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A
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i
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[
1
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[
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[
3
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it
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d
laten
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y
[
4
]
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[
5
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P
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co
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SC
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d
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in
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ap
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3
rd
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P
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w
it
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5
G
u
s
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ca
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es [
5
]
.
T
h
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co
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est
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b
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/N
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ate,
E
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is
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a
v
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y
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d
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h
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s
in
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-
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p
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s
p
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s
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f
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w
h
ite
Gau
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n
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(
A
W
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[
6
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.
T
h
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r
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o
r
d
er
f
o
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th
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b
it
-
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s
o
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p
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s
n
o
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-
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n
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v
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s
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b
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it
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co
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w
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d
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d
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.
T
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Sci,
Vo
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22
,
No
.
3
,
J
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2
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2
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4
9
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[
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[
1
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.
T
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ir
r
esp
ec
ti
v
e
o
f
th
e
ch
a
n
n
el
co
n
d
itio
n
.
A
u
n
iv
er
s
al
an
d
u
n
iq
u
e
s
eq
u
en
ce
f
o
r
b
it
-
ch
a
n
n
el
r
eli
ab
ilit
y
w
as
p
r
o
p
o
s
ed
f
o
r
co
d
in
g
le
n
g
t
h
s
s
m
aller
t
h
an
o
r
eq
u
al
to
1
0
2
4
.
T
h
is
s
eq
u
en
ce
is
co
n
s
id
er
ed
to
b
e
a
b
ase
to
f
in
d
th
e
r
eliab
ilit
y
o
r
d
er
f
o
r
th
e
b
it
-
ch
an
n
el
s
an
d
to
s
p
ec
if
y
th
e
f
r
o
ze
n
b
its
in
co
n
s
tr
u
ct
in
g
p
o
lar
c
o
d
e
s
f
o
r
5
G
s
y
s
te
m
s
[
7
]
.
I
n
ad
d
itio
n
,
o
th
er
w
o
r
k
s
w
er
e
co
n
ce
r
n
ed
w
it
h
in
cr
ea
s
in
g
th
e
m
i
n
i
m
u
m
d
i
s
tan
ce
o
f
th
e
p
o
lar
co
d
es
eith
e
r
b
y
u
s
i
n
g
o
th
er
s
u
p
p
er
co
d
e,
as
in
[
1
3
]
,
o
r
b
y
u
s
in
g
m
u
lti
k
er
n
al
p
o
lar
co
d
es,
as in
[
1
4
]
.
P
ilo
t
s
ig
n
al
s
ar
e
u
s
u
all
y
u
s
ed
in
w
ir
eless
tr
a
n
s
m
is
s
io
n
s
y
s
tem
s
to
esti
m
ate
th
e
i
m
p
u
l
s
e
r
esp
o
n
s
e
o
f
th
e
tr
an
s
m
i
s
s
io
n
ch
a
n
n
el.
T
h
e
n
u
m
b
er
an
d
t
h
e
lo
ca
tio
n
s
o
f
t
h
e
p
il
o
ts
h
av
e
a
s
i
g
n
if
ican
t
e
f
f
ec
t
o
n
th
e
w
ir
ele
s
s
s
y
s
te
m
p
er
f
o
r
m
an
ce
[
1
5
]
,
[
1
6
]
.
C
o
m
b
i
n
i
n
g
p
ilo
t
s
y
m
b
o
l
s
w
it
h
c
h
an
n
el
co
d
in
g
h
a
s
attr
a
cted
th
e
atten
t
io
n
o
f
s
ev
er
al
r
esear
ch
er
s
.
T
h
e
p
ilo
t
s
y
m
b
o
ls
ca
n
b
e
in
s
er
ted
w
i
th
i
n
th
e
en
co
d
ed
b
its
af
ter
th
e
en
co
d
in
g
p
r
o
ce
s
s
i
n
an
ar
r
an
g
e
m
e
n
t
k
n
o
w
n
as
‘
e
x
ter
n
al
p
ilo
t
in
s
er
tio
n
’
[
1
7
]
.
T
h
is
ap
p
r
o
ac
h
h
as
b
ee
n
u
til
is
e
d
in
m
a
n
y
w
o
r
k
s
to
i
m
p
r
o
v
e
th
e
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
.
