
n
ce
o
f
co
d
e
s
y
m
b
o
ls
,
ca
lled
a
co
d
e
w
o
r
d
.
T
h
e
n
u
m
b
er
o
f
s
y
m
b
o
l
s
in
ea
ch
co
d
e
w
o
r
d
is
its
len
g
th
.
T
h
e
8
-
b
it
co
d
es
th
at
ar
e
u
s
ed
t
o
r
ep
r
esen
t
th
e
in
te
n
s
ities
in
th
e
m
o
s
t
2
-
D
i
n
te
n
s
it
y
ar
r
a
y
s
c
o
n
tain
m
o
r
e
b
its
t
h
a
n
ar
e
n
ee
d
ed
to
r
ep
r
esen
t
t
h
e
in
te
n
s
it
ies.
3
.
2
.
Sp
a
t
ia
l R
edun
da
ncy
a
nd
T
e
m
po
ra
l R
edu
nd
a
ncy
B
ec
au
s
e
th
e
p
i
x
els
o
f
m
o
s
t
2
-
D
in
te
n
s
it
y
ar
r
a
y
s
ar
e
co
r
r
elate
d
s
p
atiall
y
,
th
e
i
n
f
o
r
m
atio
n
i
s
u
n
n
ec
es
s
ar
il
y
r
ep
licated
in
t
h
e
r
ep
r
esen
tat
io
n
s
o
f
t
h
e
co
r
r
elate
d
p
ix
els.
I
n
v
id
eo
s
eq
u
en
ce
,
te
m
p
o
r
all
y
co
r
r
elate
d
p
ix
els ar
e
also
d
u
p
licate
in
f
o
r
m
atio
n
.
3
.
3
.
I
rr
elev
a
nt
I
nfo
rm
a
t
io
n
Mo
s
t
2
-
D
i
n
te
n
s
i
t
y
ar
r
a
y
s
co
n
tai
n
i
n
f
o
r
m
atio
n
t
h
at
is
i
g
n
o
r
ed
b
y
th
e
h
u
m
an
v
i
s
u
a
l
s
y
s
te
m
a
n
d
ex
tr
an
eo
u
s
to
th
e
i
n
te
n
d
ed
u
s
e
o
f
th
e
i
m
ag
e.
I
t i
s
r
ed
u
n
d
an
t i
n
th
e
s
en
s
e
th
a
t it
is
n
o
t u
s
ed
.
I
m
ag
e
co
m
p
r
es
s
io
n
r
esear
ch
ai
m
s
at
r
ed
u
ci
n
g
th
e
n
u
m
b
er
o
f
b
its
n
ee
d
ed
to
r
ep
r
esen
t
an
i
m
ag
e
b
y
r
e
m
o
v
i
n
g
th
e
s
p
atial
a
n
d
s
p
ec
tr
al
r
ed
u
n
d
an
cie
s
as
m
u
c
h
as p
o
s
s
ib
le.
4.
WH
Y
DO
WE
N
E
E
D
CO
M
P
RE
SS
I
O
N?
T
h
e
f
o
llo
w
i
n
g
ch
ar
t
i
s
s
h
o
w
t
h
e
q
u
alita
tiv
e
tr
a
n
s
i
tio
n
f
r
o
m
s
i
m
p
le
te
x
t
to
f
u
l
l
-
m
o
tio
n
v
id
eo
d
ata
an
d
th
e
d
is
k
s
p
ac
e
tr
an
s
m
i
s
s
io
n
b
an
d
w
id
th
,
a
n
d
tr
an
s
m
is
s
i
o
n
ti
m
e
n
ee
d
ed
to
s
to
r
e
an
d
tr
an
s
m
i
t
s
u
c
h
u
n
co
m
p
r
e
s
s
ed
d
ata.
C
h
ar
t
co
n
tai
n
:
Mu
lt
i
m
ed
ia
d
ata
t
y
p
es
an
d
u
n
c
o
m
p
r
es
s
ed
s
to
r
ag
e
p
ac
e,
tr
an
s
m
i
s
s
io
n
b
an
d
w
id
t
h
,
an
d
tr
an
s
m
is
s
io
n
ti
m
e
r
eq
u
ir
ed
.
T
h
e
p
r
ef
ix
k
ilo
-
d
en
o
tes a
f
ac
to
r
o
f
1
0
0
0
r
ath
er
th
an
1
0
2
4
.
T
h
e
ex
a
m
p
le
s
g
iv
e
n
in
th
e
ab
o
v
e
ch
ar
t
c
lear
l
y
d
e
f
i
n
ed
t
h
e
n
ee
d
f
o
r
s
u
f
f
icie
n
t
s
to
r
ag
e
s
p
ac
e,
lar
g
e
tr
an
s
m
is
s
io
n
b
a
n
d
w
id
th
,
an
d
l
o
n
g
tr
an
s
m
is
s
io
n
ti
m
e
f
o
r
i
m
a
g
e,
au
d
io
,
an
d
v
id
eo
d
ata.
A
t
th
e
p
r
esen
t
s
tate
o
f
tec
h
n
o
lo
g
y
,
t
h
e
o
n
l
y
s
o
lu
tio
n
i
s
t
o
co
m
p
r
es
s
m
u
lti
m
ed
ia
d
ata
b
ef
o
r
e
its
s
to
r
ag
e
an
d
tr
an
s
m
is
s
io
n
,
an
d
d
ec
o
m
p
r
ess
it
at
th
e
r
ec
eiv
er
f
o
r
p
lay
b
ac
k
.
Fo
r
ex
a
m
p
le,
w
it
h
a
co
m
p
r
ess
io
n
r
atio
o
f
3
2
:
1
,
th
e
s
p
ac
e,
b
an
d
w
id
t
h
,
an
d
tr
an
s
m
i
s
s
io
n
ti
m
e
r
eq
u
ir
e
m
en
ts
ca
n
b
e
r
ed
u
ce
d
b
y
a
f
ac
to
r
o
f
3
2
,
w
it
h
ac
ce
p
tab
le
q
u
alit
y
.
5.
WH
AT
AR
E
T
H
E
DIFF
E
R
E
NT
C
L
A
SS
E
S O
F
CO
M
P
RE
SS
I
O
N
T
E
CH
N
I
Q
UE
S?
