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Science
Vo
l.
10
,
No
.
2
,
May
201
8
,
p
p
.
6
9
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2502
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4752
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In
th
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c
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m
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.
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c
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n
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l
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stl
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ff
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ted
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y
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d
d
it
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v
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h
it
e
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a
u
ss
ian
No
ise
(AWG
N)
in
w
h
i
c
h
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it
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li
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g
o
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o
rig
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l
in
f
o
rm
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ti
o
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s
to
f
a
u
lt
tra
n
sm
issio
n
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th
e
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h
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n
n
e
l.
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o
o
v
e
r
c
o
m
e
th
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lem
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y
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sin
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h
a
m
m
in
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o
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e
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n
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o
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ly
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m
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m
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p
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©
2
0
1
8
In
stit
u
te o
f
A
d
v
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n
c
e
d
E
n
g
i
n
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e
rin
g
a
n
d
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c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mr
.
G.
Ma
n
ik
a
n
d
an
,
Dep
ar
t
m
en
t o
f
E
lectr
o
n
ics a
n
d
C
o
m
m
u
n
icat
io
n
E
n
g
i
n
ee
r
in
g
,
St.
P
eter
’
s
Un
i
v
er
s
i
t
y
,
Av
ad
i,
C
h
en
n
ai.
E
m
ail:
m
r
g
.
m
a
n
ik
a
n
d
an
1
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g
m
ail.
co
m
1.
I
NT
RO
D
UCT
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O
N
I
n
an
Or
t
h
o
g
o
n
al
f
r
eq
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e
n
c
y
d
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v
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io
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m
u
lt
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lex
i
n
g
(
OFDM)
co
n
s
is
ts
o
f
c
h
an
n
el
e
n
co
d
er
an
d
ch
a
n
n
el
d
ec
o
d
er
f
o
r
en
co
d
in
g
a
n
d
d
ec
o
d
in
g
p
u
r
p
o
s
e
[
1
]
.
So
u
r
ce
e
n
co
d
er
an
d
s
o
u
r
ce
d
ec
o
d
er
ar
e
u
s
ed
to
co
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t
t
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g
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als
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ig
ita
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d
d
ig
ital
s
i
g
n
a
ls
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alo
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r
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tiv
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y
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h
e
p
u
r
p
o
s
e
o
f
ch
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n
el
en
co
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an
d
d
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FDM
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s
t
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m
i
s
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s
m
it
t
h
e
m
u
ltip
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d
is
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ig
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al
s
i
n
to
s
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g
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ch
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n
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ch
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tain
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t
w
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t
y
p
e
s
o
f
b
in
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d
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h
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ar
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b
lo
ck
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an
d
co
n
v
o
lu
tio
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al
co
d
es.
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h
e
co
m
b
i
n
atio
n
o
f
c
y
clic
co
d
e
an
d
lin
ea
r
co
d
e
is
ca
lled
as b
lo
ck
co
d
es.
B
lo
ck
co
d
es
ar
e
g
en
er
all
y
u
s
ed
f
o
r
er
r
o
r
co
r
r
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tio
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s
,
w
h
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ch
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n
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d
e
th
e
d
ata
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n
to
b
lo
ck
s
.
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n
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r
b
lo
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co
d
es a
r
e
an
er
r
o
r
co
r
r
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tio
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co
d
e
in
w
h
ich
th
e
lin
ea
r
co
d
e
s
et
is
r
ep
r
esen
ted
as c
o
d
ew
o
r
d
.
I
t is
u
s
ed
f
o
r
f
o
r
w
ar
d
er
r
o
r
co
r
r
ec
tio
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d
tr
an
s
m
itti
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th
e
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its
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t
h
e
ch
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n
el
u
s
ed
f
o
r
co
m
m
u
n
icati
o
n
.
L
i
k
e
w
is
e
c
y
cli
c
co
d
es a
r
e
also
th
e
b
lo
ck
co
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es
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s
ed
f
o
r
f
o
r
w
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co
r
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t
io
n
s
.
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n
t
h
i
s
b
lo
ck
co
d
e,
c
y
clic
s
h
i
f
t o
f
ea
ch
w
o
r
d
co
n
s
id
er
ed
as
an
o
t
h
er
co
d
e
w
o
r
d
b
elo
n
g
to
th
at
co
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e.
Dif
f
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t
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m
.
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d
ec
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ar
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a
m
m
in
g
d
ec
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,
v
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b
i
d
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o
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e
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,
ad
ap
tiv
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d
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o
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er
,
cy
c
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d
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n
d
an
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c
h
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k
(
C
R
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)
,
R
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d
So
lo
m
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d
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d
er
an
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s
o
o
n
[
2
]
[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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G.
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,
[
1
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d
escr
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m
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p
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I
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Sa
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[
2
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s
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d
E
x
ten
d
ed
Ha
m
m
in
g
SE
C
-
DE
D
-
T
A
E
D.
Sh
o
r
ten
i
n
g
al
g
o
r
ith
m
i
s
th
e
b
est
alg
o
r
it
h
m
f
o
r
h
a
m
m
i
n
g
co
d
es
to
in
cr
ea
s
e
t
h
e
p
r
o
b
ab
ilit
y
d
etec
tio
n
.
I
n
ad
d
itio
n
to
SE
C
-
DE
D
a
n
d
T
A
E
D,
SEC
-
DE
D
-
T
A
E
D
is
d
ev
elo
p
ed
in
t
h
is
b
r
ief
.