L
o
w
-
d
e
n
s
it
y
p
ar
it
y
c
h
ec
k
(
L
DP
C
)
co
d
es
w
er
e
co
m
b
i
n
ed
w
it
h
p
ilo
t s
y
m
b
o
l
s
in
[
1
8
]
,
[
1
9
]
to
r
e
d
u
ce
b
o
th
t
h
e
e
x
p
er
ien
c
ed
er
r
o
r
f
lo
o
r
an
d
th
e
e
f
f
ec
t
o
f
er
r
o
r
p
r
o
p
ag
atio
n
.
I
n
ad
d
itio
n
,
t
h
e
p
r
o
b
lem
s
o
f
p
h
a
s
e
o
f
f
s
et,
f
r
eq
u
en
c
y
o
f
f
s
et,
a
n
d
b
u
r
s
t
er
r
o
r
i
n
co
h
er
e
n
t
r
ec
ep
tio
n
f
o
r
w
ir
el
ess
co
m
m
u
n
icatio
n
s
y
s
te
m
s
w
er
e
s
o
lv
ed
.
I
n
[
2
0
]
,
[
2
1
]
,
p
ilo
t
s
y
m
b
o
ls
w
er
e
co
m
b
in
ed
w
it
h
t
h
e
tu
r
b
o
co
d
e
to
r
ed
u
ce
th
e
p
r
o
b
lem
o
f
er
r
o
r
p
r
o
p
ag
atio
n
an
d
e
n
h
an
ce
t
h
e
s
p
ec
tr
al
ef
f
icie
n
c
y
f
o
r
m
u
ltip
le
-
i
n
p
u
t
m
u
ltip
le
-
o
u
tp
u
t
s
y
s
te
m
s
a
n
d
m
u
ltip
le
ac
ce
s
s
s
p
ar
s
e
co
d
e
s
y
s
te
m
s
.
A
p
ilo
t
-
a
s
s
i
s
ted
tr
an
s
m
is
s
io
n
s
c
h
e
m
e
u
s
in
g
p
o
lar
co
d
es
w
as
p
r
esen
ted
in
[
2
2
]
-
[
2
4
]
to
i
m
p
r
o
v
e
th
e
s
y
s
te
m
p
er
f
o
r
m
an
ce
a
n
d
to
r
ed
u
ce
th
e
o
v
er
h
ea
d
i
n
ch
a
n
n
el
e
s
t
i
m
atio
n
.
T
h
e
p
ilo
t
s
y
m
b
o
ls
(
b
its
in
t
h
is
ca
s
e)
ca
n
b
e
i
n
s
er
ted
a
m
o
n
g
th
e
d
ata
b
its
p
r
io
r
to
th
e
en
co
d
in
g
p
r
o
ce
s
s
.
T
h
is
ap
p
r
o
ac
h
is
ca
ll
ed
‘
in
ter
n
al
p
ilo
t
i
n
s
er
tio
n
’
a
n
d
w
as
u
t
ilis
ed
i
n
t
h
e
p
r
ese
n
t
wo
r
k
.
A
m
et
h
o
d
w
as
s
u
g
g
e
s
ted
i
n
[
2
5
]
f
o
r
co
m
b
i
n
in
g
i
n
ter
n
al
p
ilo
t
i
n
s
er
tio
n
w
ith
th
e
tu
r
b
o
co
d
e.
T
h
e
r
esu
lt
s
s
h
o
w
ed
an
i
m
p
r
o
v
e
m
en
t
i
n
t
h
e
B
E
R
p
er
f
o
r
m
a
n
ce
,
an
d
t
h
u
s
,
a
w
id
e
r
an
g
e
o
f
co
d
in
g
r
ate
s
co
u
ld
b
e
p
r
o
v
id
ed
.
I
n
th
e
p
r
esen
t
w
o
r
k
,
in
ter
n
al
p
ilo
t
i
n
s
er
tio
n
m
et
h
o
d
s
w
er
e
u
s
ed
w
it
h
p
o
lar
co
d
es
to
en
h
a
n
ce
th
e
co
d
e
d
is
tan
ce
p
r
o
p
er
ties
an
d
th
er
eb
y
i
m
p
r
o
v
e
th
e
B
E
R
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
d
e.
