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in
g
(
UG
M)
.
I
n
[
3
]
,
Ma
n
is
h
Ku
m
ar
an
d
al
h
ad
m
ad
e
a
co
m
p
ar
is
o
n
in
t
h
e
laten
c
y
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
R
S
C
-
R
S
C
s
er
ial
c
o
n
ca
ten
a
ted
co
d
e
u
s
in
g
n
o
n
-
i
ter
ativ
e
co
n
ca
ten
ated
Viter
b
i
d
ec
o
d
in
g
to
R
S
-
R
S
C
s
er
ial
co
n
ca
ten
a
ted
s
y
s
te
m
co
d
es
u
s
i
n
g
co
n
ca
te
n
atio
n
o
f
Viter
b
i
&
B
er
k
lela
m
p
-
Ma
s
s
e
y
d
ec
o
d
in
g
.
T
h
e
s
i
m
u
latio
n
r
esu
lts
h
ad
s
h
o
w
n
t
h
at
b
y
in
cr
ea
s
in
g
th
e
co
d
e
r
ate,
th
e
late
n
c
y
d
ec
r
ea
s
es
&
R
SC
-
R
S
C
is
to
b
e
a
b
ett
er
co
d
e
r
ath
er
th
a
n
RS
-
R
SC
w
h
ic
h
h
a
s
lo
w
la
ten
c
y
.
Hen
ce
R
S
C
-
R
S
C
s
y
s
te
m
i
s
m
o
r
e
s
u
i
T
ab
le
f
o
r
lo
w
late
n
c
y
ap
p
licatio
n
s
.
I
n
[
4
]
,
I
lesan
m
i
B
a
n
j
o
Olu
waf
e
m
i
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
w
o
h
y
b
r
id
co
n
ca
te
n
a
ted
Su
p
er
-
Or
th
o
g
o
n
a
l
Sp
ac
e
-
Ti
m
e
T
r
ellis
C
o
d
es
«
SOST
T
C
»
to
p
o
lo
g
ies
o
v
er
f
lat
f
ad
in
g
ch
a
n
n
els.
T
h
e
en
co
d
in
g
o
p
er
atio
n
is
b
ased
o
n
th
e
co
n
ca
ten
a
tio
n
o
f
co
n
v
o
l
u
tio
n
a
l
co
d
es,
in
ter
leav
i
n
g
,
a
n
d
s
u
p
e
r
-
o
r
th
o
g
o
n
a
l
s
p
ac
e
-
ti
m
e
tr
elli
s
co
d
es
an
d
t
h
e
d
ec
o
d
in
g
o
f
t
h
ese
t
w
o
s
ch
e
m
e
s
w
er
e
d
o
n
e
b
y
ap
p
l
y
i
n
g
iter
ati
v
e
d
ec
o
d
in
g
p
r
o
ce
s
s
w
er
e
t
h
e
s
y
m
b
o
l
-
by
-
s
y
m
b
o
l
m
ax
i
m
u
m
a
p
o
s
ter
io
r
i
(
M
A
P
)
d
ec
o
d
er
is
u
s
ed
f
o
r
t
h
e
i
n
n
er
SOST
T
C
d
ec
o
d
e
r
an
d
a
b
it
-
by
-
b
it M
A
P
d
ec
o
d
er
is
u
s
ed
f
o
r
th
e
o
u
ter
co
n
v
o
lu
t
i
o
n
al
d
ec
o
d
er
.
I
n
[
5
]
,
th
e
w
o
r
k
o
f
Sa
m
ee
r
A
Da
w
o
o
d
an
d
a
l
h
ad
s
h
o
w
n
th
e
ef
f
ec
ti
v
en
e
s
s
o
f
tu
r
b
o
co
d
es
t
o
d
ev
elo
p
a
n
e
w
ap
p
r
o
ac
h
f
o
r
a
n
O
F
DM
s
y
s
te
m
b
a
s
ed
o
n
a
Di
s
cr
ete
Mu
lt
i
w
av
e
let
C
r
itical
-
S
a
m
p
lin
g
T
r
an
s
f
o
r
m
(
OFDM
-
DM
W
C
ST
)
.
T
h
ey
u
s
ed
o
f
tu
r
b
o
co
d
in
g
i
n
a
n
OF
DM
-
DM
W
C
ST
s
y
s
te
m
is
u
s
e
f
u
l
i
n
p
r
o
v
id
in
g
t
h
e
d
esire
d
p
er
f
o
r
m
a
n
ce
a
t
h
ig
h
e
r
d
ata
r
ates.
T
w
o
t
y
p
es
o
f
tu
r
b
o
co
d
es
w
er
e
u
s
ed
in
t
h
i
s
w
o
r
k
,
i.e
.
,
P
ar
allel
C
o
n
ca
te
n
ated
C
o
n
v
o
lu
tio
n
al
C
o
d
es (
P
C
C
C
s
)
a
n
d
Ser
ial
C
o
n
ca
ten
a
ted
C
o
n
v
o
lu
t
io
n
al
C
o
d
es (
SC
C
C
s
)
.
I
n
b
o
th
t
y
p
es,
th
e
d
ec
o
d
in
g
is
p
er
f
o
r
m
ed
b
y
t
h
e
iter
ativ
e
d
ec
o
d
in
g
alg
o
r
ith
m
b
ased
o
n
th
e
lo
g
-
MA
P
(
Ma
x
i
m
u
m
A
p
o
s
ter
io
r
i)
alg
o
r
ith
m
.
I
n
[
6
]
,
B
ass
o
u
a
n
d
Dj
eb
b
ar
i
in
tr
o
d
u
ce
d
a
n
e
w
t
y
p
e
o
f
m
ap
p
in
g
ca
lled
th
e
U
n
g
er
b
o
ec
k
g
r
ay
tr
ellis
co
d
ed
m
o
d
u
latio
n
(
T
C
M
-
UG
M)
f
o
r
s
p
ec
tr
al
ef
f
icie
n
c
y
g
r
e
ater
th
an
o
r
eq
u
al
to
3
b
its
/
s
/
Hz.
T
h
is
T
C
M
-
UGM
co
d
e
o
u
tp
er
f
o
r
m
s
t
h
e
p
er
f
o
r
m
an
ce
o
f
U
n
g
er
b
o
ec
k
T
C
M
co
d
e
b
y
0
.
2
6
d
B
o
v
er
Gau
s
s
ia
n
c
h
an
n
el
a
n
d
2
.
5
9
d
B
o
v
er
R
a
y
leig
h
f
ad
in
g
c
h
an
n
el
at
B
E
R
=
1
0
-
5
.
T
h
is
tech
n
iq
u
e
is
co
m
b
i
n
ed
w
it
h
o
u
r
ap
p
r
o
ac
h
to
g
et
tin
g
m
o
r
e
ef
f
icien
c
y
.
I
n
[
7
]
,
T
r
io
an
d
al
h
ad
p
r
o
p
o
s
ed
a
VL
SI
ar
ch
i
tectu
r
e
to
i
m
p
le
m
en
t
r
ev
er
s
ed
-
tr
elli
s
T
B
C
C
(
R
T
-
T
B
C
C
)
alg
o
r
it
h
m
.