C
o
m
p
r
ess
io
n
ca
n
b
e
d
iv
id
ed
i
n
to
t
w
o
ca
te
g
o
r
ies,
as
L
o
s
s
le
s
s
an
d
L
o
s
s
y
co
m
p
r
ess
io
n
.
1.
L
o
s
s
le
s
s
co
din
g
(
ent
ro
py
co
din
g
)
a.
Data
ca
n
b
e
d
ec
o
d
ed
t
o
f
o
r
m
e
x
ac
tl
y
th
e
s
a
m
e
b
it
s
.
b.
Used
in
.
zip
.
c.
C
an
o
n
l
y
ac
h
ie
v
e
m
o
d
er
ate
co
m
p
r
e
s
s
io
n
(
e.
g
.
2
:1
-
3
:1
)
f
o
r
n
atu
r
al
i
m
ag
e
s
.
d.
C
an
b
e
i
m
p
o
r
tan
t in
ce
r
tai
n
ap
p
licatio
n
s
s
u
c
h
as
m
ed
ical
i
m
a
g
in
g
.
T
h
e
r
ec
o
n
s
tr
u
cted
i
m
a
g
e
a
f
te
r
co
m
p
r
es
s
io
n
is
n
u
m
er
ical
l
y
id
en
tical
to
th
e
o
r
i
g
i
n
al
i
m
a
g
e.
I
n
lo
s
s
y
co
m
p
r
es
s
io
n
s
ch
e
m
e,
th
e
r
ec
o
n
s
tr
u
cted
i
m
a
g
e
co
n
tai
n
s
d
eg
r
ad
atio
n
r
elativ
e
to
th
e
o
r
ig
in
al
.
M
u
l
t
i
me
d
i
a
d
a
t
a
S
i
z
e
/
D
u
r
a
t
i
o
n
B
i
t
s/
P
i
x
e
l
Or
B
i
t
s/
S
a
m
p
l
e
U
n
c
o
mp
r
e
sse
d
S
i
z
e
(
B
f
o
r
b
y
t
e
s)
T
r
a
n
smissi
o
n
B
a
n
d
w
i
d
t
h
(
b
f
o
r
b
i
t
s)
T
r
a
n
smissi
o
n
T
i
me
A
p
a
g
e
o
f
t
e
x
t
1
1
”
x
8
.
5
”
V
a
r
y
i
n
g
r
e
so
l
u
t
i
o
n
4
–
8
K
B
32
-
6
4
K
b
/
p
a
g
e
1
.
1
-
2
.
2
se
c
T
e
l
e
p
h
o
n
e
q
u
a
l
i
t
y
sp
e
e
c
h
1
0
se
c
8
b
p
s
8
0
K
B
6
4
K
b
/
se
c
2
2
.
2
se
c
G
r
a
y
sca
l
e
i
mag
e
5
1
2
x
5
1
2
8
b
p
p
2
6
2
K
B
2
.
1
M
b
/
i
m
a
g
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1
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1
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c
C
o
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mag
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7
8
6
K
B
6
.
2
9
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b
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e
3
m
i
n
3
9
se
c
M
e
d
i
c
a
l
i
mag
e
2
0
4
8
x
2
0
4
8
1
2
b
p
p
5
.
1
6
M
B
4
1
.
3
M
b
/
i
m
a
g
e
2
3
mi
n
5
4
se
c
S
H
D
i
mag
e
2
0
4
8
x
2
0
4
8
2
4
b
p
p
1
2
.
5
8
M
B
1
0
0
M
b
/
i
mag
e
5
8
mi
n
1
5
se
c
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I
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N
:
2
2
5
2
-
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-
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Vo
l.
4
,
No
.
1
,
A
p
r
il
20
1
5
:
29
–
3
7
32
2.
L
o
s
s
ly
s
o
urce
co
di
ng
a.
Dec
o
m
p
r
ess
ed
i
m
a
g
e
is
v
i
s
u
al
l
y
s
i
m
ilar
,
b
u
t
h
as b
ee
n
c
h
a
n
g
ed
.
b.
Used
in
.
J
P
E
G.
an
d
.
MP
E
G.
c.
C
an
ac
h
ie
v
e
m
u
c
h
g
r
ea
ter
co
m
p
r
e
s
s
io
n
(
e.
g
.
2
0
:1
-
4
0
:1
)
f
o
r
n
atu
r
al
i
m
ag
e
s
.
5
.
1
.
Si
m
ple R
e
pet
it
io
n
I
n
th
i
s
I
f
i
n
a
s
eq
u
en
ce
a
s
er
ie
s
o
n
n
s
u
cc
e
s
s
i
v
e
to
k
e
n
s
ap
p
e
ar
s
w
e
ca
n
r
ep
lace
th
ese
w
it
h
a
to
k
en
a
n
d
a
co
u
n
t
n
u
m
b
er
o
f
o
cc
u
r
r
e
n
c
es.
W
e
u
s
u
all
y
n
ee
d
to
h
av
e
a
s
p
ec
ial
f
lag
to
d
en
o
te
w
h
e
n
th
e
r
ep
ea
ted
to
k
e
n
ap
p
ea
r
s
.
Fo
r
E
x
a
m
p
le
8
0
0
0
0
7
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
W
e
ca
n
r
ep
lace
w
it
h
8
f
4
7
9
f
4
0
W
h
er
e
f
is
t
h
e
f
la
g
f
o
r
ze
r
o
.
I
n
it C
o
m
p
r
es
s
io
n
s
av
i
n
g
s
d
ep
en
d
o
n
th
e
co
n
te
n
t o
f
th
e
d
ata.
A
p
p
licatio
n
s
:
1.
Su
p
p
r
ess
io
n
o
f
ze
r
o
'
s
i
n
a
f
ile
(
Z
er
o
L
en
g
t
h
S
u
p
p
r
ess
io
n
)
.
2.
Sil
en
ce
i
n
au
d
io
d
ata,
o
r
p
au
s
es in
co
n
v
er
s
atio
n
etc
.
3.
B
it
m
ap
s
.
4.
B
lan
k
s
in
te
x
t o
r
p
r
o
g
r
am
s
o
u
r
ce
f
iles
.
5.