T
h
ese
in
s
er
tio
n
m
eth
o
d
s
in
tr
o
d
u
ce
d
a
n
e
w
m
ec
h
a
n
i
s
m
f
o
r
d
ata
r
ate
co
n
tr
o
l
o
n
th
e
b
asis
o
f
t
h
e
d
is
tan
ce
p
r
o
p
e
r
ties
o
f
th
e
co
d
e.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
av
o
id
co
d
e
r
ec
o
n
s
tr
u
ctio
n
a
n
d
p
r
o
v
id
e
a
u
n
i
v
er
s
al
r
ate
co
n
tr
o
l
m
ec
h
an
i
s
m
f
o
r
t
h
e
g
i
v
en
p
o
lar
co
d
e
in
d
ep
en
d
en
t
o
f
t
h
e
ch
a
n
n
el
c
o
n
d
itio
n
.
T
h
e
r
em
ai
n
d
er
o
f
th
is
p
ap
er
is
o
r
g
an
is
ed
as
f
o
ll
o
w
s
:
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
f
o
r
i
n
s
er
ti
n
g
p
ilo
t b
its
ar
e
d
escr
ib
ed
in
s
ec
tio
n
2
.
T
h
e
s
y
s
te
m
m
o
d
el
is
p
r
ese
n
ted
i
n
s
ec
tio
n
3
.
R
e
s
u
l
t
s
an
d
th
e
f
ea
t
u
r
es
o
f
t
h
e
p
r
o
p
o
s
ed
m
e
th
o
d
s
ar
e
g
i
v
e
n
i
n
s
ec
tio
n
4
.
Fin
al
l
y
,
t
h
e
co
n
cl
u
d
in
g
r
e
m
ar
k
s
o
f
t
h
e
p
ap
er
ar
e
p
r
esen
ted
in
se
ctio
n
5.
2.
P
I
L
O
T
I
NS
E
R
T
I
O
N
M
E
T
H
O
DS
T
w
o
m
eth
o
d
s
f
o
r
p
ilo
t
in
s
er
t
io
n
ar
e
in
tr
o
d
u
ce
d
h
er
e.
T
h
e
p
ilo
ts
ar
e
in
s
er
ted
b
ef
o
r
e
t
h
e
en
co
d
in
g
p
r
o
ce
s
s
.
T
h
e
lo
ca
tio
n
s
o
f
th
e
p
ilo
t
b
its
ar
e
d
eter
m
in
ed
b
y
th
ese
m
et
h
o
d
s
,
an
d
th
en
,
th
e
p
ilo
t
d
ata
b
it
(
b
in
ar
y
‘
1
’
)
i
s
i
n
s
er
ted
.
T
h
is
ca
n
b
e
co
n
s
id
er
ed
to
b
e
a
t
y
p
e
o
f
p
r
e
-
e
n
co
d
in
g
p
r
o
ce
s
s
.
T
h
e
i
n
ten
tio
n
h
er
e
is
to
i
m
p
r
o
v
e
th
e
er
r
o
r
p
er
f
o
r
m
an
ce
f
o
r
a
g
i
v
en
p
o
lar
co
d
e
b
y
c
h
a
n
g
in
g
t
h
e
d
is
tan
ce
p
r
o
p
er
ties
o
f
t
h
e
co
d
e.
T
h
is
is
ac
h
ie
v
ed
b
y
eit
h
er
r
e
m
o
v
in
g
t
h
e
co
d
e
wo
r
d
s
th
at
h
av
e
th
e
least
Ha
m
m
i
n
g
w
ei
g
h
t
s
o
r
r
ed
u
cin
g
th
e
i
r
m
u
ltip
licit
y
o
r
d
er
.
T
h
e
tw
o
m
et
h
o
d
s
,
n
a
m
ed
Me
t
h
o
d
-
1
an
d
Me
th
o
d
-
2
,
s
h
ar
e
th
e
co
m
m
o
n
p
r
eli
m
i
n
ar
y
s
tep
s
,
w
h
ic
h
ar
e
d
escr
ib
e
d
h
er
e
f
ir
s
t.
C
o
n
s
id
er
a
p
o
lar
co
d
e
PC
(
N
,
K)
h
av
in
g
a
co
d
e
len
g
t
h
o
f
N
b
its
an
d
a
d
ata
b
lo
ck
s
ize
o
f
K
b
its
.