T
h
is
al
g
o
r
ith
m
i
s
d
esi
g
n
ed
b
y
m
o
d
i
f
y
i
n
g
d
ir
ec
t
-
ter
m
in
a
tin
g
m
a
x
i
m
u
m
-
l
ik
el
ih
o
o
d
(
ML
)
d
ec
o
d
in
g
p
r
o
ce
s
s
to
ac
h
iev
e
b
etter
co
r
r
ec
tio
n
r
ate
w
h
ic
h
r
ed
u
ce
s
th
e
co
m
p
u
tatio
n
al
t
i
m
e
an
d
r
eso
u
r
ce
s
co
m
p
ar
ed
to
th
e
ex
is
ti
n
g
s
o
lu
t
io
n
.
3.
T
CM
:
T
RE
L
L
I
S CO
D
E
D
M
O
DULAT
I
O
N
A
cc
o
r
d
in
g
to
Un
g
er
b
o
ec
k
i
n
1
9
8
2
,
w
h
ate
v
er
t
h
e
s
p
ec
tr
al
ef
f
icie
n
c
y
co
n
s
id
er
ed
f
o
r
t
h
e
tr
a
n
s
m
i
s
s
io
n
an
d
f
o
r
a
co
d
e
as
co
m
p
lex
as
it
ca
n
b
e,
th
e
asy
m
p
to
tic
g
ai
n
o
f
co
d
in
g
g
i
v
e
n
b
y
a
T
C
M
is
al
m
o
s
t
m
a
x
i
m
a
l
u
s
i
n
g
a
s
i
n
g
le
b
i
n
ar
y
ele
m
e
n
t
o
f
r
ed
u
n
d
an
c
y
p
er
s
y
m
b
o
l
tr
an
s
m
itted
.
T
h
u
s
,
f
o
r
a
T
C
M
co
n
s
tr
u
cted
f
r
o
m
a
co
n
s
tellat
io
n
w
i
th
M
=
2
n
+1
p
o
in
ts
,
th
e
s
p
ec
tr
al
e
f
f
icie
n
c
y
o
f
t
h
e
tr
a
n
s
m
is
s
io
n
is
n
b
it
s
/
s
/
Hz
a
n
d
t
h
e
p
er
f
o
r
m
a
n
ce
s
o
f
t
h
e
T
C
M
ar
e
co
m
p
ar
ed
w
it
h
t
h
o
s
e
o
f
a
m
o
d
u
latio
n
to
2
n
s
tate
s
;
t
h
at
is
to
s
a
y
,
h
a
v
i
n
g
a
2
-
p
o
in
t
co
n
s
te
llatio
n
.
T
h
e
co
n
s
t
ellatio
n
o
f
a
T
C
M,
th
er
e
f
o
r
e,
h
as
t
w
ice
as
m
a
n
y
p
o
in
ts
as
t
h
at
o
f
th
e
u
n
co
d
ed
m
o
d
u
latio
n
h
a
v
i
n
g
t
h
e
s
a
m
e
s
p
ec
tr
al
ef
f
icie
n
c
y
.
Su
p
p
o
s
e,
th
er
ef
o
r
e,
th
a
t
w
e
wan
t
to
tr
an
s
m
i
t
a
b
lo
ck
o
f
n
b
i
n
ar
y
ele
m
e
n
ts
co
m
in
g
f
r
o
m
t
h
e
s
o
u
r
ce
o
f
in
f
o
r
m
atio
n
.
I
t
i
s
d
iv
id
ed
in
to
t
w
o
b
lo
ck
s
o
f
r
esp
ec
tiv
e
le
n
g
th
s
,
ñ
a
n
d
(
n
-
ñ
)
.
T
h
e
len
g
th
o
f
ñ
b
lo
ck
is
t
h
e
n
co
d
ed
w
it
h
a
co
n
v
o
lu
tio
n
en
co
d
er
p
er
f
o
r
m
a
n
ce
R
c
=
to
v
m
e
m
o
r
ie
s
(
2
V
s
tates);
th
e
s
ec
o
n
d
b
lo
ck
is
u
n
c
h
a
n
g
ed
.
T
h
e
(
ñ
+
1
)
b
its
f
r
o
m
t
h
e
en
co
d
er
ar
e
th
en
u
s
ed
to
s
elec
t
a
s
u
b
-
co
n
s
tellatio
n
2
n
-
ñ
p
o
in
t
w
h
i
le
th
e
(n
-
ñ
)
u
n
co
d
ed
b
its
ar
e
u
s
ed
to
s
elec
t a
p
ar
ticu
lar
ite
m
in
t
h
i
s
s
u
b
-
co
n
s
te
llatio
n
.
Fig
u
r
e
1
s
h
o
w
s
t
h
e
s
y
n
o
p
tic
d
i
ag
r
a
m
o
f
a
n
en
co
d
er
f
o
r
Un
g
e
r
b
o
ec
k
T
C
M.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
I
mp
r
o
vin
g
Th
e
P
erfo
r
ma
n
ce
Of
V
iter
b
i D
ec
o
d
er u
s
in
g
W
in
d
o
w
S
ystem
(
R
ek
ka
l Ka
h
in
a
)
613
Fig
u
r
e
1
.
S
y
n
o
p
tic
d
iag
r
a
m
o
f
an
en
co
d
er
f
o
r
Un
g
er
b
o
ec
k
T
C
M
3
.
1
.
Rules
f
o
r
B
uil
din
g
t
he
T
re
l
li
s
T
h
e
im
p
le
m
e
n
tatio
n
o
f
th
e
d
ec
o
d
er
r
e
q
u
ir
es
th
e
co
n
s
tr
u
ctio
n
o
f
a
tr
ellis
o
f
t
h
e
T
C
M.
T
o
b
u
ild
s
u
c
h
a
tr
ellis
,
s
o
m
e
r
u
les
m
u
s
t
b
e
f
o
llo
w
ed
i
f
o
n
e
w
is
h
es
to
m
a
x
i
m
ize
t
h
e
f
r
ee
d
is
ta
n
ce
.
Fo
r
th
i
s
,
U
n
g
er
b
o
ec
k
p
r
o
p
o
s
es th
e
f
o
llo
w
in
g
t
h
r
ee
r
u
les:
T
h
e
M
=2
n
+1
s
ig
n
als
o
f
th
e
in
itial
(
u
n
p
ar
titi
o
n
ed
)
co
n
s
tellatio
n
m
u
s
t
b
e
u
s
ed
w
it
h
th
e
s
a
m
e
f
r
eq
u
en
c
y
.
Fi
g
u
r
e
2
s
h
o
w
s
t
h
e
s
et
P
ar
titi
o
n
in
g
m
e
th
o
d
ap
p
lied
to
th
e
8
P
SK [
2
]
Fig
u
r
e
2
.
Set P
ar
titi
o
n
in
g
m
et
h
o
d
ap
p
lied
to
th
e
8
P
SK [
2
]
T
h
e
2
n
-
ñ
p
ar
allel
b
r
a
n
ch
e
s
,
if
th
e
y
ex
i
s
t,
m
u
s
t
b
e
as
s
o
ciate
d
w
it
h
s
ig
n
al
s
b
elo
n
g
in
g
to
t
h
e
s
a
m
e
2
n
-
ñ
s
u
b
-
co
n
s
te
llatio
n
.
T
h
e
2
n
b
r
an
ch
es
t
h
at
leav
e
a
s
tate
o
r
r
ea
ch
a
s
tate
m
u
s
t
b
e
ass
o
ciate
d
w
i
th
s
i
g
n
als
b
elo
n
g
in
g
to
th
e
s
a
m
e
2
n
p
o
in
t s
u
b
-
co
n
s
tellatio
n
.