T
h
e
ap
p
r
o
ac
h
o
f
h
a
n
d
lin
g
t
h
e
co
d
e
w
o
r
d
i
s
s
a
m
e
b
u
t
ex
ten
d
i
n
g
t
h
e
m
o
r
e
n
u
m
b
er
o
f
b
it
to
d
etec
t
th
e
m
o
r
e
n
u
m
b
er
o
f
b
its
.
A
n
e
w
p
ar
ity
ch
ec
k
m
atr
ice
s
f
o
r
SEC
-
D
AE
D
h
a
m
m
in
g
co
d
es a
n
d
SEC
-
DE
D
-
T
A
E
D
h
a
m
m
in
g
co
d
es a
r
e
d
ev
elo
p
ed
in
th
i
s
b
r
ief
.
I
n
th
e
liter
at
u
r
e
o
f
N
u
ta
n
S
h
e
p
,
[
3
]
co
n
v
en
tio
n
al
h
a
m
m
i
n
g
co
d
es
f
o
r
(
7
,
4
)
is
i
m
p
le
m
e
n
t
ed
in
Ver
y
L
ar
g
e
Sca
le
I
n
te
g
r
atio
n
(
V
L
S
I
)
Sy
s
te
m
d
esig
n
e
n
v
ir
o
n
m
e
n
t
.
W
ith
th
e
h
e
lp
o
f
Ver
ilo
g
Ha
r
d
w
ar
e
Descr
ip
tio
n
L
a
n
g
u
a
g
e
(
Ver
ilo
g
HD
L
)
an
d
Ver
y
h
i
g
h
s
p
ee
d
in
te
g
r
atio
n
cir
cu
it
Har
d
w
ar
e
Descr
ip
tio
n
L
a
n
g
u
a
g
e
(
VHD
L
)
,
alg
o
r
ith
m
f
o
r
h
a
m
m
i
n
g
co
d
es
is
i
m
p
le
m
e
n
ted
i
n
th
is
liter
atu
r
e.
T
h
e
m
in
i
m
u
m
h
a
m
m
i
n
g
d
is
ta
n
ce
o
f
SE
C
d
esig
n
is
3
,
w
h
ic
h
m
ea
n
t
h
r
ee
p
ar
ity
b
it
s
ar
e
u
s
ed
to
d
etec
t a
n
d
co
r
r
ec
t a
s
in
g
le
b
it e
r
r
o
r
u
s
i
n
g
h
a
m
m
i
n
g
co
d
e.
I
n
th
e
b
r
ief
o
f
No
o
r
b
ash
a,
F
[
4
]
o
p
ti
m
ized
en
co
d
in
g
an
d
d
ec
o
d
in
g
p
r
o
ce
s
s
o
f
h
a
m
m
i
n
g
co
d
es
is
p
r
esen
ted
b
y
u
s
i
n
g
C
o
m
p
le
m
e
n
tar
y
Me
tal
O
x
id
e
Se
m
i
-
co
n
d
u
cto
r
(
C
MO
S)
tec
h
n
o
lo
g
y
.
Ha
m
m
in
g
E
C
C
co
d
es
ar
e
v
er
if
ied
u
s
i
n
g
5
0
n
m
,
7
0
n
m
a
n
d
9
0
n
m
tec
h
n
o
lo
g
y
.
Fie
ld
P
r
o
g
r
a
m
m
ab
le
Ga
te
A
r
r
a
y
(
FP
G
A
)
i
m
p
le
m
en
ta
tio
n
m
eth
o
d
s
f
o
r
d
ev
elo
p
ed
Ham
m
i
n
g
E
C
C
co
d
es
a
r
e
p
r
o
v
id
ed
in
th
is
b
r
ief
.
T
h
e
y
h
a
v
e
s
i
m
u
lated
an
d
test
ed
t
h
e
s
y
s
te
m
a
n
d
g
o
t
an
e
x
ce
lle
n
t
p
er
f
o
r
m
a
n
ce
at
5
0
GHz
.
T
h
e
r
eliab
ilit
y
o
f
d
ev
elo
p
ed
h
a
m
m
i
n
g
SEC
-
DE
C
co
d
es
m
ea
s
u
r
ed
at
a
v
o
lta
g
e
o
f
1
V,
0
.
7
V
a
n
d
0
.
5
V.
T
h
e
d
ec
o
d
in
g
o
f
h
a
m
m
i
n
g
co
d
es
ca
n
g
iv
e
ac
cu
r
ate
r
esu
l
t e
v
e
n
tr
an
s
m
i
s
s
i
o
n
tech
n
iq
u
e
h
as a
s
i
n
g
le
b
it e
r
r
o
r
.
I
n
t
h
e
s
tu
d
y
o
f
C
h
a,
S,
[
5
]
C
h
ec
k
b
it
P
r
e
-
co
m
p
u
tatio
n
m
et
h
o
d
s
is
u
s
ed
f
o
r
SE
C
a
n
d
DE
D.
T
h
e
H
-
m
atr
i
x
o
f
th
e
d
e
v
elo
p
ed
SEC
-
DE
D
co
d
e
is
th
e
s
a
m
e
as
th
a
t
o
f
th
e
o
d
d
-
w
eig
h
t
-
co
l
u
m
n
co
d
e
d
u
r
in
g
t
h
e
w
r
ite
o
p
er
atio
n
an
d
is
d
esi
g
n
ed
b
y
r
ep
lacin
g
0
’
s
w
ith
1
’
s
at
t
h
e
las
t
r
o
w
o
f
th
e
r
ea
d
o
p
er
atio
n
.
T
h
is
d
es
ig
n
ac
h
iev
e
s
r
ed
u
ctio
n
s
in
t
h
e
n
u
m
b
er
o
f
g
ates,
late
n
c
y
an
d
p
o
w
er
co
n
s
u
m
p
tio
n
o
f
t
h
e
E
C
C
p
r
o
ce
s
s
i
n
g
cir
cu
i
ts
b
y
u
p
to
9
.