I
n
itiall
y
,
all
2
K
p
o
s
s
i
b
le
in
p
u
t
d
ata
s
eq
u
en
ce
s
{
X
i
}
ar
e
g
en
er
ated
,
an
d
th
eir
co
r
r
esp
o
n
d
in
g
co
d
e
w
o
r
d
s
{
C
i
}
ar
e
d
eter
m
in
ed
to
g
et
h
er
w
it
h
th
e
ir
Ha
m
m
in
g
w
ei
g
h
ts
H
w
a
s
f
o
llo
w
s
:
H
w
=
[
h
min
, h
1
, h
2
,
.
.
.
,
h
max
]
(
1
)
w
h
er
e
h
min
an
d
h
max
ar
e
th
e
m
i
n
i
m
u
m
an
d
th
e
m
ax
i
m
u
m
Ha
m
m
i
n
g
w
ei
g
h
t
f
o
r
th
e
co
d
e,
r
esp
ec
tiv
el
y
.
T
h
e
w
ei
g
h
t d
is
tr
ib
u
t
io
n
v
ec
to
r
A
o
f
th
e
co
d
e,
w
it
h
{
A
hi
}
as its
co
m
p
o
n
en
ts
,
ca
n
b
e
ex
p
r
es
s
ed
as
f
o
llo
w
s
:
A
=
[
A
hmin
, A
h1
, A
h2
, …, A
hmax
]
(
2
)
w
h
er
e
A
hi
r
ep
r
esen
t
s
t
h
e
n
u
m
b
er
o
f
co
d
e
w
o
r
d
s
h
av
i
n
g
Ha
m
m
i
n
g
w
ei
g
h
t
h
i
.
T
h
e
f
ir
s
t
an
d
t
h
e
las
t
co
m
p
o
n
e
n
t
s
o
f
A
(
A
hmin
a
n
d
A
hmax
)
r
ep
r
ese
n
t
t
h
e
n
u
m
b
er
o
f
co
d
e
w
o
r
d
s
h
av
i
n
g
t
h
e
m
in
i
m
u
m
an
d
t
h
e
m
ax
i
m
u
m
w
ei
g
h
ts
,
r
esp
ec
tiv
el
y
,
w
h
ile
o
t
h
er
{
A
hi
}
h
o
ld
w
ei
g
h
ts
b
et
w
ee
n
t
h
e
m
in
i
m
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m
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t
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,
r
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Me
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t
h
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o
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ct
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e
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atr
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B
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i
n
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T
h
e
v
ec
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R
՝
is
co
n
s
tr
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cted
as
d
escr
ib
ed
in
Me
t
h
o
d
-
1
.
T
h
er
ef
o
r
e,
th
e
i
n
d
ex
o
f
t
h
e
co
m
p
o
n
e
n
t
w
it
h
t
h
e
m
ax
i
m
u
m
v
al
u
e
in
R
՝
is
s
e
lect
ed
as th
e
p
ilo
t p
o
s
itio
n
.
T
h
e
in
ter
n
al
p
ilo
t in
s
er
tio
n
p
r
o
ce
d
u
r
e
f
o
r
th
e
p
o
lar
co
d
e
w
it
h
t
h
e
t
w
o
co
n
s
id
er
ed
m
et
h
o
d
s
is
clar
if
ied
b
y
A
l
g
o
r
ith
m
-
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
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n
d
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esia
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J
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n
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m
p
Sci,
Vo
l.
22
,
No
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3
,
J
u
n
e
2
0
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:
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4
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1498
3.
SYST
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M
M
O
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L
A
f
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m
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ased
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G
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ar
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ter
s
is
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in
th
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w
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k
to
ev
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ate
th
e
B
E
R
p
er
f
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ase
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l
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p
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t
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tp
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t
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MI
MO
)
[
2
7
]
-
[
2
9
]
.
T
h
e
ch
an
n
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m
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co
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GP
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o
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GHz
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GHz
f
o
r
m
ax
i
m
u
m
b
an
d
w
id
t
h
o
f
2
GHz
[
2
7
]
.
Mo
d
el
D
(
in
d
o
o
r
o
f
f
ice
w
i
th
s
h
o
r
t
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d
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ted
in
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ab
les
1
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d
2
.
T
h
e
j
u
s
tif
ica
tio
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t
h
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ed
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eter
s
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alu
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etail
s
o
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eir
s
et
t
in
g
s
ca
n
b
e
f
o
u
n
d
else
w
h
er
e
[
2
7
]
-
[
2
9
]
.