T
h
e
f
ir
s
t
r
u
le
p
r
o
v
id
es t
h
e
tr
ell
is
w
it
h
a
r
eg
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lar
p
atter
n
.
R
u
le
s
2
a
n
d
3
en
s
u
r
e
th
a
t t
h
e
f
r
ee
d
is
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ce
o
f
th
e
T
C
M
is
a
l
w
a
y
s
g
r
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ter
th
an
th
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m
in
i
m
u
m
E
u
c
lid
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n
d
is
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ce
o
f
t
h
e
u
n
co
d
ed
m
o
d
u
latio
n
ta
k
en
as
r
ef
er
en
ce
f
o
r
t
h
e
co
d
in
g
g
ai
n
ca
lcu
latio
n
.
T
h
u
s
th
e
a
s
y
m
p
to
tic
co
d
in
g
g
a
in
is
:
Ga
=
1
0
lo
g
10
(
)
(
1
)
4.
AL
G
O
RI
T
H
M
S O
F
DE
CO
DIN
G
T
CM
E
NCO
DE
R
T
h
e
m
o
s
t
co
m
m
o
n
d
ec
o
d
in
g
is
b
ased
o
n
th
e
Viter
b
i
alg
o
r
ith
m
[
8
]
.
I
t
co
n
s
is
ts
i
n
f
i
n
d
in
g
in
th
e
tr
ee
th
e
p
at
h
w
h
ich
co
r
r
esp
o
n
d
s
t
o
th
e
m
o
s
t
p
r
o
b
ab
le
s
eq
u
en
c
e,
th
at
i
s
to
s
a
y
,
t
h
at
w
h
ic
h
is
at
t
h
e
m
i
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i
m
u
m
d
is
tan
ce
o
f
r
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ed
s
eq
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e
n
ce
o
r
th
e
m
o
s
t
p
r
o
b
ab
le
s
eq
u
en
ce
.
T
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
il
lu
s
tr
ates
th
e
Vi
ter
b
i
an
d
MA
P
alg
o
r
it
h
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
6
1
1
–
6
2
1
614
4
.
1
.
Alg
o
rit
h
m
o
f
Vit
er
bi
T
h
e
aim
o
f
t
h
e
m
ax
i
m
u
m
li
k
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o
o
d
d
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d
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g
is
to
lo
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k
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th
e
tr
elli
s
co
d
e
“
C
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h
e
n
e
ar
est
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m
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t
l
ik
el
y
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f
t
h
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eiv
ed
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eq
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ce
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i.e
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o
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er
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n
)
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T
h
e
d
is
ta
n
ce
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m
p
lo
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ed
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n
th
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g
o
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E
u
clid
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ce
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n
th
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s
e
o
f
s
o
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i
n
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u
t,
o
r
th
e
h
a
m
m
i
n
g
d
is
tan
ce
,
in
t
h
e
ca
s
e
o
f
f
ar
m
s
in
p
u
t
s
.
T
h
u
s
t
h
e
d
ec
o
d
in
g
p
r
o
b
le
m
i
s
:
g
iv
e
n
(
p
er
tr
ellis
in
ter
v
al,
w
h
er
e
d
eter
m
in
e
t
h
e
m
o
s
t
li
k
el
y
tr
an
s
m
i
tted
p
ath
t
h
r
o
u
g
h
t
h
e
tr
ellis
.
I
f
w
e
a
s
s
u
m
e
th
a
t
th
e
u
s
e
s
o
f
th
e
B
S
C
(
th
e
b
in
ar
y
s
y
m
m
etr
ic
ch
an
n
el)
ar
e
in
d
ep
en
d
en
t
(
i.e
.
,
w
e
h
a
v
e
r
an
d
o
m
er
r
o
r
s
)
,
th
e
p
r
o
b
lem
r
ed
u
ce
s
to
m
i
n
i
m
i
zin
g
t
h
e
Ha
m
m
i
n
g
d
is
tan
ce
b
et
w
ee
n
th
e
{
}
an
d
o
u
r
esti
m
a
te
o
f
th
e
{
}
,
d
en
o
ted
as
{
̂
}
:
e
(
̂
)
=
∑
∑
̂
(
2
)
Fig
u
r
e
3
.
T
r
an
s
itio
n
d
ia
g
r
a
m
f
o
r
Viter
b
i a
lg
o
r
ith
m
A
lis
t
o
f
all
th
e
tr
an
s
itio
n
p
er
s
tate
a
n
d
th
e
ir
v
al
u
es
f
o
r
(
̂
̂
̂
)
ar
e
g
iv
e
n
i
n
Fig
u
r
e
3
.
Fo
r
ea
ch
tr
elli
s
tr
a
n
s
itio
n
w
e
d
o
th
e
f
o
llo
w
in
g
.
L
et
,
=
b
e
th
e
a
cc
u
m
u
lated
s
tate
m
etr
ic,
th
at
i
s
,
th
e
s
u
m
i
n
(
1
)
u
p
to
tr
ellis
in
t
er
v
al
i;
th
e
i
n
p
u
t
f
o
r
th
e
d
is
cr
ete
ti
m
e
tr
an
s
itio
n
is
(
)
f
o
r
ea
ch
s
tate,
:
a)
C
o
m
p
u
te
̂
̂
̂
[
∑
̂
]
(
3
)
b)
C
all
t
h
e
b
est
̂
̂
̂
th
e
w
i
n
n
in
g
tr
a
n
s
itio
n
a
n
d
s
to
r
e
it a
s
w
ell
as M
(
)
,
th
e
s
tate
m
etr
ic
f
o
r
t
h
e
w
in
n
i
n
g
tr
an
s
iti
o
n
.
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h
en
th
e
s
e
s
tep
s
ar
e
i
m
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le
m
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ted
,
w
e
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e
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t
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th
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e
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i
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tr
a
n
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itio
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p
at
h
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er
s
tate,
p
er
tr
ellis
in
ter
v
a
l.
T
h
e
co
llectio
n
s
o
f
th
ese
w
i
n
n
i
n
g
tr
an
s
itio
n
p
ath
s
o
v
er
ti
m
e
ar
e
ca
lled
s
u
r
v
iv
o
r
p
ath
s
.
T
h
e
d
ec
o
d
in
g
p
ath
is
th
en
t
h
e
m
i
n
i
m
u
m
o
f
o
v
er
all
s
u
r
v
i
v
o
r
p
ath
s
.
I
n
r
e
alit
y
,
o
n
e
s
h
o
u
ld
w
ait
u
n
ti
l
s
u
r
v
i
v
o
r
p
ath
s
m
er
g
e,
t
h
at
i
s
,
w
h
e
n
t
h
eir
in
it
ial
s
eg
m
e
n
ts
co
i
n
cid
e.
I
n
p
r
ac
tice,
o
n
e
s
to
r
es
t
h
e
r
esu
lt
f
o
r
tr
ellis
i
n
ter
v
al
s
an
d
th
e
n
m
a
k
es t
h
e
c
h
o
ice
o
f
t
h
e
b
est s
u
r
v
i
v
o
r
p
ath
; th
a
t is t
h
e
p
ath
w
it
h
t
h
e
s
m
a
lles
t
m
(
.
)
.