3
%,
1
8
.
4
%
an
d
1
4
.
1
%
f
o
r
6
4
in
f
o
r
m
at
io
n
b
its
i
n
a
w
o
r
d
.
T
h
is
liter
atu
r
e
p
r
o
v
id
es
alter
n
ate
s
o
lu
tio
n
f
o
r
th
e
d
esig
n
o
f
SE
C
-
DE
D.
Usu
al
l
y
,
r
eliab
ilit
y
p
r
o
b
le
m
o
f
d
ata
tr
an
s
m
i
s
s
io
n
is
i
m
p
r
o
v
ed
b
y
c
h
a
n
n
e
l
co
d
in
g
w
h
i
ch
e
m
p
lo
y
s
f
o
r
w
ar
d
er
r
o
r
co
r
r
ec
tio
n
(
FEC)
tech
n
iq
u
e
s
.
FE
C
tec
h
n
iq
u
e
ca
n
d
etec
t
a
n
d
c
o
r
r
ec
t
a
s
in
g
le
b
it
er
r
o
r
w
it
h
t
h
e
h
elp
o
f
ch
ec
k
o
r
r
ed
u
n
d
an
t
b
it
s
.
T
h
ese
ch
ec
k
b
its
ar
e
d
eter
m
i
n
ed
f
r
o
m
d
ata
b
its
an
d
ap
p
en
d
ed
to
d
ata
b
its
to
g
et
th
e
co
d
e
w
o
r
d
o
f
o
r
ig
i
n
al
d
ata
b
its
.
I
f
A
W
GN
a
f
f
ec
ts
t
h
e
d
ata
b
its
o
th
er
th
an
c
h
ec
k
b
its
o
f
co
d
e
w
o
r
d
,
er
r
o
r
c
o
u
ld
b
e
ea
s
il
y
d
etec
ted
an
d
co
r
r
ec
t.
I
f
ch
ec
k
b
its
ar
e
also
co
r
r
u
p
ted
b
y
A
W
GN,
t
h
en
FE
C
ca
n
n
o
t
d
etec
t
an
d
co
r
r
ec
t
an
er
r
o
r
.
Ham
m
i
n
g
(
4
0
,
3
2
)
SEC
-
DE
D
co
d
e
is
d
ev
elo
p
ed
to
in
cr
ea
s
e
th
e
E
r
r
o
r
Dete
ctio
n
an
d
C
o
r
r
ec
tio
n
(
E
D
A
C
)
ab
ilit
y
.
H
a
m
m
in
g
(
4
0
,
3
2
)
SEC
-
DE
D
c
o
d
es
h
av
e
8
-
b
its
p
ar
it
y
m
e
m
o
r
y
f
o
r
s
i
n
g
le
er
r
o
r
co
r
r
ec
tio
n
an
d
d
o
u
b
le
er
r
o
r
d
e
tectio
n
.
An
al
g
o
r
ith
m
b
ased
m
u
tu
a
l
ex
p
r
es
s
io
n
s
ar
e
d
ev
elo
p
ed
in
t
h
is
r
e
v
ie
w
to
m
i
n
i
m
ize
t
h
e
E
D
AC
c
ir
cu
it
ar
ea
,
an
d
d
ela
y
p
ar
a
m
eter
s
.
T
h
e
r
esu
lt
s
o
f
(
4
0
,
3
2
)
h
a
m
m
in
g
S
E
C
-
DE
D
co
d
es
ar
e
co
m
p
ar
ed
to
(
3
9
,
3
2
)
Hsi
ao
c
o
d
e.
T
h
e
cr
itical
p
ath
o
f
en
co
d
er
an
d
d
ec
o
d
er
co
m
p
u
tatio
n
ca
u
s
e
s
m
o
r
e
d
ela
y
an
d
p
o
w
er
.
B
u
t
h
a
m
m
i
n
g
co
d
es
h
a
v
e
o
n
l
y
s
m
o
o
th
e
n
ed
p
ath
f
o
r
en
co
d
i
n
g
a
n
d
d
ec
o
d
in
g
p
r
o
ce
s
s
th
an
Hsi
ao
co
d
es.
T
h
e
d
ev
elo
p
ed
h
a
m
m
i
n
g
(
4
0
,
3
2
)
SEC
-
DE
D
c
o
d
es
o
f
f
er
s
2
.
9
7
%
r
ed
u
ctio
n
o
f
en
co
d
in
g
d
ela
y
t
h
a
n
Hsi
ao
(
3
9
,
3
2
)
er
r
o
r
c
o
r
r
ec
tio
n
co
d
e.
T
h
e
m
e
n
tio
n
ed
b
lo
ck
co
d
es
ar
e
eith
er
lin
ea
r
o
r
cy
clic
er
r
o
r
co
r
r
ec
tio
n
co
d
es.
A
m
o
n
g
th
o
s
e
tech
n
iq
u
es,
h
a
m
m
i
n
g
e
n
co
d
er
an
d
d
ec
o
d
er
a
r
e
th
e
ef
f
ici
en
t
er
r
o
r
co
r
r
ec
tin
g
co
d
es
f
o
r
v
er
y
lar
g
e
s
ca
le
in
te
g
r
atio
n
(
V
L
SI)
i
m
p
le
m
en
t
atio
n
.
E
r
r
o
r
f
r
ee
d
ata
tr
an
s
m
i
s
s
io
n
f
r
o
m
o
n
e
e
n
d
to
o
th
er
en
d
in
th
e
w
ir
eles
s
ch
an
n
el
i
s
n
o
t
p
o
s
s
ib
le.