A
l
g
o
r
ith
m
-
1
:
P
ilo
t in
s
er
tio
n
al
g
o
r
ith
m
f
o
r
p
o
lar
co
d
es
1
Specify N, K, and N
p
; // N
p
: number of
inserting
pilots
2
s
v
= { }; // s
v
: a set holds indexes
for pilot positions
3
Generate {X
i
}, {C
i
}, H
w
and A;
4
Select pilot insertion method (M);
5
For
i= 1 to N
p
6
If
M =” Method
-
1”
then
7
h
i
=h
min
, where h
min
ϵ H
w
;
8
Else
9
h
i
=h
cent
, where h
cent
ϵ H
w
;
10
End
If
11
B
hi
Call Constructing_matrix_B ({X
i
}, {C
i
}, hi) // B
hi
: matrix hold data set X
i
hi
12
R
Call
Constructing_vector_R (B
hi
, K) // R : a vector hold zeros
multiplicity at B
hi
columns
13
i
max
Max ( R ) //
i
max
: an index of maximum element
in R
14
If
R ho
ld single maximum element
then
15
s
i
=
i
max
16
Else
17
s
u
= { } //
s
u
: a set holds indexes share max. value in R
18
s
u
indexes
of maximum elements in vector R
19
If
M=” Method
-
1”
then
20
h
k
= h
1
, where h
1
ϵ H
w
// h
k
: a Hamming weight used if R hold
multiple maximum element
21
Else
22
h
k
= h
min
, where h
min
ϵ H
w
23
End if
24
s
i
Call
Finding_Best_Position
(h
k
, {X
i
}, {C
i
}, K, s
u
)
25
End if
26
s
v
s
i
27
∀
p ≤ K, p ϵ s
v
, set {X
i
} at p to 1 // p: an index
for data block
28
generate {C
i
}, H
w
, and A
29
End for
30
Return s
v
Su
b
r
o
u
ti
n
e
-
1
: Co
n
s
tr
u
cti
n
g
m
atr
ix
B
1
Constructing_matrix_B ({X
i
},{C
i
},h
i
)
2
∀
c
∈
{C
i
} and weight(c)= h
i
,
then c ϵ C
i
hi
// C
i
hi
: a set of codewords
with Hamming weight h
i
3
∀
x
∈
{X
i
}
and encode(x)
→
c where c ϵ C
i
hi
,
then x ϵ X
i
hi
// X
i
hi
: a data set
that produce C
i
hi
4
B
hi
{X
i
hi
}
5
Return
B
hi
Su
b
r
o
u
ti
n
e
-
2
:
C
o
n
s
tr
u
cti
n
g
v
ec
to
r
R
1 Constructing_vector_R (B
hi
, K)
2
For
i = 1 to K
3 R(i)
zeros count at B
hi
(:,i)
/
/
C
o
u
nt
s
t
h
e
n
um
b
e
r
of
z
e
ro
s
a
t
e
a
c
h
c
o
l
um
n
o
f
B
hi
4
End for
5 Return R
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
I
n
tern
a
l p
ilo
t in
s
erti
o
n
fo
r
p
o
l
a
r
co
d
es
(
W
a
lled
K
.
A
b
d
u
lw
a
h
a
b
)
1499
Su
b
r
o
u
ti
n
e
-
3
: Fin
d
i
n
g
B
est P
o
s
itio
n
1 Finding_Best_Position (h
k
,{X
i
},{C
i
}, K, s
u
)
2 B
hk
Call
Constructing_matrix_B ({X
i
}, {C
i
}, h
k
)
//
B
hk
: a matrix holds
the data set X
i
hk
3 R
’
Call Constructing_vector_R
’
( B
hk
, K, s
u
)
//
R
’
: a vector holds zeros
multiplicity at
B
hk
columns
4
k
max
Max (
R
’
)
//
k
max
: an index for the maximum element
in
R
’
5
Return
k
max
Su
b
r
o
u
ti
n
e
-
4
: Co
n
s
tr
u
ctio
n
v
e
cto
r
R
’
1
Constructing_vector_ R
’
(
B
hk
, K, s
u
)
2
For
i = 1 to K
3
If
i
∈
s
u
then
4
R
’
(i)
count zeros at
B
hk
(:,i)
5
End if
6
End
for
7
Return R
’
T
a
b
l
e
1
.