T
h
e
Viter
b
i
alg
o
r
ith
m
,
th
er
e
f
o
r
e,
r
eq
u
ir
es
th
e
co
m
p
u
tat
io
n
o
f
2
k
l
m
etr
ics
a
t
ea
ch
s
tep
t,
h
e
n
ce
a
co
m
p
le
x
it
y
o
f
W
˟
,
lin
ea
r
i
n
W
.
Ho
w
ev
er
,
t
h
e
co
m
p
le
x
it
y
r
e
m
ai
n
s
e
x
p
o
n
e
n
tial i
n
k
a
n
d
L
,
w
h
ic
h
li
m
it
s
t
h
e
u
s
e
o
f
t
h
e
co
d
es
o
f
s
m
all
s
ize
(
k
L
o
f
7
to
1
0
m
a
x
i
m
u
m
)
.
T
h
e
w
id
th
W
o
f
t
h
e
d
ec
o
d
in
g
w
i
n
d
o
w
is
tak
e
n
i
n
p
r
ac
tice
to
ab
o
u
t
5
L
.
T
h
is
g
u
ar
an
tees
(
e
m
p
ir
icall
y
)
th
at
t
h
e
s
u
r
v
i
v
o
r
s
co
n
v
er
g
e
to
a
s
in
g
le
p
ath
i
n
s
id
e
th
e
d
ec
o
d
in
g
w
i
n
d
o
w
.
T
h
e
Viter
b
i
alg
o
r
ith
m
,
t
h
er
ef
o
r
e,
r
eq
u
ir
es
th
e
s
to
r
ag
e
o
f
cu
m
u
lat
iv
e
m
etr
ics
an
d
s
u
r
v
iv
o
r
s
o
f
le
n
g
th
5
k
L
b
its
[
9
]
.
4
.
2
.
Alg
o
rit
h
m
o
f
M
AP
T
h
is
alg
o
r
it
h
m
i
s
b
ased
o
n
t
h
e
ca
lc
u
latio
n
o
f
t
h
e
p
r
o
b
ab
ilit
y
o
f
o
cc
u
r
r
en
ce
o
f
a
b
it
(
1
o
r
0
)
in
a
ce
r
tain
p
o
s
itio
n
.
W
e
h
a
v
e
at
o
u
r
d
is
p
o
s
al
a
s
tr
in
g
o
f
le
n
g
th
T
,
w
h
ic
h
co
m
e
s
f
r
o
m
t
h
e
co
d
i
n
g
o
f
a
n
i
n
f
o
r
m
atio
n
w
o
r
d
o
f
s
ize
.
T
h
e
m
et
h
o
d
co
n
s
is
t
s
in
ca
lcu
lati
n
g
iter
ati
v
el
y
th
e
a
p
o
s
ter
io
r
i
p
r
o
b
ab
i
lity
o
f
ea
ch
b
it,
f
ir
s
t
as
a
f
u
n
ctio
n
o
f
t
h
e
v
al
u
es
o
f
th
e
p
r
o
b
ab
ilit
ies
f
o
r
th
e
b
its
p
r
ec
ed
in
g
it,
an
d
t
h
e
n
as
a
f
u
n
ctio
n
o
f
t
h
e
p
o
s
ter
io
r
b
its
.
Fo
r
th
is
r
ea
s
o
n
,
th
e
al
g
o
r
ith
m
is
ca
l
led
"
f
o
r
w
ar
d
-
b
ac
k
w
ar
d
alg
o
r
ith
m
"
.
W
e
p
lace
eq
u
al
i
m
p
o
r
tan
ce
o
n
t
h
e
"
b
ef
o
r
e
"
b
its
an
d
th
e
"
af
ter
"
b
i
ts
.
Her
e,
Y
is
t
h
e
s
tr
in
g
o
f
b
its
r
e
ce
iv
ed
an
d
t
is
t
h
e
p
o
s
it
io
n
o
f
th
e
b
it
in
th
e
s
tr
i
n
g
.
Si
m
ilar
l
y
,
w
e
h
a
v
e
d
en
o
ted
,
th
e
s
et
o
f
tr
an
s
itio
n
s
f
r
o
m
s
tate
to
s
tate
,
as
s
o
o
n
as
w
e
h
a
v
e
h
ad
th
e
b
it
„
i
‟
at
th
e
in
p
u
t
.
L
et
M
b
e
th
e
n
u
m
b
e
r
o
f
p
o
s
s
ib
le
s
tates.
W
e
tr
y
to
ca
lcu
late
th
e
lo
g
-
lik
elih
o
o
d
r
atio
lo
g
ar
ith
m
v
al
u
e
(
λ
(
u
(
t)
)
(
lo
g
-
li
k
eli
h
o
o
d
r
atio
)
:
(
u
(
t)
)
=
ln
[
]
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
I
mp
r
o
vin
g
Th
e
P
erfo
r
ma
n
ce
Of
V
iter
b
i D
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in
g
W
in
d
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ystem
(
R
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ka
l Ka
h
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a
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w
h
er
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u
(
t)
d
en
o
tes t
h
e
o
u
tp
u
t
o
f
th
e
e
n
co
d
er
.
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r
t
w
o
g
i
v
e
n
s
tate
s
,
o
n
e
d
ef
i
n
es a
j
o
in
t p
r
o
b
ab
ilit
y
:
(
l‟
,
l)
=
P
(
=l‟
,
=
)
=
P (
u
(
t)
=
i,
=
)
(
5
)
is
th
e
b
it t
h
at
s
e
n
d
s
in
t
h
e
l
‟
t
o
l (
is
0
w
h
en
t
h
er
e
is
n
o
tr
an
s
itio
n
f
r
o
m
1
‟
to
1
)
.
W
e
th
u
s
h
a
v
e
th
e
f
o
llo
w
in
g
r
e
latio
n
:
P
(
u
(
t)
=
)=
∑
(
6
)
T
o
ca
lcu
late
σ
,
w
e
m
u
s
t i
n
tr
o
d
u
ce
th
e
j
o
in
t p
r
o
b
ab
ilit
y
d
e
n
s
it
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:
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l)
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P
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u
(
t)
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1
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w
h
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en
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m
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n
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e
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to
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Y.
Si
m
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l
y
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w
e
d
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i
n
e
t
h
e
co
n
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itio
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al
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r
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b
ab
ilit
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l)
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=
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g
t
h
e
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es r
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le,
w
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o
b
tain
th
e
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n
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=
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llo
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e
n
ts
,
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s
e
ti
m
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p
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o
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w
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u
t t
h
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ter
m
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et:
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(
l)
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r
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1
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C
o
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tin
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late
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r
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r
th
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h
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o
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{
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r
b
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1
3
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A
p
p
l
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r
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w
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f
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d
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1
4
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w
h
er
e:
(
l‟
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l)
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U(
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1
5
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t
h
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o
r
e
in
c
lu
d
e:
(
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(
l)
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(
l)
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{
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(
l‟
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*
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(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
6
1
1
–
6
2
1
616
b
y
s
i
m
ilar
ca
lcu
la
tio
n
s
,
w
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o
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t
ain
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(
l)
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∑
∑
{
}
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l‟
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*
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l‟
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l)
(
1
7
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a
s
ch
ar
ac
ter
izes t
h
e
n
o
is
e,
w
h
ich
is
w
h
ite
Ga
u
s
s
ia
n
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o
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e
ca
n
w
r
ite:
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l )
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if
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t)
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n
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8
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e
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as
th
e
s
tate
is
ch
an
g
ed
f
r
o
m
s
tate
to
s
tate.