So
to
d
etec
t
an
d
co
r
r
ec
t
th
e
er
r
o
r
s
in
th
e
r
ec
ei
v
er
s
id
e
i
s
th
e
i
m
p
o
r
tan
t
p
r
o
ce
s
s
to
g
et
an
er
r
o
r
f
r
ee
d
ata.
Ham
m
i
n
g
co
d
es
ar
e
w
id
el
y
u
s
ed
to
f
in
d
an
d
co
r
r
ec
t
th
e
er
r
o
r
s
.
I
n
g
en
er
al
s
o
f
t
er
r
o
r
s
ar
e
g
en
er
ated
b
y
SR
A
M
m
e
m
o
r
y
d
ev
ice
th
i
s
ca
n
b
e
r
ed
u
ce
d
b
y
h
a
m
m
i
n
g
d
ec
o
d
er
.
Sin
g
le
er
r
o
r
co
r
r
ec
tio
n
co
d
es
ar
e
u
s
ed
to
co
r
r
ec
t
th
e
er
r
o
r
s
w
it
h
o
u
t
an
y
d
ela
y
o
f
t
h
e
cir
c
u
its
.
Ha
m
m
i
n
g
co
d
e
is
u
s
ed
to
p
r
o
tect
th
e
ex
ter
n
al
m
e
m
o
r
y
,
w
h
en
p
ar
it
y
b
it
i
s
a
d
d
ed
to
th
e
co
d
e
w
o
r
d
;
it
tak
e
s
m
o
r
e
a
m
o
u
n
t
o
f
m
e
m
o
r
y
.
Ha
m
m
i
n
g
co
d
es
ar
e
ea
s
y
to
co
n
s
tr
u
c
t
[
4
]
.
Viter
b
i
an
d
tu
r
b
o
co
d
es
ar
e
m
o
s
tl
y
u
s
ed
in
t
h
e
en
co
d
er
p
ar
t
d
u
r
in
g
th
e
tr
an
s
m
i
s
s
io
n
o
f
d
ata.
I
n
th
e
h
a
m
m
i
n
g
er
r
o
r
d
etec
tio
n
a
n
d
er
r
o
r
co
r
r
ec
tio
n
co
d
es
ar
e
u
s
ed
to
d
etec
t
a
n
d
co
r
r
ec
t
a
s
in
g
le
er
r
o
r
[
5
]
.
T
h
e
co
r
r
ec
tio
n
an
d
d
etec
tio
n
o
f
er
r
o
r
s
in
t
h
e
h
a
m
m
i
n
g
co
d
es
ca
n
b
e
d
o
n
e
b
y
m
i
n
i
m
u
m
d
is
tan
ce
a
n
d
w
it
h
i
n
t
h
e
b
lo
ck
le
n
g
t
h
.
T
h
e
d
is
tan
c
e
ca
n
b
e
m
ea
s
u
r
ed
b
y
ca
lcu
lati
n
g
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
p
ar
it
y
b
it
s
an
d
in
p
u
t
w
o
r
d
len
g
t
h
.
B
ec
au
s
e
o
f
th
is
r
ea
s
o
n
h
a
m
m
i
n
g
co
d
e
s
ar
e
u
s
ed
in
t
h
e
OFD
M
co
m
m
u
n
icat
io
n
s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
10
,
No
.
2
,
Ma
y
2
0
1
8
:
6
9
6
–
7
0
3
698
2.
H
AM
M
I
NG
CO
DE
F
O
R
E
RRO
R
DE
T
E
C
T
I
O
N
A
ND
CO
RREC
T
I
O
N
Ha
m
m
i
n
g
co
d
e
co
m
e
s
u
n
d
er
th
e
f
a
m
il
y
o
f
li
n
ea
r
b
lo
ck
co
d
e.
T
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
t
h
e
h
a
m
m
i
n
g
co
d
e
is
to
d
etec
tin
g
an
d
co
r
r
e
ctin
g
th
e
er
r
o
r
in
th
e
r
ec
eiv
er
.
I
t
w
a
s
in
v
en
ted
b
y
R
itc
h
ar
d
Ha
m
m
i
n
g
i
n
1
9
5
0
.
Ha
m
m
i
n
g
co
d
e
h
as
ab
ilit
y
to
d
etec
t
an
d
co
r
r
ec
te
d
th
e
s
in
g
le
b
it
er
r
o
r
,
w
it
h
a
m
in
i
m
u
m
h
a
m
m
in
g
d
is
ta
n
ce
[
6
]
.
I
n
g
e
n
er
al
th
e
p
ar
it
y
b
it
s
ar
e
u
s
ed
to
d
etec
t
an
d
co
r
r
ec
t
th
e
s
in
g
le
er
r
o
r
.
Ha
m
m
i
n
g
d
is
ta
n
ce
(
m
)
i
s
n
o
t
h
in
g
b
u
t
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
in
p
u
t
w
o
r
d
len
g
th
a
n
d
p
ar
it
y
b
its
.
T
h
e
n
u
m
er
ical
r
ep
r
esen
tatio
n
o
f
h
a
m
m
i
n
g
co
d
es
ar
e
ch
ar
ac
ter
ized
f
o
r
m
≥
3
w
it
h
t
h
e
f
o
llo
w
in
g
,
1
2
m
n
(
1
)
m
n
k
(
2
)
3
m
i
n
d
(
3
)
W
h
er
e,
n
r
ep
r
esen
t
th
e
s
ize
o
f
b
lo
ck
,
k
r
ep
r
esen
t
s
t
h
e
n
u
m
b
er
o
f
in
f
o
r
m
atio
n
b
its
,
th
e
n
u
m
b
er
o
f
p
ar
ity
b
its
ca
n
b
e
r
ep
r
esen
ted
as
m
,
d
m
in
is
t
h
e
m
i
n
i
m
u
m
h
a
m
m
in
g
d
is
ta
n
ce
.