S
i
m
u
l
a
t
i
o
n
p
a
r
a
m
e
t
e
r
s
o
f
5
G
t
r
a
n
s
m
i
s
s
i
o
n
s
y
s
t
e
m
T
h
e
P
a
r
a
me
t
e
r
V
a
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e
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r
Ty
p
e
C
a
r
r
i
e
r
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r
e
q
u
e
n
c
y
2
8
G
H
z
B
a
n
d
w
i
d
t
h
4
0
0
M
H
z
M
o
d
u
l
a
t
i
o
n
Q
P
S
K
N
o
.
o
f
S
u
b
c
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r
r
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s i
n
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4
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e
n
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t
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o
f
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i
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e
f
i
x
2
8
8
S
u
b
-
C
a
r
r
i
e
r
S
p
a
c
i
n
g
1
2
0
k
H
z
O
F
D
M
F
r
a
me
D
u
r
a
t
i
o
n
8
.
3
3
μs
M
I
M
O
Ty
p
e
4
x
4
(
S
T
B
C
)
T
a
b
l
e
2
.
S
i
m
u
l
a
t
i
o
n
p
a
r
a
m
e
t
e
r
s
o
f
f
a
d
i
n
g
c
h
a
n
n
e
l
m
o
d
e
l
T
h
e
P
a
r
a
me
t
e
r
V
a
l
u
e
N
o
.
o
f
mu
l
t
i
p
a
t
h
s
3
P
a
t
h
G
a
i
n
s
[
-
0
.
2
-
1
8
.
8
-
2
1
]
d
B
N
o
r
mal
i
z
e
d
P
a
t
h
D
e
l
a
y
[
0
0
.
0
3
5
0
.
6
1
2
]
D
e
l
a
y
S
p
r
e
a
d
1
6
n
s
K
-
F
a
c
t
o
r
1
3
.
3
d
B
V
e
l
o
c
i
t
y
3
k
m/
H
r
M
a
x
.
D
o
p
p
l
e
r
S
h
i
f
t
7
7
.
7
8
4
Hz
4.
SI
M
UL
AT
I
O
N
T
E
ST
S
AN
D
DIS
CU
SS
I
O
N
P
o
lar
co
d
es
w
ith
s
h
o
r
t
len
g
t
h
s
an
d
lo
w
co
d
in
g
r
ate
s
w
er
e
co
n
s
id
er
ed
th
e
b
est
c
h
o
ice
f
o
r
5
G
s
y
s
te
m
a
m
o
n
g
all
t
h
e
co
d
in
g
s
ch
e
m
es
[
2
]
.
T
h
e
co
m
p
lex
it
y
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
is
m
a
in
l
y
b
as
ed
o
n
th
e
v
al
u
e
o
f
K;
th
er
ef
o
r
e,
r
elativ
el
y
s
m
all
v
alu
e
s
o
f
N
an
d
K
w
er
e
u
s
ed
in
th
e
s
i
m
u
lat
io
n
test
s
.
I
n
f
ac
t
,
t
w
o
s
h
o
r
t
le
n
g
t
h
s
p
o
lar
co
d
es
w
er
e
co
n
s
id
er
ed
in
t
h
e
test
s
:
t
h
e
f
ir
s
t
w
a
s
w
it
h
N=
3
2
an
d
K=
1
2
(
i.e
.
P
C
(
3
2
,
1
2
)
)
an
d
th
e
s
ec
o
n
d
o
n
e
w
it
h
N=
3
2
an
d
K=
1
6
(
i.e
.
P
C
(
3
2
,
1
6
)
)
.
Up
to
f
o
u
r
p
ilo
t
s
w
er
e
ass
u
m
ed
in
t
h
e
s
i
m
u
la
t
io
n
t
ests
.
A
n
S
C
L
d
ec
o
d
er
w
as
u
s
ed
w
it
h
d
if
f
er
en
t
lis
t
s
izes
(
L
)
o
f
8
,
1
6
,
an
d
3
2
.