B
ac
k
g
r
o
u
n
d
s
in
i
m
a
g
es.
6.
Oth
er
r
eg
u
lar
i
m
a
g
e
o
r
d
ata
to
k
en
s
.
5
.
2
.
RL
E
T
h
is
en
co
d
in
g
m
et
h
o
d
[
3
4
]
is
f
r
eq
u
en
tl
y
ap
p
lied
to
i
m
a
g
es
(
o
r
p
ix
els
in
a
s
ca
n
li
n
e)
.
I
n
th
i
s
in
s
tan
ce
,
s
eq
u
en
ce
s
o
f
i
m
a
g
e
ele
m
e
n
t
s
(
X1
,
X2
…
…….
,
Xn
)
ar
e
m
ap
p
ed
to
p
air
s
(
c1
,
l1
)
,
(
c2
,
l2
)
,
…….
.
,
(
cn
,
l
n
)
w
h
er
e
ci
r
ep
r
esen
t
i
m
ag
e
in
te
n
s
it
y
o
r
co
lo
r
an
d
li
th
e
len
g
t
h
o
f
th
e
i
th
r
u
n
o
f
p
i
x
els
(
No
t
d
is
s
i
m
ilar
to
ze
r
o
len
g
t
h
s
u
p
p
r
ess
io
n
ab
o
v
e)
.
T
h
e
s
av
i
n
g
s
ar
e
d
ep
en
d
en
t
o
n
th
e
d
ata.
I
n
th
e
w
o
r
s
t
ca
s
e
(
R
a
n
d
o
m
No
is
e)
en
co
d
in
g
i
s
g
r
ea
ter
th
a
n
o
r
ig
i
n
al
f
i
le.
A
p
p
licatio
n
s
:
I
t is a
s
m
al
l c
o
m
p
r
ess
io
n
co
m
p
o
n
en
t u
s
ed
in
J
P
E
G
co
m
p
r
es
s
io
n
.
5
.
3
.
P
a
t
t
er
n Sub
s
t
it
utio
n
T
h
is
is
a
s
i
m
p
le
f
o
r
m
o
f
s
tati
s
tical
en
co
d
in
g
.
Her
e
w
e
s
u
b
s
ti
tu
te
a
f
r
eq
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e
n
tl
y
r
ep
ea
tin
g
p
atter
n
(
s
)
w
i
th
a
co
d
e.
T
h
e
co
d
e
is
s
h
o
r
ter
th
an
p
atter
n
g
i
v
i
n
g
u
s
co
m
p
r
es
s
io
n
.
Mo
r
e
ty
p
icall
y
to
k
e
n
s
ar
e
as
s
i
g
n
ed
ac
co
r
d
in
g
to
f
r
eq
u
en
c
y
o
f
o
cc
u
r
r
en
ce
o
f
p
at
ter
n
s
:
1.
C
o
u
n
t o
cc
u
r
r
en
ce
o
f
to
k
en
s
2.
So
r
t in
Desce
n
d
in
g
o
r
d
er
3.
Ass
i
g
n
s
o
m
e
s
y
m
b
o
ls
to
h
i
g
h
e
s
t c
o
u
n
t to
k
e
n
s
5
.
4
.
E
ntr
o
py
E
nco
din
g
L
o
s
s
less
co
m
p
r
es
s
io
n
f
r
eq
u
e
n
tl
y
i
n
v
o
lv
es
s
o
m
e
f
o
r
m
o
f
e
n
tr
o
p
y
e
n
co
d
in
g
a
n
d
is
b
ased
o
n
in
f
o
r
m
atio
n
t
h
eo
r
etic
tech
n
iq
u
es.
Sh
a
n
n
o
n
is
f
at
h
er
o
f
in
f
o
r
m
atio
n
t
h
eo
r
y
.
5
.
5
.
H
uff
m
a
n Co
di
ng
Hu
f
f
m
a
n
co
d
in
g
[
2
4
]
is
b
ased
o
n
t
h
e
f
r
eq
u
e
n
c
y
o
f
o
cc
u
r
r
en
ce
o
f
a
d
ata
ite
m
(
p
ix
el
in
i
m
ag
es).
T
h
e
p
r
in
cip
le
is
to
u
s
e
a
lo
w
er
n
u
m
b
er
o
f
b
it
s
to
e
n
co
d
e
th
e
d
ata
th
at
o
cc
u
r
s
m
o
r
e
f
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eq
u
en
tl
y
.
C
o
d
es
ar
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s
to
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ed
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a
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e
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o
o
k
w
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h
m
a
y
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e
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cted
f
o
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ch
i
m
ag
e
o
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a
s
et
o
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i
m
ag
e
s
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I
n
all
ca
s
es
th
e
co
d
e
b
o
o
k
p
lu
s
en
co
d
ed
d
ata
m
u
s
t b
e
tr
an
s
m
it
ted
to
en
ab
le
d
ec
o
d
in
g
.
5
.
6
.
Ada
ptiv
e
H
uf
f
m
a
n Co
di
ng
T
h
e
k
e
y
i
s
to
h
av
e
b
o
t
h
en
co
d
er
an
d
d
ec
o
d
er
to
u
s
e
ex
ac
tl
y
t
h
e
s
a
m
e
i
n
it
ializatio
n
an
d
u
p
d
ate
m
o
d
el
r
o
u
tin
es.
Up
d
ate
m
o
d
el
d
o
es t
w
o
t
h
in
g
s
:
1.
in
cr
e
m
e
n
t t
h
e
co
u
n
t
2.
u
p
d
ate
th
e
Hu
f
f
m
an
tr
ee
[
2
5
]
Du
r
in
g
th
e
u
p
d
ates,
th
e
Hu
f
f
m
an
tr
ee
w
ill
b
e
m
ai
n
tai
n
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s
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lin
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p
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o
p
er
ty
,
i.e
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th
e
n
o
d
es
(
in
ter
n
al
an
d
leaf
)
ar
e
ar
r
an
g
ed
i
n
o
r
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er
o
f
in
cr
ea
s
in
g
w
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g
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ts
,
W
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s
w
ap
p
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es
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ar
y
,
t
h
e
f
ar
th
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s
t
n
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e
w
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
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C
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5
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7
.