4
.
3
.
Si
m
pl
if
ied v
er
s
io
ns
o
f
t
he
M
AP
a
lg
o
rit
h
m
T
h
e
B
C
J
R
al
g
o
r
ith
m
,
o
r
M
AP
,
s
u
f
f
er
s
f
r
o
m
o
n
e
i
m
p
o
r
tan
t
d
is
ad
v
a
n
ta
g
e:
i
t
m
u
s
t
ca
r
r
y
o
u
t
m
an
y
m
u
ltip
licatio
n
s
.
I
n
o
r
d
er
to
r
ed
u
ce
th
is
co
m
p
u
tatio
n
a
l
co
m
p
le
x
it
y
,
s
ev
er
al
s
i
m
p
li
f
ied
v
er
s
io
n
s
w
er
e
in
tr
o
d
u
ce
d
as
(
SOV
A
)
i
n
1
9
8
9
[
1
0
]
,
th
e
m
ax
-
lo
g
-
M
A
P
alg
o
r
ith
m
1
9
9
0
-
1
9
9
4
[
1
1
]
,
[
1
2
]
,
an
d
th
e
lo
g
-
M
A
P
alg
o
r
ith
m
in
1
9
9
5
[
1
3
]
.
T
h
e
m
u
ltip
licatio
n
o
p
er
ati
o
n
s
ar
e
r
ep
lace
d
b
y
th
e
ad
d
itio
n
,
an
d
th
r
ee
n
e
w
v
ar
iab
le
s
ar
e
d
ef
in
ed
as
A
,
B
an
d
Γ,
as f
o
llo
w
i
n
g
:
Γ
k
(
s
‟
,
s
)
=l
n
γ
k
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s
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,
s
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=
ln
C
k
+
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{
{
w
h
er
e
{
(
|
|
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(
1
9
)
Fo
r
th
e
co
n
v
o
lu
tio
n
al
en
co
d
er
o
f
r
at
e
,
w
e
u
s
e
th
e
s
y
m
b
o
l
b
y
s
y
m
b
o
l
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P
A
l
g
o
r
ith
m
f
o
r
n
o
n
-
b
in
ar
y
tr
elli
s
es.
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o
u
g
h
l
y
s
p
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k
in
g
,
w
e
ca
n
s
ta
te
th
at
th
e
c
o
m
p
le
x
it
y
o
f
th
e
B
C
J
R
al
g
o
r
ith
m
is
ab
o
u
t
th
r
ee
ti
m
e
s
th
at
o
f
th
e
Vi
ter
b
i a
lg
o
r
ith
m
.
5.
T
H
E
P
RO
P
O
SE
D
AP
P
RO
A
CH
5
.
1
.
Vit
er
bi I
m
p
ro
v
ed
b
y
Wind
o
w
Sy
s
t
e
m
W
e
s
a
w
in
t
h
e
p
r
ev
io
u
s
s
ec
t
i
o
n
s
h
o
w
it
w
as
p
o
s
s
ib
le,
u
s
i
n
g
an
alg
o
r
it
h
m
,
to
co
r
r
ec
t
an
er
r
o
n
eo
u
s
m
es
s
ag
e.
I
n
t
h
is
p
ar
t,
w
e
tal
k
ab
o
u
t
m
et
h
o
d
s
o
f
en
co
d
in
g
an
d
d
ec
o
d
in
g
in
f
o
r
m
a
tio
n
th
at
r
eq
u
ir
es
s
o
m
e
co
m
p
u
ti
n
g
p
o
w
er
,
w
h
ich
ca
n
ca
u
s
e
s
o
m
e
p
r
o
b
le
m
s
(
f
o
r
ex
a
m
p
le
i
n
e
m
b
ed
d
ed
s
y
s
te
m
s
wh
er
e
th
er
e
i
s
li
m
ited
co
m
p
u
ti
n
g
p
o
w
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d
t
h
e
ca
lc
u
latio
n
m
u
s
t
b
e
d
o
n
e
in
r
ea
l
ti
m
e)
.
Fi
n
all
y
,
o
n
l
y
lo
w
er
r
o
r
p
er
ce
n
tag
e
m
es
s
a
g
e
s
(
en
co
d
ed
w
i
th
o
u
t
er
r
o
r
s
)
ca
n
b
e
co
r
r
ec
ted
u
p
o
n
r
ec
eip
t.
Fo
r
th
is
p
u
r
p
o
s
e,
it
is
p
r
o
p
o
s
ed
in
o
u
r
ap
p
r
o
ac
h
to
u
s
i
n
g
th
e
w
i
n
d
o
w
s
y
s
te
m
i
n
t
h
e
en
co
d
in
g
an
d
d
ec
o
d
in
g
p
h
ase
o
f
th
e
i
n
f
o
r
m
atio
n
i
n
o
r
d
er
to
m
i
n
i
m
ize
th
e
er
r
o
r
o
n
a
s
in
g
le
w
i
n
d
o
w
w
h
o
s
e
len
g
t
h
eq
u
al
to
th
e
n
u
m
b
er
o
f
m
e
m
o
r
y
p
lu
s
1
.
I
n
th
is
s
ec
tio
n
,
w
e
u
s
e
t
h
e
w
i
n
d
o
w
in
co
n
v
o
l
u
tio
n
al
co
d
in
g
an
d
d
ec
o
d
in
g
.
T
o
ex
p
lain
th
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
w
i
n
d
o
w
s
y
s
te
m
a
n
d
th
e
clas
s
ical
ap
p
r
o
ac
h
,
w
e
ch
o
o
s
e
to
p
r
esen
t th
e
f
o
llo
w
in
g
ex
a
m
p
le:
Fig
u
r
e
4
s
h
o
w
s
t
h
e
s
tr
u
ct
u
r
e
o
f
th
e
co
n
v
o
l
u
tio
n
a
l e
n
co
d
er
w
i
th
r
ate
R
=1
/2
.
Fig
u
r
e
4
.
Diag
r
a
m
o
f
a
co
n
v
o
l
u
tio
n
al
e
n
co
d
er
o
f
o
u
tp
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
I
mp
r
o
vin
g
Th
e
P
erfo
r
ma
n
ce
Of
V
iter
b
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s
in
g
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in
d
o
w
S
ystem
(
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ek
ka
l Ka
h
in
a
)
617
I
n
T
ab
le
1
w
e
s
ee
t
h
at
"
Y"
is
a
f
u
n
c
tio
n
w
h
ic
h
d
ep
en
d
s
o
n
t
h
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i
n
p
u
t
X
a
n
d
t
h
e
v
al
u
es
o
f
s
tates
S0
,
S1
(
X,
S0
,
S1
)
[
Yi
=
F (
Xi,
S0
,
S1
)
]
.
I
n
itializatio
n
o
n
v
a
lu
e
s
o
f
S0
=
0
; S1
=
0
;
Fig
u
r
e
5
s
h
o
w
s
t
h
e
t
r
an
s
m
i
s
s
i
o
n
ch
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n
o
f
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v
o
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en
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er
.
Fig
u
r
e
5
.
T
r
an
s
m
i
s
s
i
o
n
ch
ai
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o
f
co
n
v
o
l
u
tio
n
e
n
co
d
er
T
ab
le
1
.