N
u
m
b
er
o
f
p
ar
ity
b
its
is
eq
u
al
to
th
e
m
i
n
i
m
u
m
h
a
m
m
in
g
d
is
t
an
ce
.
I
f
t
h
e
h
a
m
m
in
g
d
is
tan
ce
is
t
h
r
ee
,
it
n
ee
d
s
t
h
r
ee
p
ar
it
y
b
its
f
o
r
s
i
n
g
le
er
r
o
r
co
r
r
ec
tio
n
(
SEC).
T
h
e
f
o
llo
w
i
n
g
al
g
o
r
ith
m
to
g
e
n
er
ate
t
h
e
H
a
m
m
in
g
co
d
e
w
o
r
d
o
f
in
f
o
r
m
a
t
io
n
b
its
,
Step
1
: N
u
m
b
er
th
e
p
o
s
itio
n
s
o
f
b
its
s
tar
ti
n
g
f
r
o
m
1
to
n
,
w
h
er
e
n
is
th
e
la
s
t p
o
s
itio
n
o
f
th
e
b
its
.
Step
2
: A
ll p
o
s
itio
n
s
ar
e
r
ep
r
esen
t
s
in
b
i
n
ar
y
f
o
r
m
1
,
1
0
,
1
1
,
1
0
0
,
1
0
1
,
1
1
0
,
1
1
1
,
1
0
0
0
,
1
0
0
1
,
etc.
Step
3
: A
ll b
it p
o
s
itio
n
s
th
a
t a
r
e
p
o
w
er
o
f
t
w
o
co
n
s
id
er
ed
as a
p
ar
ity
b
its
.
P
ar
ity
b
its
ar
e
i
m
p
o
r
ta
n
t
i
n
th
e
h
a
m
m
i
n
g
co
d
e
f
o
r
s
in
g
le
er
r
o
r
d
etec
tio
n
an
d
co
r
r
ec
tio
n
.
T
h
e
p
o
s
itio
n
o
f
th
e
p
ar
it
y
b
it
s
is
m
en
t
io
n
ed
as f
o
llo
w
s
,
First
P
ar
it
y
P
o
s
itio
n
2
0
:
C
h
ec
k
1
b
it
an
d
s
k
ip
1
b
it
s
tep
p
o
s
itio
n
s
ar
e
f
o
llo
w
ed
s
u
ch
a
s
1
,
3
,
5
,
7
,
9
…….
Seco
n
d
P
ar
it
y
P
o
s
itio
n
2
1
:
C
h
ec
k
t
h
e
2
b
its
a
n
d
s
k
ip
2
b
its
s
tep
p
o
s
itio
n
s
ar
e
f
o
llo
w
ed
s
u
ch
as
2
,
3
,
6
,
7
,
1
0
,
1
1
,
1
4
,
1
5
…….
T
h
ir
d
P
ar
ity
P
o
s
itio
n
2
2
:
C
h
e
ck
3
b
it
s
a
n
d
s
k
ip
3
b
it
s
s
tep
p
o
s
itio
n
ar
e
f
o
llo
w
ed
s
u
c
h
as
4
,
5
,
6
,
7
,
1
2
,
1
3
,
1
4
,
1
5
,
2
0
,
2
1
,
2
2
,
2
3
,
2
4
…….
.
Fo
u
r
th
P
ar
it
y
P
o
s
itio
n
2
3
:
C
h
ec
k
8
b
its
an
d
Sk
ip
8
b
its
s
tep
p
o
s
itio
n
s
ar
e
f
o
llo
w
ed
s
u
c
h
a
s
8
-
1
5
,
2
4
-
3
1
,
4
0
-
4
7
.
.
.
.
.
.
.
.
.
.
.
.
.
T
h
e
to
tal
n
u
m
b
er
o
f
1
’
s
i
n
t
h
e
p
o
s
itio
n
is
e
v
en
,
t
h
e
p
ar
it
y
i
s
s
et
to
0
.
T
h
e
to
tal
n
u
m
b
er
o
f
1
’
s
i
n
th
e
p
o
s
itio
n
is
o
d
d
,
th
e
p
ar
ity
s
e
t
to
1
.
T
h
is
is
th
e
m
et
h
o
d
to
f
in
d
th
e
co
d
e
w
o
r
d
o
f
h
a
m
m
in
g
co
d
es.
Sin
g
le
b
it
er
r
o
r
in
th
e
h
a
m
m
in
g
co
d
e
ca
n
b
e
d
etec
t a
n
d
co
r
r
ec
t
b
y
u
s
i
n
g
s
y
n
d
r
o
m
e
v
ec
to
r
s
.
T
h
e
p
r
o
d
u
ct
o
f
lex
ico
g
r
ap
h
i
c
m
atr
i
x
an
d
co
d
e
w
o
r
d
o
f
t
h
e
in
f
o
r
m
atio
n
is
ca
lled
a
s
s
y
n
d
r
o
m
e
v
ec
to
r
.
T
h
e
v
alu
e
o
f
s
y
n
d
r
o
m
e
is
ze
r
o
;
ass
u
m
e
th
er
e
is
n
o
er
r
o
r
in
th
e
d
ata
tr
a
n
s
m
i
s
s
io
n
.
3.