Arit
h
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Co
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g
Hu
f
f
m
a
n
co
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g
a
n
d
t
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e
lik
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s
e
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i
n
te
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m
b
er
(
k
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o
f
b
it
s
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o
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o
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h
en
ce
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s
n
ev
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th
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1
.
So
m
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g
.
,
w
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en
s
en
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n
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1
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it i
m
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co
m
p
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ess
io
n
b
ec
o
m
e
s
i
m
p
o
s
s
ib
le.
[
1
5
]
5
.
8
.
L
Z
W
L
Z
W
co
m
p
r
ess
io
n
r
e
p
lace
s
s
tr
in
g
s
o
f
ch
ar
ac
ter
s
w
i
th
s
i
n
g
le
co
d
es.
I
t d
o
es
n
o
t
d
o
an
y
an
al
y
s
i
s
o
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th
e
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co
m
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tex
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n
s
tead
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u
s
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ad
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er
y
n
e
w
s
tr
i
n
g
o
f
c
h
a
r
ac
ter
s
it
s
ee
s
to
a
tab
le
o
f
s
tr
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s
.
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o
m
p
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ter
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L
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al
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ith
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ir
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ith
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as s
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it c
o
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5
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9
5
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ef
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to
s
u
b
s
tr
in
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.
L
Z
W
co
m
p
r
ess
io
n
w
o
r
k
s
b
est
f
o
r
f
iles
co
n
tain
in
g
l
o
ts
o
f
r
e
p
etitiv
e
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ata.
T
h
is
is
o
f
te
n
t
h
e
ca
s
e
w
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th
tex
t
a
n
d
m
o
n
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c
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m
e
i
m
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e
s
.
Fil
es
t
h
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ar
e
co
m
p
r
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ed
b
u
t
th
at
d
o
n
o
t
co
n
tai
n
an
y
r
ep
eti
tiv
e
i
n
f
o
r
m
atio
n
at
all
ca
n
ev
e
n
g
r
o
w
b
ig
g
er
.
A
d
v
an
ta
g
es a
n
d
Dis
ad
v
an
ta
g
e
s
:
L
Z
W
co
m
p
r
ess
io
n
is
f
ast.
A
p
p
licatio
n
s
:
L
Z
W
co
m
p
r
ess
io
n
ca
n
b
e
u
s
e
d
in
a
v
ar
iet
y
o
f
f
i
le
f
o
r
m
at
s
[
3
0
]
.
1.
T
I
FF
f
iles
2.
GI
F f
ile
s
6.
H
UF
F
M
AN
AL
G
O
R
I
T
H
M
Hu
f
f
m
a
n
co
d
in
g
is
a
n
en
tr
o
p
y
e
n
co
d
in
g
alg
o
r
it
h
m
u
s
ed
f
o
r
lo
s
s
less
d
ata
co
m
p
r
ess
io
n
i
n
co
m
p
u
ter
s
cien
ce
an
d
i
n
f
o
r
m
atio
n
t
h
eo
r
y
.
T
h
e
ter
m
r
ef
er
s
to
t
h
e
u
s
e
o
f
a
v
ar
iab
le
-
len
g
t
h
co
d
e
t
ab
le
f
o
r
en
co
d
in
g
a
s
o
u
r
ce
s
y
m
b
o
l
(
s
u
c
h
a
s
a
c
h
ar
ac
ter
in
a
f
ile)
w
h
er
e
t
h
e
v
ar
iab
le
-
len
g
t
h
co
d
e
tab
le
h
as
b
ee
n
d
er
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ed
i
n
a
p
ar
ticu
lar
w
a
y
b
ased
o
n
t
h
e
es
ti
m
ated
p
r
o
b
ab
ilit
y
o
f
o
cc
u
r
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n
ce
f
o
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s
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ib
le
v
al
u
e
o
f
th
e
s
o
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r
ce
s
y
m
b
o
l.
Hu
f
f
m
a
n
co
d
in
g
u
s
es a
s
p
ec
if
i
c
m
et
h
o
d
f
o
r
ch
o
o
s
in
g
t
h
e
r
ep
r
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tatio
n
f
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r
ea
ch
s
y
m
b
o
l,
r
esu
lt
in
g
i
n
a
p
r
ef
i
x
-
f
r
ee
co
d
e
(
th
at
i
s
,
t
h
e
b
it
s
tr
in
g
r
ep
r
esen
ti
n
g
s
o
m
e
p
ar
tic
u
lar
s
y
m
b
o
l
is
n
e
v
er
a
p
r
ef
i
x
o
f
th
e
b
it
s
tr
i
n
g
r
ep
r
esen
tin
g
a
n
y
o
th
er
s
y
m
b
o
l)
th
at
ex
p
r
ess
e
s
t
h
e
m
o
s
t
co
m
m
o
n
c
h
ar
ac
ter
s
u
s
in
g
s
h
o
r
te
r
s
tr
in
g
s
o
f
b
it
s
t
h
a
n
ar
e
u
s
ed
f
o
r
less
co
m
m
o
n
s
o
u
r
ce
s
y
m
b
o
ls
.
H
u
f
f
m
a
n
w
a
s
ab
le
to
d
esig
n
t
h
e
m
o
s
t
ef
f
icie
n
t
co
m
p
r
ess
io
n
m
et
h
o
d
o
f
th
i
s
t
y
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e:
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o
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m
ap
p
in
g
o
f
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d
iv
id
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s
o
u
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ce
s
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m
b
o
ls
to
u
n
iq
u
e
s
tr
i
n
g
s
o
f
b
its
w
ill
p
r
o
d
u
ce
a
s
m
al
ler
av
er
ag
e
o
u
tp
u
t
s
ize
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en
th
e
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t
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al
s
y
m
b
o
l
f
r
eq
u
e
n
cies
a
g
r
ee
w
it
h
t
h
o
s
e
u
s
ed
t
o
cr
ea
te
th
e
co
d
e.
A
m
et
h
o
d
w
a
s
later
f
o
u
n
d
to
d
o
th
is
i
n
li
n
ea
r
ti
m
e
i
f
in
p
u
t
p
r
o
b
ab
ilit
ies
(
also
k
n
o
w
n
a
s
w
ei
g
h
ts
)
ar
e
s
o
r
te
d
.