Scen
ar
io
s
o
f
co
d
in
g
Xi
x0
x1
x2
x3
x4
x5
x6
x7
x8
(
F
)
Xi
S0
S1
x0
0
0
x1
x0
0
x2
x1
x0
x3
x2
x1
x4
x3
x2
x5
x4
x3
x6
x5
x4
x7
x6
x5
x8
x7
x6
Yi
y0
y1
y2
y3
y4
y5
y6
y7
y8
A
cc
o
r
d
in
g
to
T
ab
le
1
,
w
e
ca
n
d
is
tin
g
u
is
h
t
h
at
m
o
s
t
o
f
t
h
e
“Xi”
s
u
r
v
i
v
e
o
n
m
a
n
y
“
Yi”
b
y
th
e
s
ize
o
f
th
e
co
n
s
tr
ain
t o
f
th
e
co
d
e
(
in
o
u
r
ca
s
e,
th
e
s
ize
o
f
th
e
co
n
s
tr
a
in
t e
q
u
al
s
th
r
ee
(
0
3
)
)
.
T
h
at
is
to
s
ay
t
h
at
th
e
co
d
e
y
0
,
f
o
r
its
en
co
d
in
g
,
d
ep
en
d
o
n
“X0
,
S0
,
S1
”,
y
1
d
ep
en
d
in
g
o
n
“
X1
,
X0
,
S1
”,
an
d
th
e
co
d
e
y
2
d
ep
en
d
s
o
n
“
X2
,
X1
,
X0
”.
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ce
,
w
e
s
ee
t
h
at
X0
ap
p
ea
r
s
t
h
r
ee
ti
m
es
f
o
r
t
h
e
e
n
co
d
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g
o
f
“
Y0
,
Y1
,
an
d
Y2
”.
T
h
e
d
is
ad
v
an
tag
e
o
f
t
h
is
p
h
e
n
o
m
e
n
o
n
i
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e
d
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o
d
in
g
b
y
th
e
VI
T
E
R
B
I
alg
o
r
ith
m
.
I
f
all
th
e
b
its
o
f
"
Yi
"
ar
e
er
r
o
n
eo
u
s
,
th
e
al
g
o
r
ith
m
d
ec
o
d
es
a
"
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er
r
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n
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s
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d
t
h
i
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er
r
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r
ex
p
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e
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ize
o
f
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h
e
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n
s
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ain
t
o
f
t
h
e
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an
d
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n
s
eq
u
e
n
tl
y
,
all
t
h
at
f
o
llo
w
s
is
w
r
o
n
g
.
T
o
o
v
er
co
m
e
t
h
is
p
h
e
n
o
m
e
n
o
n
w
e
p
r
o
p
o
s
e
th
e
w
in
d
o
w
o
n
t
h
e
s
iz
e
o
f
th
e
co
n
s
tr
ai
n
t o
f
th
e
co
d
e
as in
d
icate
d
in
T
ab
le
2.
a.
T
h
e
s
ize
o
f
th
e
co
n
s
tr
ain
t i
s
3
(
it is
th
e
n
u
m
b
er
o
f
m
e
m
o
r
y
+
1
)
.
I
n
itializatio
n
: S0
=
0
; S1
=
0
;
b.
I
f
all
th
e
b
it
s
o
f
a
"
Yi"
a
r
e
er
r
o
n
eo
u
s
,
t
h
e
al
g
o
r
ith
m
d
ec
o
d
es a
"
Xi
"
w
r
o
n
g
,
b
u
t o
n
l
y
o
n
a
wi
n
d
o
w
.
T
ab
le
2
.
C
o
n
v
o
lu
tio
n
a
l e
n
co
d
i
n
g
b
y
th
e
w
i
n
d
o
w
s
y
s
te
m
Fig
u
r
e
6
s
h
o
w
s
a
tr
a
n
s
m
is
s
io
n
ch
ain
o
f
a
co
n
v
o
l
u
tio
n
a
l e
n
co
d
er
u
n
d
er
th
e
co
n
s
tr
ai
n
t le
n
g
th
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
6
1
1
–
6
2
1
618
Fig
u
r
e
6
.
A
tr
an
s
m
is
s
io
n
c
h
ai
n
o
f
a
co
n
v
o
lu
tio
n
al
en
co
d
er
u
n
d
er
th
e
co
n
s
tr
ai
n
t le
n
g
th
5
.
2
.
RSCpo
ly
2
t
re
llis
f
o
r
Rec
urs
i
v
e
Sy
s
t
e
m
a
t
ic
Co
nv
o
lutio
na
l (
RSC)
E
nco
der
T
h
e
p
r
o
p
o
s
ed
f
u
n
ctio
n
R
S
C
p
o
l
y
2
tr
ellis
S
y
n
ta
x
: T
r
ellis
=
R
S
C
p
o
l
y
2
tr
ellis
(
H)
;
W
h
er
e
R
S
C
p
o
l
y
2
tr
ellis
f
u
n
c
tio
n
ac
ce
p
ts
a
p
o
l
y
n
o
m
ial
d
escr
ip
tio
n
o
f
a
r
ec
u
r
s
i
v
e
s
y
s
te
m
a
tic
co
n
v
o
lu
tio
n
al
(
R
SC
)
en
co
d
er
an
d
r
etu
r
n
s
t
h
e
co
r
r
esp
o
n
d
in
g
tr
elli
s
s
tr
u
c
tu
r
e
d
escr
ip
tio
n
.
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h
e
o
u
tp
u
t
o
f
R
S
C
p
o
l
y
2
tr
ellis
i
s
s
u
i
T
ab
le
as
an
i
n
p
u
t
to
th
e
co
n
v
e
n
c
an
d
v
itd
ec
f
u
n
ctio
n
s
an
d
as
a
m
a
s
k
p
ar
a
m
eter
f
o
r
t
h
e
C
o
n
v
o
lu
tio
n
al
E
n
co
d
er
,
Viter
b
i D
ec
o
d
er
in
th
e
C
o
m
m
u
n
ica
tio
n
s
B
lo
c
k.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
r
ec
u
r
s
i
v
e
s
y
s
te
m
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tic
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n
v
o
lu
tio
n
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en
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er
w
ith
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ate
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h
ic
h
is
r
ep
r
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a
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H:
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]
Fig
u
r
e
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.
R
ec
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r
s
i
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e
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y
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te
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at
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c
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n
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er
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it
h
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ate
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e
d
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ib
e
th
e
f
u
n
ctio
n
w
h
i
ch
cr
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tes
th
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tr
el
lis
s
tr
u
ct
u
r
e
o
f
a
r
ec
u
r
s
iv
e
s
y
s
te
m
atic
co
n
v
o
lu
tio
n
al
en
co
d
er
f
r
o
m
th
e
m
atr
i
x
H.
W
e
h
av
e
th
o
s
e
p
ar
a
m
eter
s
:
a.
Nu
m
b
er
o
f
i
n
p
u
t
s
y
m
b
o
ls
:
n
u
m
I
n
p
u
tS
y
m
b
o
l
s
)
w
h
ic
h
eq
u
al
to
2
(
T
h
e
s
u
m
o
f
t
h
e
r
o
w
s
o
f
t
h
e
m
a
tr
ix
H)
-
1
b.
Nu
m
b
er
o
f
o
u
tp
u
t
s
y
m
b
o
ls
:
(
n
u
m
O
u
tp
u
t
S
y
m
b
o
ls
)
w
h
ic
h
eq
u
al
to
2
(
T
h
e
s
u
m
o
f
t
h
e
r
o
w
s
o
f
t
h
e
m
atr
i
x
H)
c.