SI
N
G
L
E
E
RRO
R
CO
RR
E
C
T
I
O
N
(
S
E
C)
H
AM
M
I
NG
CO
DE
S
L
e
x
ico
g
r
ap
h
ic
h
a
m
m
i
n
g
m
atr
ix
i
s
u
s
ed
to
d
eter
m
i
n
e
t
h
e
er
r
o
n
eo
u
s
b
it
in
t
h
e
SE
C
h
a
m
m
i
n
g
co
d
e.
Gen
er
all
y
,
h
a
m
m
i
n
g
co
d
e
is
r
ep
r
esen
ted
as
(
n
,
k
)
.
W
h
er
e
n
r
ep
r
esen
ts
t
h
e
b
lo
ck
s
ize,
k
r
e
p
r
esen
ts
t
h
e
n
u
m
b
er
o
f
in
f
o
r
m
at
io
n
b
its
.
L
et
u
s
co
n
s
id
er
(
7
,
4
)
h
a
m
m
i
n
g
co
d
e,
‘
7
’
r
ep
r
ese
n
ts
t
h
e
b
lo
ck
s
ize,
‘
4
’
r
ep
r
ese
n
ts
t
h
e
in
f
o
r
m
atio
n
le
n
g
t
h
.
T
h
e
co
d
e
ca
n
b
e
w
r
itte
n
as
f
o
llo
w
s
,
H
=
|
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
|
(
4
)
L
et,
t
h
e
f
o
u
r
b
it i
n
f
o
r
m
atio
n
,
i
n
p
u
t =
1
0
1
1
C
o
d
e
w
o
r
d
len
g
th
=
I
n
f
o
r
m
a
tio
n
b
it len
g
t
h
+
P
ar
ity
b
it le
n
g
th
=
4
+3
=
7
C
o
d
e
w
o
r
d
ca
n
b
e
f
o
r
m
u
lated
as f
o
llo
w
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
S
E
C
-
TAE
D
b
a
s
ed
E
r
r
o
r
Dete
ctio
n
a
n
d
C
o
r
r
ec
tio
n
Tech
n
iq
u
e…
(
G.
Ma
n
ika
n
d
a
n
)
699
P
ar
ity
1
=
E
v
e
n
P
ar
it
y
o
f
[
p
ar
ity
1
,
1
,
p
ar
ity
2
,
1
]
=
1
^
1
=
0
P
ar
ity
2
=
E
v
en
P
ar
it
y
o
f
[
p
ar
it
y
2
,
1
,
1
,
1
]
=
1
^
1
^
1
=
1
P
ar
ity
3
=
E
v
en
p
ar
it
y
o
f
[
0
,
p
ar
it
y
3
,
1
,
1
]
=
0
^
1
^
1
=
0
No
w
t
h
e
co
d
e
w
o
r
d
is
“
0
1
1
0
1
1
1
”
Nex
t to
f
i
n
d
th
e
s
y
n
d
r
o
m
e
v
ec
to
r
f
o
r
d
etec
tin
g
t
h
e
er
r
o
r
,
S
y
n
d
r
o
m
e
=
[
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
]
(
5
)
I
n
eq
n
(
5
)
r
ep
r
esen
ts
t
h
e
s
y
n
d
r
o
m
e
v
ec
to
r
,
it
i
s
f
o
r
m
ed
b
y
tr
an
s
p
o
s
e
o
f
le
x
ico
g
r
ap
h
ic
m
atr
ix
.
Mu
ltip
l
y
th
e
co
d
e
w
o
r
d
w
it
h
th
e
s
y
n
d
r
o
m
e
m
atr
i
x
f
o
r
id
en
t
if
y
th
e
er
r
o
r
.
S=
[
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
]
[
0
1
1
0
0
1
1
]
(
6
)
S
[
0
0
0
]
(
7
)
E
q
n
(
7
)
r
e
p
r
esen
ts
th
e
s
y
n
d
r
o
m
e
v
ec
to
r
;
t
h
e
ab
o
v
e
v
ec
to
r
is
n
u
ll
v
ec
to
r
,
s
o
ass
u
m
e
t
h
er
e
is
n
o
er
r
o
r
in
t
h
e
d
ata
tr
an
s
m
i
s
s
io
n
.
I
f
s
u
p
p
o
s
e,
S=
[
0
1
0
]
th
e
r
ec
eiv
ed
co
n
tain
s
o
m
e
er
r
o
r
in
th
e
p
lace
o
f
s
y
n
d
r
o
m
e
v
ec
to
r
.
Af
ter
f
i
n
d
i
n
g
t
h
e
er
r
o
r
lo
ca
tio
n
o
f
th
e
s
y
n
d
r
o
m
e
v
ec
t
o
r
,
co
r
r
ec
t th
e
s
in
g
le
b
it e
r
r
o
r
.
4.
SI
N
G
L
E
E
RRO
R
CO
RR
E
C
T
I
O
N
–
T
R
I
P
L
E
ADJ
ACE
NT
E
R
RO
R
DE
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N
(
SE
C
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T
A
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Q
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t
h
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SE
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E
D
tec
h
n
iq
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e
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etec
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r
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ct
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ased
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h
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it
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as
w
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as
tr
ip
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ad
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h
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x
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ed
Ha
m
m
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g
SE
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co
d
e
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s
i
m
i
lar
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le
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r
d
etec
t
io
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m
et
h
o
d
.
Ha
m
m
i
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g
(
1
2
,
8
)
SEC
-
D
A
E
D
co
d
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co
u
ld
ca
u
s
e
m
is
co
r
r
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tio
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f
o
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d
etec
tin
g
tr
ip
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ad
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en
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r
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r
s
.