Fo
r
a
s
et
o
f
s
y
m
b
o
ls
w
it
h
a
u
n
i
f
o
r
m
p
r
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b
ab
ilit
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d
is
tr
ib
u
tio
n
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d
a
n
u
m
b
er
o
f
m
e
m
b
er
s
w
h
ic
h
is
a
p
o
w
er
o
f
t
w
o
,
Hu
f
f
m
a
n
co
d
in
g
is
eq
u
i
v
ale
n
t
to
s
i
m
p
le
b
in
ar
y
b
lo
c
k
en
co
d
i
n
g
[
4
0
]
e.
g
.
,
ASC
I
I
co
d
in
g
.
6
.
1
.
B
a
s
ic
T
ec
hn
iq
ue
Ass
u
m
e
y
o
u
h
a
v
e
a
s
o
u
r
ce
g
e
n
er
ati
n
g
4
d
if
f
er
en
t
s
y
m
b
o
ls
{
a
1,
a
2,
a
3,
a
4
}
w
it
h
p
r
o
b
a
b
ilit
y
{0
.
4
5
;0
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3
5
;
0
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2
5
;
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0
5
}.
Gen
er
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a
b
in
ar
y
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ee
f
r
o
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le
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t
to
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tak
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t
h
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t
w
o
le
s
s
p
r
o
b
ab
le
s
y
m
b
o
ls
,
p
u
t
tin
g
th
e
m
to
g
et
h
e
r
to
f
o
r
m
a
n
o
t
h
er
eq
u
i
v
ale
n
t s
y
m
b
o
l
h
a
v
in
g
a
p
r
o
b
ab
ilit
y
th
at
eq
u
als
th
e
s
u
m
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
l.
4
,
No
.
1
,
A
p
r
il
20
1
5
:
29
–
3
7
34
th
e
t
w
o
s
y
m
b
o
ls
.
Kee
p
o
n
d
o
i
n
g
it
u
n
til
y
o
u
h
a
v
e
j
u
s
t
o
n
e
s
y
m
b
o
l.
T
h
en
r
ea
d
th
e
tr
ee
b
ac
k
w
ar
d
s
,
f
r
o
m
r
i
g
h
t
to
lef
t,
ass
i
g
n
i
n
g
d
i
f
f
er
e
n
t b
its
to
d
if
f
er
en
t b
r
an
ch
e
s
.
T
h
e
f
in
al
h
u
f
f
m
an
co
d
e
is
:
6
.
2
.
Sy
m
bo
l C
o
de
T
h
e
tech
n
iq
u
e
w
o
r
k
s
b
y
cr
ea
t
in
g
a
b
i
n
ar
y
tr
ee
o
f
n
o
d
es.
T
h
ese
ca
n
b
e
s
to
r
ed
in
a
r
eg
u
lar
ar
r
ay
,
t
h
e
s
ize
o
f
w
h
ic
h
d
ep
en
d
s
o
n
th
e
n
u
m
b
er
o
f
s
y
m
b
o
ls
(
N)
.
A
n
o
d
e
ca
n
b
e
eith
er
a
lea
f
n
o
d
e
o
r
an
in
ter
n
al
n
o
d
e.
I
n
itiall
y
,
all
n
o
d
es
ar
e
leaf
n
o
d
es,
w
h
ich
co
n
ta
in
t
h
e
s
y
m
b
o
l
its
elf
,
t
h
e
w
ei
g
h
t
(
f
r
eq
u
en
c
y
o
f
ap
p
ea
r
an
ce
)
o
f
th
e
s
y
m
b
o
l
a
n
d
o
p
tio
n
all
y
,
a
l
in
k
to
a
p
ar
e
n
t
n
o
d
e
w
h
ic
h
m
ak
es
it
ea
s
y
to
r
ea
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th
e
co
d
e
(
in
r
e
v
er
s
e)
s
tar
tin
g
f
r
o
m
a
leaf
n
o
d
e.
I
n
ter
n
al
n
o
d
es
co
n
tain
s
y
m
b
o
l
w
eig
h
t,
li
n
k
s
to
t
w
o
ch
ild
n
o
d
es
an
d
t
h
e
o
p
tio
n
al
lin
k
to
a
p
ar
en
t
n
o
d
e.
As
a
co
m
m
o
n
co
n
v
e
n
tio
n
,
b
it
'
0
'
r
ep
r
esen
t
s
f
o
llo
w
in
g
t
h
e
le
f
t
ch
ild
an
d
b
it
'
1
'
r
ep
r
ese
n
ts
f
o
llo
w
in
g
t
h
e
r
ig
h
t
c
h
ild
.
A
f
i
n
is
h
ed
tr
ee
h
a
s
N
lea
f
n
o
d
es
an
d
N−
1
in
ter
n
al
n
o
d
es.
A
li
n
ea
r
-
ti
m
e
m
e
th
o
d
to
cr
ea
te
a
Hu
f
f
m
a
n
tr
ee
is
to
u
s
e
t
w
o
q
u
eu
e
s
,
th
e
f
ir
s
t
o
n
e
co
n
t
ain
i
n
g
t
h
e
in
i
tial
w
ei
g
h
t
s
(
alo
n
g
w
i
th
p
o
in
ter
s
to
th
e
as
s
o
ciate
d
leav
es),
a
n
d
co
m
b
in
ed
w
ei
g
h
ts
(
alo
n
g
w
it
h
p
o
in
ter
s
to
th
e
tr
ee
s
)
b
ein
g
p
u
t
in
th
e
b
ac
k
o
f
t
h
e
s
ec
o
n
d
q
u
eu
e.
T
h
is
as
s
u
r
e
s
th
at
th
e
lo
w
est
w
ei
g
h
t is al
w
a
y
s
k
ep
t a
t th
e
f
r
o
n
t o
f
o
n
e
o
f
th
e
t
w
o
q
u
e
u
es.
7.
DE
V
E
L
O
P
M
E
NT
O
F
H
UF
F
M
AN
CO
DING
AND
DE
C
O
DING
A
L
G
O
RI
T
H
M
Step
1
-
R
ea
d
th
e
i
m
a
g
e
o
n
to
t
h
e
w
o
r
k
s
p
ac
e
o
f
t
h
e
m
a
tlab
.