Nu
m
b
er
o
f
s
tates (
n
u
m
S
tate)
w
h
ic
h
eq
u
al
to
2
(
T
h
e
s
u
m
o
f
t
h
e
co
lu
m
n
s
o
f
t
h
e
m
a
tr
ix
H)
-
1
d.
Ma
tr
ix
o
f
n
e
x
t
s
tate
s
(
n
e
x
tS
t
ate)
w
h
ich
h
as
a
d
i
m
e
n
s
io
n
o
f
2
n
u
m
State
s
x
2
n
u
m
I
n
p
u
tS
y
m
b
o
ls
an
d
n
ex
t
s
tate
eq
u
al
s
to
:
{
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
I
mp
r
o
vin
g
Th
e
P
erfo
r
ma
n
ce
Of
V
iter
b
i D
ec
o
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er u
s
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g
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in
d
o
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ystem
(
R
ek
ka
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in
a
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e.
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h
e
m
atr
i
x
o
f
o
u
tp
u
t
s
y
m
b
o
ls
(
o
u
tp
u
ts
)
w
h
ic
h
h
a
s
a
d
i
m
e
n
s
io
n
o
f
2
n
u
m
State
x
2
n
u
m
I
n
p
u
tS
y
m
b
o
l
s
an
d
th
e
o
u
tp
u
ts
eq
u
a
l to
:
{
6.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
Fig
u
r
e
8
,
Fig
u
r
e
9
an
d
Fi
g
u
r
e
1
0
s
h
o
w
a
co
m
p
ar
i
s
o
n
b
et
w
e
en
th
e
c
lass
ical
Viter
b
i
d
ec
o
d
er
an
d
th
e
Viter
b
i
w
ith
w
i
n
d
o
w
s
y
s
te
m
d
ec
o
d
er
o
f
T
C
M
QP
SK/8
P
SK a
n
d
T
C
M
j
o
in
ed
b
y
a
n
e
w
t
y
p
e
o
f
m
ap
p
in
g
ca
lled
th
e
Un
g
er
b
o
ec
k
g
r
a
y
tr
elli
s
co
d
ed
m
o
d
u
latio
n
(
T
C
M
-
UG
M)
d
escr
ib
ed
in
s
ec
tio
n
2
“
R
elate
d
w
o
r
k
s
”
w
it
h
r
ates o
f
1
/2
,
1
/3
an
d
2
/3
.
a.
W
e
ca
n
o
b
s
er
v
e,
a
t
h
ig
h
s
i
g
n
al
-
to
-
n
o
is
e
r
atio
s
,
t
h
at
t
h
e
s
i
m
u
latio
n
cu
r
v
e
u
s
i
n
g
V
iter
b
i
w
it
h
w
i
n
d
o
w
s
y
s
te
m
o
u
tp
er
f
o
r
m
s
t
h
e
class
ical
Viter
b
i b
y
a
g
ai
n
e
q
u
al
to
1
d
B
at
B
E
R
=
.
b.
I
n
o
r
d
er
to
in
v
esti
g
ate
m
o
r
e
p
er
f
o
r
m
a
n
ce
,
th
e
Un
g
er
b
o
ec
k
g
r
a
y
m
ap
p
in
g
i
s
co
n
s
id
er
ed
w
it
h
T
C
M
en
co
d
er
.
T
h
e
s
i
m
u
latio
n
r
esu
lt
u
s
in
g
T
C
M
-
UGM
an
d
th
e
Viter
b
i
d
ec
o
d
er
w
it
h
win
d
o
w
s
y
s
te
m
o
u
tp
er
f
o
r
m
s
T
C
M
an
d
th
e
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b
i
d
ec
o
d
er
w
it
h
w
i
n
d
o
w
s
y
s
te
m
b
y
a
g
ai
n
eq
u
al
to
2
.
7
d
B
(
ap
p
r
o
x
)
an
d
o
u
tp
e
r
f
o
r
m
s
T
C
M
w
it
h
a
clas
s
ical
Viter
b
i d
ec
o
d
er
b
y
a
g
ain
o
f
3
.
8
d
B
(
ap
p
r
o
x
)
.
Fig
u
r
e
8
.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
4
s
tates T
C
M
QP
SK,
T
C
M
-
W
in
QP
SK a
n
d
T
C
M
-
U
GM
-
W
i
n
QP
SK o
v
er
A
W
GN
c
h
an
n
el
Fig
u
r
e
9
.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
4
s
tates T
C
M
8
P
SK,
T
C
M
-
W
in
8
P
SK a
n
d
T
C
M
-
U
GM
-
W
i
n
8
P
SK o
v
er
A
W
GN
c
h
an
n
el
Fig
u
r
e
1
0
.
C
o
m
p
ar
is
o
n
b
et
w
e
en
8
s
tates T
C
M
8
P
SK,
T
C
M
-
W
in
8
P
SK a
n
d
T
C
M
-
U
GM
-
W
i
n
8
P
SK o
v
er
A
W
GN
c
h
an
n
el
Fig
u
r
e
1
1
.
C
o
m
p
ar
is
o
n
b
et
w
e
en
4
s
tates T
C
M
QP
SK
w
it
h
Viter
b
i
h
ar
d
d
ec
o
d
er
an
d
Viter
b
i so
f
t d
ec
o
d
er
o
v
er
A
W
GN
c
h
an
n
el.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
6
1
1
–
6
2
1
620
T
h
e
s
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m
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la
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n
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illu
s
tr
ated
in
Fig
u
r
e
1
1
s
h
o
w
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at
4
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State
s
T
C
M
-
QP
SK
w
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h
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s
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t
d
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C
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SK
w
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th
th
e
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h
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d
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4
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n
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e
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h
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y
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n
g
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i so
f
t d
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o
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er
at
B
E
R
=
.
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u
r
e
1
2
s
h
o
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s
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at
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h
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ig
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al
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to
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n
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e
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atio
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t
h
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th
e
c
u
r
v
e
o
f
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g
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m
ap
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th
e
s
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m
e
as
m
ax
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m
ap
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o
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er
s
b
u
t
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th
o
u
tp
er
f
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r
m
th
e
Viter
b
i
s
o
f
t
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d
m
a
p
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o
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ith
m
s
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d
th
e
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ai
n
ca
n
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e
ea
s
ily
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b
tain
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f
r
o
m
t
h
e
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g
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m
ap
o
r
m
a
x
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g
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m
ap
w
h
ic
h
eq
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al
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2
d
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at
B
E
R
co
m
p
ar
ed
to
th
e
Viter
b
i
s
o
f
t.
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h
e
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R
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er
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m
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n
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is
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s
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o
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E
R
L
o
g
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Ma
p
=
B
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m
ax
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g
-
m
ap
<
B
E
R
Vitr
eb
i So
f
t <
B
E
R
MA
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.
Fig
u
r
e
1
2
.
C
o
m
p
ar
is
o
n
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et
w
e
en
R
S
C
T
C
M
8
P
SK
w
it
h
a
M
A
P
,
L
o
g
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Ma
p
,
an
d
Ma
x
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lo
g
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m
ap
an
d
Viter
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i s
o
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t
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o
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er
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ch
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n
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l.
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CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
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e
s
i
m
u
latio
n
in
M
A
T
L
A
B
w
a
s
u
s
ed
to
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alu
ate
t
h
e
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er
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r
m
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ce
o
f
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er
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i
u
s
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g
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n
d
o
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te
m
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m
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e
cla
s
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ica
l
Viter
b
i.