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t
r
eq
u
ir
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m
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e
t
h
a
n
o
n
e
p
ar
it
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it
‘
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r
p
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f
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m
in
g
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e
SE
C
-
T
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E
D
o
p
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atio
n
.
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th
e
SEC
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T
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E
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m
et
h
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d
p
r
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s
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(
1
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h
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f
icien
c
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th
a
n
th
e
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o
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m
al
m
et
h
o
d
[
7
]
.
Ham
m
i
n
g
(
1
3
,
8
)
SEC
-
T
A
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D
m
et
h
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ad
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ar
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it
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m
e
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b
y
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h
a
n
ce
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th
e
ex
te
n
d
ed
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a
m
m
in
g
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d
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
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as
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ip
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t
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[
8
]
.
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n
th
e
p
r
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s
ed
m
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th
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ize
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m
m
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g
(
1
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-
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ee
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s
f
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th
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j
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r
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r
s
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o
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m
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h
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o
d
u
s
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m
m
i
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g
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o
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e
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tr
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j
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en
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.
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f
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ize
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a
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tr
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p
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j
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r
.
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co
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t
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m
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at
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e
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elp
to
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ce
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it
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d
f
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m
at
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p
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ts
5
-
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-
1
2
ar
e
tr
ip
le
er
r
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r
co
m
b
i
n
atio
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s
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ce
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h
elp
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v
e
t
h
e
b
it
d
etec
tiv
e
p
r
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b
ab
ilit
y
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h
e
ch
ar
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ter
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s
u
c
h
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b
d
ia
m
o
n
d
s
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er
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o
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s
er
v
ed
[
9
]
.
Fig
u
r
e
1
.
Flo
w
C
h
ar
t o
f
B
it P
lace
m
en
t Str
ate
g
y
I
n
t
h
e
d
o
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b
le
ad
j
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d
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n
h
as
o
n
l
y
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m
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f
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it
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lace
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en
t
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l
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t
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er
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ce
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etec
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l
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ased
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n
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ateg
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m
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lace
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en
t
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r
d
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t
th
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ad
j
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s
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i
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ar
e
1
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d
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.
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it
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et
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ev
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s
[
1
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]
.
Hig
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s
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ee
d
er
r
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etec
t
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s
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h
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h
ig
h
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ata
r
ate
[
1
1
]
[
1
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
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Dete
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701
6.
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ith
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it
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en
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ith
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h
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en
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m
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g
co
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u
s
ed
i
n
t
h
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co
d
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h
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f
f
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d
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h
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m
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s
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in
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f
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m
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(
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j
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is
s
h
o
w
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in
tab
le
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tab
le
3
.
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h
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co
m
p
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n
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s
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r
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p
r
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ted
in
t
h
e
tab
le
4
.
T
ab
le
1
.
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u
b
le
A
d
j
ac
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r
r
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r
Dete
ctio
n
f
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r
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m
m
i
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g
(
1
2
,
8
)
B
i
t
P
l
a
c
e
me
n
t
D
e
t
e
c
t
i
o
n
1
2
3
4
5
6
7
8
9
10
11
12
1
/
1
1
9%
1
12
2
3
6
8
7
9
4
10
5
11
9
/
1
1
8
2
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ab
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r
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p
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Dete
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f
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m
m
i
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(
1
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1
2
3
4
5
6
7
8
9
10
11
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p
1
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1
1
9%
6
8
1
7
11
3
5
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2
4
p
10
12
9
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1
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2
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ab
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3
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r
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p
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s
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r
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p
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ce
n
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r
r
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r
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n
f
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r
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m
m
i
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t
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l
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t
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c
t
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o
n
1
2
3
4
5
6
7
8
9
10
11
12
1
/
1
0
1
0
%
7
11
2
6
10
1
4
8
3
5
9
12
9
/
1
0
9
0
%
T
ab
le
4
.
C
o
m
p
ar
is
o
n
An
al
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s
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s
o
f
th
e
Ha
m
m
in
g
a
n
d
Viter
b
i b
ased
E
r
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RE
F
E
R
E
NC
E
S
[1
]
X
u
,
J.
Zh
a
n
g
,
e
t
a
l.
,
“
On
F
o
rw
a
rd
Err
o
r
C
o
rre
c
ti
o
n
w
it
h
Ha
m
m
in
g
Co
d
e
f
o
r
M
u
lt
i
-
p
a
th
c
o
m
m
u
n
ica
ti
o
n
s”
,
IE
EE
,
2
0
1
2
.
[2
]
S
a
n
c
h
e
z
-
M
a
c
ian
,
e
t
a
l.
,
"
Ha
m
m
i
n
g
S
E
C
-
DA
ED
a
n
d
e
x
ten
d
e
d
h
a
m
m
in
g
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EC
-
DED
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ED
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o
d
e
s
t
h
ro
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g
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se
lec
ti
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e
sh
o
rten
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n
g
a
n
d
b
it
p
lac
e
m
e
n
t.
"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
De
v
ice
a
n
d
M
a
ter
ia
ls
Reli
a
b
il
it
y
,
v
o
l.
1
4
,
Is
su
e
.
1
,
p
p
:
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7
4
-
5
7
6
,
2
0
1
4
.
[3
]
Nu
tan
S
h
e
p
a
n
d
P
.
H.
B
h
a
g
a
t,
“
Im
p
le
m
e
n
tatio
n
o
f
Ha
m
m
in
g
c
o
d
e
u
si
n
g
V
L
S
I
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
T
re
n
d
s
a
n
d
T
e
c
h
n
o
l
o
g
y
(
IJ
ET
T
)
,
v
o
l.