Step
2
-
C
o
n
v
er
t t
h
e
g
i
v
e
n
co
lo
u
r
i
m
a
g
e
i
n
to
g
r
e
y
le
v
el
i
m
a
g
e
.
Step
3
-
C
all
a
f
u
n
ctio
n
w
h
ich
w
il
l f
i
n
d
th
e
s
y
m
b
o
ls
(
i.e
.
p
ix
e
l v
alu
e
w
h
ic
h
is
n
o
n
-
r
ep
ea
ted
)
.
Step
4
-
C
all
a
f
u
n
ctio
n
w
h
ich
w
il
l c
alcu
la
te
th
e
p
r
o
b
ab
ilit
y
o
f
ea
ch
s
y
m
b
o
l.
Step
5
-
P
r
o
b
ab
ilit
y
o
f
s
y
m
b
o
l
s
ar
e
ar
r
an
g
ed
in
d
ec
r
ea
s
in
g
o
r
d
er
an
d
lo
w
er
p
r
o
b
ab
ilit
ies
ar
e
m
er
g
ed
an
d
t
h
is
s
tep
is
co
n
ti
n
u
ed
u
n
til o
n
l
y
t
wo
p
r
o
b
ab
ilit
ies ar
e
lef
t a
n
d
co
d
es a
r
e
ass
i
g
n
ed
ac
co
r
d
in
g
to
r
u
le
t
h
at
:th
e
h
i
g
h
est
p
r
o
b
a
b
le
s
y
m
b
o
l
w
ill
h
av
e
a
s
h
o
r
ter
len
g
t
h
co
d
e.
Step
6
-
Fu
r
t
h
er
H
u
f
f
m
a
n
en
co
d
in
g
i
s
p
er
f
o
r
m
ed
i.e
.
m
ap
p
in
g
o
f
t
h
e
co
d
e
w
o
r
d
s
to
th
e
co
r
r
esp
o
n
d
in
g
s
y
m
b
o
ls
w
il
l r
esu
l
t in
a
co
m
p
r
es
s
ed
d
ata.
Step
7
-
T
h
e
o
r
ig
in
al
i
m
a
g
e
is
r
ec
o
n
s
tr
u
cted
i.e
.
d
ec
o
m
p
r
ess
io
n
is
d
o
n
e
b
y
u
s
i
n
g
Hu
f
f
m
an
d
ec
o
d
in
g
.
Step
8
-
Gen
er
ate
a
tr
ee
eq
u
i
v
al
en
t to
th
e
e
n
co
d
in
g
tr
ee
.
Step
9
-
R
ea
d
in
p
u
t c
h
ar
a
cter
wis
e
an
d
lef
t to
th
e
tab
le
u
n
til la
s
t e
le
m
e
n
t i
s
r
ea
ch
ed
in
t
h
e
ta
b
le
.
Step
1
0
-
Ou
tp
u
t
th
e
c
h
ar
ac
ter
en
co
d
e
in
th
e
lea
f
an
d
r
etu
r
n
to
th
e
r
o
o
t,
an
d
co
n
tin
u
e
t
h
e
s
tep
9
u
n
til
all
t
h
e
co
d
es o
f
co
r
r
esp
o
n
d
in
g
s
y
m
b
o
ls
ar
e
k
n
o
w
n
.
8.
RE
SU
L
T
S
Th
e
in
p
u
t
i
m
a
g
e
s
h
o
w
n
i
n
F
ig
u
r
e
1
to
w
h
ich
th
e
ab
o
v
e
H
u
f
f
m
an
co
d
in
g
al
g
o
r
ith
m
i
s
ap
p
lied
f
o
r
th
e
g
en
er
atio
n
o
f
co
d
es
an
d
th
en
d
ec
o
m
p
r
ess
io
n
alg
o
r
it
h
m
(
i.e
.
Hu
f
f
m
a
n
d
ec
o
d
in
g
)
is
ap
p
lied
to
g
et
th
e
o
r
ig
in
al
i
m
a
g
e
b
ac
k
f
r
o
m
t
h
e
g
e
n
er
at
ed
c
o
d
es,
w
h
ich
is
s
h
o
w
n
i
n
th
e
Fig
u
r
e
2.
T
h
e
n
u
m
b
er
o
f
s
av
ed
b
its
is
t
h
e
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
n
o
o
f
b
its
r
eq
u
ir
ed
to
r
ep
r
esen
t
t
h
e
in
p
u
t
i
m
ag
e
i.e
.
s
h
o
w
n
i
n
th
e
F
ig
u
r
e
1
b
y
co
n
s
id
er
in
g
ea
c
h
s
y
m
b
o
l
ca
n
t
ak
e
a
m
a
x
i
m
u
m
co
d
e
len
g
t
h
o
f
8
b
it
s
a
n
d
th
e
n
o
o
f
b
it
s
ta
k
e
n
b
y
t
h
e
H
u
f
f
m
a
n
co
d
e
to
r
ep
r
esen
t
th
e
co
m
p
r
e
s
s
ed
i
m
ag
e
i.e
.
Sa
v
ed
b
its
=
(
8
*
(
r
*
c)
-
(
l1
*
l2
)
)
=3
2
1
2
,
r
an
d
c
r
ep
r
esen
ts
s
ize
o
f
th
e
i
n
p
u
t
m
atr
i
x
,
l1
a
n
d
l2
r
ep
r
esen
ts
t
h
e
s
ize
o
f
H
u
f
f
m
a
n
c
o
d
e.
T
h
e
co
m
p
r
ess
io
n
r
atio
is
th
e
r
atio
o
f
n
u
m
b
e
r
o
f
b
its
r
eq
u
ir
ed
to
r
ep
r
esen
t th
e
i
m
a
g
e
u
s
i
n
g
H
u
f
f
m
a
n
co
d
e
to
th
e
n
o
o
f
b
it
s
u
s
ed
to
r
ep
r
esen
t t
h
e
in
p
u
t i
m
a
g
e.
i.e
.
C
o
m
p
r
es
s
io
n
r
atio
=
(
l1
*
l
2
)
/
(
8
*
r
*
c)
=
0
.