T
h
e
s
i
m
u
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n
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er
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ch
a
n
n
e
l
w
i
th
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ate
s
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d
2
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,
h
av
e
s
h
o
w
n
t
h
at
at
a
B
E
R
o
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0
-
6
,
th
e
Vite
r
b
i
d
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r
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it
h
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n
d
o
w
s
y
s
t
e
m
o
u
tp
er
f
o
r
m
s
t
h
e
class
ical
Viter
b
i
b
y
1
d
B
.
Mo
r
eo
v
er
,
w
e
p
r
o
p
o
s
e
th
e
u
s
e
o
f
th
e
Un
g
er
b
eo
ck
g
r
a
y
m
ap
p
in
g
to
ac
h
iev
e
m
o
r
e
p
er
f
o
r
m
a
n
ce
w
it
h
T
C
M
en
co
d
er
w
h
er
e
t
h
e
g
ai
n
o
f
2
.
7
d
B
w
as
ac
h
ie
v
ed
co
m
p
ar
ed
to
th
e
T
C
M
w
ith
th
e
Viter
b
i
d
ec
o
d
er
b
y
w
i
n
d
o
w
s
y
s
te
m
an
d
t
h
e
g
ai
n
o
f
3
.
8
d
B
is
o
b
s
er
v
ed
co
m
p
ar
ed
to
th
e
o
r
ig
in
al
T
C
M
w
i
th
th
e
class
ical
Vi
ter
b
i d
ec
o
d
er
.
Fro
m
th
e
ab
o
v
e
r
e
s
u
l
ts
,
it
ca
n
also
b
e
s
ee
n
th
a
t
w
it
h
r
ate
2
/3
th
e
T
C
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w
it
h
r
ec
u
r
s
iv
e
s
y
s
te
m
a
tic
co
n
v
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lu
tio
n
al
(
R
SC
)
en
co
d
er
w
it
h
lo
g
-
m
ap
o
r
m
ax
-
lo
g
-
m
ap
d
ec
o
d
er
s
g
iv
es
b
etter
r
esu
lts
th
a
n
Viter
b
i
s
o
f
t
w
it
h
a
g
a
in
o
f
2
d
B
at
B
E
R
=
1
0
-
4
.
I
t
is
al
s
o
clea
r
l
y
s
h
o
w
n
th
at
Viter
b
i
s
o
f
t
o
u
tp
er
f
o
r
m
s
t
h
e
MA
P
al
g
o
r
ith
m
w
h
ic
h
i
s
k
n
o
w
n
a
s
b
ein
g
g
r
ee
d
y
i
n
m
e
m
o
r
y
s
p
ac
e
a
n
d
in
t
h
e
co
m
p
u
ti
n
g
ti
m
e
w
h
ic
h
i
n
cr
ea
s
e
s
m
o
r
e
i
f
w
e
in
cr
e
ase
t
h
e
r
ate
a
n
d
t
h
e
n
u
m
b
er
o
f
m
e
m
o
r
y
.
C
o
n
s
eq
u
en
t
l
y
,
th
e
d
ec
o
d
in
g
o
p
er
ati
o
n
b
ec
o
m
es
lo
n
g
.
Fo
r
t
h
is
r
ea
s
o
n
,
th
e
y
h
a
v
e
s
i
m
p
li
f
ied
M
A
P
w
it
h
o
th
er
s
v
ar
y
i
n
g
as
lo
g
-
M
A
P
an
d
m
a
x
-
lo
g
-
M
A
P
th
at
ar
e
u
s
ed
o
n
th
e
n
e
w
tr
en
d
o
f
en
co
d
er
s
lik
e
tu
r
b
o
-
co
d
e
w
h
e
r
e
th
e
r
esear
c
h
er
s
ar
e
p
lace
d
a
lo
t
o
f
h
o
p
es
in
t
h
is
la
s
t
tec
h
n
iq
u
e
(
t
u
r
b
o
co
d
es)
b
ec
au
s
e
w
e
ap
p
r
o
ac
h
th
e
li
m
it
g
iv
e
n
b
y
t
h
e
s
ec
o
n
d
t
h
eo
r
e
m
o
f
Sh
a
n
n
o
n
.
RE
F
E
R
E
NC
E
S
[1
]
L
.
Co
n
d
e
C
a
n
a
n
c
ia,
“
T
u
rb
o
-
c
o
d
e
s
e
t
mo
d
u
l
a
ti
o
n
à
g
ra
n
d
e
e
ff
ica
c
it
é
sp
e
c
tra
le,”
th
e
se
d
e
d
o
c
to
ra
t
d
e
l‟u
n
iv
e
rsité
d
e
Bre
tag
n
e
Oc
c
id
e
n
tale
,
F
ra
n
c
e
,
Ju
i
n
2
0
0
4
.
[2
]
Un
g
e
rb
o
e
c
k
,
“
Ch
a
n
n
e
l
c
o
d
i
n
g
w
i
th
m
u
lt
il
e
v
e
l/
p
h
a
se
sig
n
a
ls,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Iin
f
o
rm
a
ti
o
n
T
h
e
o
ry
,
v
o
l.
IT
-
2
8
,
N
1
,
Ja
n
.
1
9
8
2
,
p
p
.
5
5
-
67.
[3
]
M
a
n
ish
K
u
m
a
r,
J
y
o
ti
S
a
x
e
n
a
,
P
e
rf
o
r
m
a
n
c
e
Co
m
p
a
riso
n
o
f
L
a
ten
c
y
f
o
r
RS
C
-
RS
C
a
n
d
R
S
-
RS
C
Co
n
c
a
ten
a
ted
Co
d
e
s
,
I
n
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
E
l
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s
(
IJ
EE
I),
V
o
l
.
1
,
No
.
3
,
S
e
p
te
m
b
e
r
2
0
1
3
,
p
p
.
7
8
~
8
3
,
IS
S
N:
2
0
8
9
-
3
2
7
2
,
DO
I:
1
0
.
1
1
5
9
1
/
ij
e
e
i.
v
1
i3
.
7
7
.
[4
]
Iles
a
n
m
i
Ba
n
jo
Olu
w
a
f
e
m
i,
H
y
b
rid
C
o
n
c
a
ten
a
ted
C
o
d
i
n
g
S
c
h
e
m
e
f
o
r
M
IM
O
S
y
ste
m
s,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
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
.
5
,
No
.
3
,
Ju
n
e
2
0
1
5
,
p
p
.
4
6
4
~
4
7
6
,
IS
S
N:
2
0
8
8
-
8
7
0
8
.
[5
]
S
a
m
e
e
r
A
Da
w
o
o
d
,
F
.
M
a
lek
,
M
S
A
n
u
a
r,
HA
Ra
h
im
,
En
h
a
n
c
e
m
e
n
t
th
e
P
e
rf
o
rm
a
n
c
e
o
f
O
F
DM
b
a
se
d
o
n
M
u
lt
iw
a
v
e
lets
Us
in
g
T
u
rb
o
C
o
d
e
s
,
T
EL
KOM
NIKA
(
T
e
lec
o
mm
u
n
ica
ti
o
n
C
o
mp
u
ti
n
g
El
e
c
tro
n
ics
a
n
d
Co
n
tr
o
l
)
,
Vo
l
.
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