T
h
e
s
i
m
u
latio
n
te
s
ts
w
er
e
c
ar
r
ied
o
u
t
to
s
tu
d
y
th
e
ef
f
ec
t
o
f
p
ilo
t
i
n
s
er
tio
n
o
n
th
e
d
is
ta
n
ce
p
r
o
p
er
ties
an
d
th
e
B
E
R
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
n
s
id
er
ed
p
o
lar
co
d
es.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
b
o
th
t
h
e
o
r
ig
i
n
al
p
o
lar
co
d
e
(
w
it
h
o
u
t
p
ilo
t
in
s
er
tio
n
)
a
n
d
th
e
m
o
d
i
f
ied
p
o
lar
co
d
e
(
w
it
h
p
ilo
t
in
s
er
tio
n
)
w
a
s
co
m
p
ar
ed
ac
co
r
d
in
g
to
th
e
co
r
r
esp
o
n
d
in
g
B
E
R
p
er
f
o
r
m
an
c
e
o
v
er
A
W
GN
an
d
f
ad
in
g
ch
a
n
n
els.
T
h
e
co
m
p
ar
is
o
n
w
as
b
ased
o
n
t
h
e
SN
R
g
ain
(
in
d
ec
ib
els)
ac
h
iev
ed
b
y
th
e
m
o
d
i
f
ied
p
o
lar
co
d
e
at
a
B
E
R
o
f
1
0
−4
.
T
est
r
esu
lt
s
w
it
h
u
n
clea
r
i
m
p
r
o
v
e
m
en
t,
b
ec
au
s
e
o
f
t
h
e
s
elec
t
io
n
o
f
t
h
e
lis
t
s
ize
an
d
th
e
n
u
m
b
er
o
f
p
ilo
t
s
,
ar
e
n
o
t p
r
esen
ted
.
I
n
s
tead
,
r
e
m
ar
k
s
o
n
s
u
c
h
ca
s
es a
r
e
g
iv
e
n
i
n
th
e
f
o
ll
o
w
i
n
g
s
u
b
s
ec
tio
n
s
.
4
.
1
.
D
is
t
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ain
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ata
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ith
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[
5
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,
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7
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.
T
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p
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et
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e
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p
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f
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m
a
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ce
in
m
o
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t
o
f
th
e
c
o
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s
id
er
ed
ar
r
an
g
e
m
e
n
ts
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elate
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s
t
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m
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s
ac
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d
in
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to
th
e
o
b
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d
is
tan
ce
p
r
o
p
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ties
.
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n
s
o
m
e
o
f
t
h
e
test
ar
r
an
g
e
m
en
ts
,
t
h
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m
et
h
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d
s
d
id
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o
w
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m
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m
en
t
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th
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s
elec
te
d
p
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t p
o
s
itio
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s
e
n
co
u
n
ter
ed
t
h
e
lo
ca
tio
n
o
f
r
eliab
le
b
it
-
c
h
a
n
n
el
s
.
T
h
is
r
e
s
u
l
ted
in
a
v
io
latio
n
o
f
t
h
e
p
o
lar
co
d
e
co
n
s
tr
u
ctio
n
r
u
le
s
.
A
cc
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r
d
in
g
to
th
e
w
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h
t
d
is
t
r
ib
u
tio
n
o
f
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h
e
m
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d
if
ied
co
d
es,
th
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p
er
f
o
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m
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i
m
p
r
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v
e
d
w
h
e
n
th
e
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ts
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er
e
in
s
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ted
in
p
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s
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tio
n
s
o
f
t
h
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lo
w
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lia
b
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n
f
o
r
m
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it
-
c
h
a
n
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ls
w
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th
o
n
e
o
f
th
e
f
o
llo
w
i
n
g
t
w
o
co
n
d
itio
n
s
b
ei
n
g
s
ati
s
f
ied
(
f
o
r
m
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o
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t
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t
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d
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itio
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s
o
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th
e
n
u
m
b
er
o
f
p
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ts
,
as
s
h
o
w
n
in
T
ab
les
3
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d
4
)
:
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h
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w
as
a
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ed
u
ctio
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in
th
e
n
u
m
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w
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.
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F
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NC
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S
[
1
]
E.
A
rik
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n
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“
Ch
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n
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P
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lariz
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ti
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n
:
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th
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str
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Ca
p
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p
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ss
Ch
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ls,”
IEE
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ra
n
sa
c
ti
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.
[
2
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W
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b
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F
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.
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sh
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4
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I.
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a
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A
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V
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L
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De
c
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Co
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a
n
sa
c
ti
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4
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[
5
]
A
.
S
ti
m
m
in
g
,
M
.
P
a
rizi
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a
n
d
A
.
Bu
rg
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Pr
o
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in
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,
v
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6
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.
[
6
]
H.
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sh
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in
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In
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A
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.
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.
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i,
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