8
4
5
6
,
T
h
e
o
u
tp
u
t
i
m
a
g
e
is
th
e
d
ec
o
m
p
r
ess
e
d
im
a
g
e
i.e
.
f
r
o
m
th
e
Fig
u
r
e
2
it is
clea
r
th
at
t
h
e
d
ec
o
m
p
r
es
s
ed
i
m
a
g
e
is
ap
p
r
o
x
i
m
atel
y
eq
u
al
to
t
h
e
in
p
u
t i
m
ag
e.
a1
0
a2
10
a3
1
1
1
a4
1
1
0
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
C
o
mp
r
ess
io
n
Tech
n
iq
u
es V
s
Hu
ffma
n
C
o
d
in
g
(
V
ika
s
K
u
ma
r
)
35
Fig
u
r
e
1.
I
n
p
u
t i
m
a
g
e
Fig
u
r
e
2
.
Dec
o
m
p
r
es
s
i
m
a
g
e
9.
M
AIN P
RO
P
E
RT
I
E
S
1.
Un
iq
u
e
P
r
ef
i
x
P
r
o
p
er
ty
:
n
o
co
d
e
is
a
p
r
ef
ix
to
a
n
y
o
t
h
er
co
d
e
(
all
s
y
m
b
o
ls
ar
e
at
t
h
e
leaf
n
o
d
es)
g
r
ea
t
f
o
r
d
ec
o
d
er
,
u
n
a
m
b
i
g
u
o
u
s
.
2.
I
f
p
r
io
r
s
tatis
tics
ar
e
av
ai
lab
le
an
d
ac
cu
r
ate,
th
e
n
H
u
f
f
m
a
n
co
d
in
g
is
v
er
y
g
o
o
d
.
3.
T
h
e
f
r
eq
u
en
cie
s
u
s
ed
ca
n
b
e
g
en
er
ic
o
n
es
f
o
r
th
e
ap
p
licatio
n
d
o
m
ai
n
t
h
at
ar
e
b
as
ed
o
n
av
er
ag
e
ex
p
er
ien
ce
,
o
r
th
e
y
ca
n
b
e
th
e
ac
tu
al
f
r
eq
u
en
cie
s
f
o
u
n
d
i
n
th
e
tex
t b
ein
g
co
m
p
r
ess
ed
.
4.
Hu
f
f
m
a
n
co
d
in
g
is
o
p
ti
m
al
w
h
en
th
e
p
r
o
b
ab
ilit
y
o
f
ea
c
h
in
p
u
t s
y
m
b
o
l is a
n
e
g
ati
v
e
p
o
w
er
o
f
t
w
o
.
5.
T
h
e
w
o
r
s
t
ca
s
e
f
o
r
Hu
f
f
m
an
co
d
in
g
ca
n
h
ap
p
en
w
h
e
n
t
h
e
p
r
o
b
a
b
ilit
y
o
f
a
s
y
m
b
o
l
6
ce
ed
s
2
-
1
=
0
.
5
,
m
ak
in
g
t
h
e
u
p
p
er
li
m
it
o
f
i
n
ef
f
icien
c
y
u
n
b
o
u
n
d
ed
.
T
h
ese
s
itu
a
tio
n
s
o
f
te
n
r
esp
o
n
d
w
el
l
to
a
f
o
r
m
o
f
b
lo
ck
in
g
ca
lled
r
u
n
-
le
n
g
th
e
n
c
o
d
in
g
.
10.
ADVA
N
T
A
G
E
S
a.
A
l
g
o
r
ith
m
i
s
ea
s
y
to
i
m
p
le
m
e
n
t
b.
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r
o
d
u
ce
a
lo
s
s
less
co
m
p
r
e
s
s
io
n
o
f
i
m
ag
e
s
11.
DIS
AD
VANT
AG
E
S
a.
E
f
f
icien
c
y
d
ep
en
d
s
o
n
t
h
e
ac
c
u
r
ac
y
o
f
t
h
e
s
ta
tis
tic
a
l
m
o
d
el
u
s
ed
an
d
t
y
p
e
o
f
i
m
a
g
e
.
b.
A
l
g
o
r
ith
m
v
ar
ies
w
it
h
d
if
f
er
e
n
t f
o
r
m
at
s
,
b
u
t f
e
w
g
et
a
n
y
b
ett
er
th
an
8
:1
co
m
p
r
ess
io
n
.
c.
C
o
m
p
r
ess
io
n
o
f
i
m
a
g
e
f
ile
s
t
h
at
co
n
tai
n
lo
n
g
r
u
n
s
o
f
id
en
t
ic
al
p
ix
el
s
b
y
H
u
f
f
m
a
n
i
s
n
o
t a
s
ef
f
icie
n
t
w
h
e
n
co
m
p
ar
ed
to
R
L
E
.
d.
T
h
e
Hu
f
f
m
an
en
co
d
in
g
p
r
o
ce
s
s
is
u
s
u
all
y
d
o
n
e
i
n
t
w
o
p
ass
e
s
.
Du
r
i
n
g
th
e
f
ir
s
t
p
ass
,
a
s
tati
s
tical
m
o
d
el
i
s
b
u
ilt,
a
n
d
t
h
en
in
t
h
e
s
ec
o
n
d
p
ass
t
h
e
i
m
a
g
e
d
ata
is
en
co
d
ed
b
ased
o
n
t
h
e
g
en
er
ated
m
o
d
el.
Fro
m
h
er
e
we
ca
n
s
ee
t
h
a
t
Hu
f
f
m
an
e
n
co
d
in
g
i
s
a
r
elativ
el
y
s
lo
w
p
r
o
ce
s
s
as
ti
m
e
is
r
eq
u
ir
ed
to
b
u
il
d
th
e
s
tatis
tical
m
o
d
el
i
n
o
r
d
er
to
ar
ch
iv
e
an
e
f
f
icien
t c
o
m
p
r
ess
io
n
r
ate.
12.
CO
NCLU
SI
O
N
T
h
e
ex
p
er
i
m
en
t
s
h
o
w
s
t
h
at
t
h
e
h
ig
h
er
d
ata
r
ed
u
n
d
an
c
y
h
elp
s
to
ac
h
ie
v
e
m
o
r
e
co
m
p
r
e
s
s
io
n
.