4
,
Iss
u
e
.
3
,
p
p
:
1
8
6
-
1
9
0
,
2
0
1
3
.
[4
]
No
o
rb
a
sh
a
.
F
,
e
t
a
l.
,
“
V
L
S
I
I
m
p
le
m
e
n
tatio
n
o
f
En
c
r
y
p
ti
o
n
a
n
d
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c
ry
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ti
o
n
S
y
ste
m
Us
in
g
Ha
m
m
in
g
Co
d
e
A
l
g
o
rit
h
m
”
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ter
n
a
ti
o
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a
l
J
o
u
r
n
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l
o
f
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
a
n
d
A
p
p
li
c
a
ti
o
n
s
(
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ER
A)
,
v
o
l.
4
,
Iss
u
e
.
4
,
p
p
:
5
2
-
5
5
,
2
0
1
4
.
[5
]
Ch
a
.
S
.
,
a
n
d
Yo
o
n
.
H,
“
Eff
icie
n
t
Im
p
le
m
e
n
tatio
n
o
f
S
in
g
le
Err
o
r
Co
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c
ti
o
n
a
n
d
Do
u
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le
Err
o
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tec
ti
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n
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d
e
w
it
h
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c
k
Bit
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re
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o
m
p
u
tatio
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f
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r
M
e
m
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ries
”
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o
u
rn
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l
o
f
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e
mic
o
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to
r
T
e
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n
d
S
c
ien
c
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(
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S
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S
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o
l.
1
2
,
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u
e
.
4
,
p
p
:
4
1
8
-
4
2
5
,
2
0
1
2
.
[6
]
Cu
i.
Y,
e
t
a
l.
,
“
Res
e
a
rc
h
a
n
d
im
p
lem
e
n
ta
ti
o
n
o
f
S
EC
-
DED
Ha
m
min
g
c
o
d
e
a
l
g
o
rit
h
m
”
.
In
T
ENCON
2
0
1
3
-
2
0
1
3
IEE
E
Re
g
io
n
1
0
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n
f
e
re
n
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e
(3
1
1
9
4
)
,
p
p
:
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-
5
,
2
0
1
3
.
[7
]
M
a
n
c
h
a
n
d
a
.
G
,
e
t
a
l.
,
“
De
si
g
n
o
f
M
u
lt
id
irec
t
io
n
a
l
P
a
ri
ty
Co
d
e
Us
in
g
H
a
m
m
in
g
Co
d
e
T
e
c
h
n
iq
u
e
f
o
r
Err
o
r
De
tec
ti
o
n
a
n
d
Co
rre
c
ti
o
n
”
,
I
n
d
i
a
n
J
o
u
r
n
a
l
o
f
Res
e
a
rc
h
(
IJ
R)
,
Vo
l.
3
,
Iss
u
e
.
5
,
p
p
:
7
9
-
8
1
,
2
0
1
4
.
[8
]
Zh
a
o
.
J
a
n
d
S
h
i.
Y.
“
A
n
o
v
e
l
a
p
p
r
o
a
c
h
t
o
im
p
ro
v
in
g
b
u
rs
t
e
r
ro
rs
c
o
rr
e
c
ti
o
n
c
a
p
a
b
il
it
y
o
f
H
a
mm
in
g
c
o
d
e
”,
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
Co
m
m
u
n
ica
ti
o
n
s,
Circu
i
ts an
d
S
y
ste
m
s,
ICCCA
S
2
0
0
7
,
p
p
:
1
1
9
3
-
1
1
9
6
,
IEE
E,
2
0
0
7
.
[9
]
M
e
h
d
y
.
M
.
A
,
e
t
a
l.
,
“
S
i
m
u
latio
n
a
n
d
M
o
d
e
li
n
g
o
f
S
il
ico
n
Ba
se
d
S
in
g
le
El
e
c
tro
n
T
ra
n
sisto
r”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
v
o
l.
8
,
Iss
u
e
.
2
,
2
0
1
8
.
[1
0
]
P
u
sp
it
a
.
F
.
M
.
a
n
d
Irm
e
il
y
a
n
a
.
I.
,
“
Bit
Err
o
r
Ra
te
(BER)
Qo
S
A
tt
rib
u
te
i
n
S
o
lv
in
g
W
irele
ss
P
ricin
g
S
c
h
e
m
e
o
n
S
in
g
le
L
in
k
M
u
lt
i
S
e
rv
ice
Ne
tw
o
rk
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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e
c
trica
l
a
n
d
Co
m
p
u
te
r
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g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
Iss
u
e
.
1
,
2
0
1
7
.
[1
1
]
S
a
lh
.
A,
e
t
a
l.
,
“
M
a
x
im
izin
g
En
e
rg
y
E
ff
icie
n
c
y
f
o
r
Co
n
su
m
p
ti
o
n
Circu
it
P
o
w
e
r
in
Do
w
n
li
n
k
M
a
ss
iv
e
M
IM
O
W
irele
ss
Ne
t
w
o
rk
s”
,
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ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
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),
v
o
l.
7
,
Iss
u
e
.
6
,
pp
:
2
9
7
7
-
2
9
8
5
,
2
0
1
7
.
[1
2
]
S
h
il
p
h
a
G
,
“
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o
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o
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e
r
1
2
8
p
o
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t
ra
d
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f
f
t
f
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r
lt
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a
p
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n
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In
ter
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ti
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n
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l
J
o
u
rn
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l
o
f
M
C
sq
u
a
re
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c
ien
ti
fi
c
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a
rc
h
(
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M
S
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v
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l.
6
,
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u
e
.
1
,
p
p
:
6
6
-
7
4
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.