T
h
e
ab
o
v
e
p
r
esen
ted
a
n
e
w
co
m
p
r
ess
io
n
a
n
d
d
ec
o
m
p
r
ess
io
n
tec
h
n
iq
u
e
b
ased
o
n
Hu
f
f
m
an
co
d
in
g
a
n
d
d
ec
o
d
in
g
f
o
r
s
ca
n
tes
tin
g
to
r
ed
u
ce
tes
t
d
ata
v
o
lu
m
e,
test
ap
p
licatio
n
ti
m
e.
E
x
p
er
i
m
e
n
tal
r
es
u
lt
s
s
h
o
w
t
h
at
u
p
to
a
0
.
8
4
5
6
co
m
p
r
ess
io
n
r
at
io
f
o
r
t
h
e
ab
o
v
e
i
m
ag
e
is
o
b
tain
ed
.
h
en
ce
w
e
co
n
cl
u
d
e
t
h
at
H
u
f
f
m
a
n
co
d
in
g
is
e
f
f
icie
n
t
tech
n
iq
u
e
f
o
r
i
m
a
g
e
co
m
p
r
es
s
io
n
an
d
d
ec
o
m
p
r
ess
io
n
to
s
o
m
e
e
x
ten
t.
A
s
t
h
e
f
u
tu
r
e
w
o
r
k
o
n
co
m
p
r
ess
io
n
o
f
i
m
a
g
es
f
o
r
s
to
r
in
g
a
n
d
tr
an
s
m
itti
n
g
i
m
ag
e
s
ca
n
b
e
d
o
n
e
b
y
o
t
h
er
lo
s
s
less
m
et
h
o
d
s
o
f
i
m
a
g
e
co
m
p
r
ess
io
n
b
ec
au
s
e
as
w
e
h
a
v
e
co
n
cl
u
d
e
d
ab
o
v
e
th
e
r
esu
lt
t
h
e
d
ec
o
m
p
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ess
ed
i
m
ag
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i
s
al
m
o
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t
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o
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icate
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s
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.
So
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et
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t a
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P
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G
m
et
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,
E
n
tr
o
p
y
co
d
in
g
,
etc.
RE
F
E
R
E
NC
E
S
[1
]
T
e
rn
a
r
y
T
re
e
,
F
.
G
.
K
Hu
ffm
a
n
Co
d
i
n
g
T
e
c
h
n
iq
u
e
,
Dr.
P
u
sh
p
a
R.
S
u
ri,
M
a
d
h
u
G
o
e
l,
“
De
p
a
rtme
n
t
o
f
Co
m
p
u
ter
S
c
ien
c
e
&
A
p
p
li
c
a
ti
o
n
s
”
,
Ku
r
u
k
sh
e
tra
Un
iv
e
rsity
,
Ku
ru
k
sh
e
tra,
In
d
ia
[2
]
M
a
ss
a
c
h
u
se
tt
s In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
D
e
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
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e
rin
g
a
n
d
Co
m
p
u
ter S
c
ie
n
c
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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[3
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Co
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Us
in
g
F
ra
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rier T
ra
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ica
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,
By
P
a
rv
in
d
e
r
Ka
u
r.
[4
]
“
RL
-
Hu
ffm
a
n
En
c
o
d
in
g
f
o
r
T
e
s
t
Co
m
p
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a
n
d
P
o
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Re
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S
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p
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rd
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n
d
M
o
h
a
m
m
a
d
h
teh
ra
n
i
p
o
u
r
”
,
T
h
e
Un
iv
e
rsit
y
o
f
Tex
a
s at
Da
ll
a
s.
[5
]
He
m
a
su
n
d
a
ra
Ra
o
,
“
A
No
v
e
l
V
L
S
I
A
rc
h
it
e
c
tu
re
o
f
H
y
b
rid
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a
g
e
Co
m
p
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o
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b
a
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n
Re
v
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rsib
le
Blo
c
k
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d
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T
ra
n
s
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o
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m
C”
,
S
tu
d
e
n
t
M
e
m
b
e
r,
IEE
E
,
M
.
M
a
d
h
a
v
i
L
a
th
a
,
M
e
m
b
e
r,
IEE
E
[6
]
D.A
.
Hu
ffm
a
n
,
“
A
M
e
th
o
d
f
o
r
th
e
c
o
n
stru
c
ti
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o
f
M
in
im
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m
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d
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n
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y
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s
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,
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c
.
IRE
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v
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n
o
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0
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p
p
.
1
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8
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1
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1
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1
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5
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.
[7
]
A
.
B.
Watso
n
,
“
Im
a
g
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Co
m
p
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ss
io
n
u
si
n
g
th
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DCT
”
,
M
a
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a
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o
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rn
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l
,
1
9
9
5
,
p
p
.
8
1
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8
8
.
[8
]
Da
v
id
A
.
Hu
ffm
a
n
,
P
r
o
f
il
e
Ba
c
k
g
ro
u
n
d
S
to
ry
:
S
c
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f
ic Am
e
rica
n
,
p
p
.
5
4
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5
8
,
1
9
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1
[9
]
M
a
n
o
j
A
g
g
ra
w
a
l,
A
jai
Na
ra
y
a
n
, “
Eff
icie
n
t
Hu
ffm
a
n
De
c
o
d
in
g
”
[1
0
]
C.
S
a
ra
v
a
n
a
n
A
s
sista
n
t
P
ro
f
e
ss
o
r,
“
Co
m
p
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ter
Ce
n
tre,
N
a
ti
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l
In
stit
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o
f
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h
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y
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,
Du
rg
a
p
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t
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n
g
a
l,
In
d
ia,
P
i
n
–
7
1
3
2
0
9
.
R
.
P
ON
ALAG
US
A
M
Y
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p
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M
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ti
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In
stit
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h
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p
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,
T
a
m
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,
I
n
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P
in
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6
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1
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h
tt
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//
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J.
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a
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A
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e
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A
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.
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[
3
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(
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c
k
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ry
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:
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v
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2
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T
h
o
m
a
s H.
,
Co
rm
e
n
,
Ch
a
rles
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,
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n
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ld
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.
,
R
iv
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st,
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f
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In
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to
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s
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o
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it
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n
.
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IJ
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2252
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C
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V
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37
BI
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RAP
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AUTHO
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m
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Evaluation Warning : The document was created with Spire.PDF for Python.