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1
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2
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3
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d
s
o
f
ten
o
v
e
r
lo
o
k
th
e
o
p
tim
izatio
n
o
f
er
r
o
r
p
r
o
p
ag
atio
n
in
f
u
ll
ad
d
er
s
f
o
r
lar
g
e
-
s
ca
le
ap
p
licatio
n
s
.
T
h
e
r
e
is
a
n
ee
d
f
o
r
f
u
r
th
er
in
v
esti
g
atio
n
in
to
o
p
tim
izin
g
er
r
o
r
p
r
o
p
ag
atio
n
in
a
p
p
r
o
x
im
ate
f
u
ll
ad
d
er
s
,
p
a
r
ticu
la
r
ly
in
lar
g
e
-
s
ca
le
ap
p
licatio
n
s
.
I
n
th
is
p
ap
er
,
a
n
ew
ty
p
e
o
f
ap
p
r
o
x
im
ate
a
d
d
er
is
p
r
o
p
o
s
ed
an
d
an
aly
s
ed
f
o
r
d
if
f
er
e
n
t
b
it
s
izes.
Fo
r
f
air
a
n
aly
s
is
,
th
e
p
r
o
p
o
s
ed
ad
d
er
is
ap
p
lied
i
n
im
ag
e
p
r
o
ce
s
s
in
g
ap
p
licatio
n
s
o
f
d
is
cr
ete
co
s
in
e
tr
an
s
f
o
r
m
(
DC
T
)
.
T
h
is
wo
r
k
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws.
I
n
s
ec
tio
n
2
ex
p
lain
s
th
e
ex
is
tin
g
wo
r
k
s
.
T
h
e
d
esig
n
o
f
th
e
p
r
o
p
o
s
ed
ad
d
er
an
d
its
tr
an
s
f
o
r
m
im
p
lem
e
n
tatio
n
s
ar
e
g
iv
en
in
s
ect
io
n
3
.
I
n
s
ec
tio
n
4
illu
s
tr
ates
th
e
ex
p
er
im
en
tal
r
esu
lts
.
Fin
ally
,
t
h
e
co
n
clu
s
io
n
is
d
escr
ib
ed
in
s
ect
io
n
5.
2.
RE
L
AT
E
D
WO
RK
Am
ir
af
s
h
ar
et
a
l
.
[
7
]
co
n
s
tr
u
c
ted
a
n
ew
r
ip
p
le
ca
r
r
y
ad
d
er
with
th
e
lo
g
ic
o
f
ca
r
r
y
d
is
r
eg
ar
d
in
g
.
T
h
e
n
ew
lo
g
ic
lev
el
m
o
d
if
icatio
n
i
s
p
r
o
p
o
s
ed
to
r
ed
u
ce
a
n
o
v
er
a
ll
p
r
o
p
a
g
atio
n
d
elay
.
T
h
e
p
r
o
p
o
s
ed
ad
d
e
r
r
ed
u
ce
s
ar
ea
p
o
wer
a
n
d
d
elay
b
y
ab
o
u
t
8
.
5
6
%,
1
9
.
5
%,
a
n
d
1
2
.
4
% wh
en
co
m
p
a
r
ed
to
o
th
er
a
d
d
er
s
.
I
n
th
eir
s
tu
d
y
,
Fan
et
a
l
.
[
8
]
p
r
esen
t
an
ap
p
r
o
x
i
m
ate
ad
d
er
b
ased
o
n
tr
an
s
is
to
r
-
lev
el
m
o
d
if
icatio
n
s
.
T
h
e
tr
an
s
is
to
r
ac
t
s
as
a
s
witch
to
c
o
n
tr
o
l
th
e
ca
r
r
y
p
r
o
p
ag
atio
n
.
E
x
p
er
im
e
n
tal
r
esu
lts
o
n
s
y
n
o
p
s
is
co
m
p
iler
r
esu
lts
s
h
o
w
th
at
th
e
p
r
o
p
o
s
e
d
ad
d
er
ac
h
iev
es 6
.
3
% a
r
ea
r
ed
u
ctio
n
as a
n
av
e
r
ag
e
o
f
v
a
r
y
in
g
b
it si
ze
s
.
T
h
e
m
u
lti
-
b
it
a
d
d
er
u
s
in
g
a
p
a
r
allel
p
r
ef
ix
a
d
d
er
is
p
r
o
p
o
s
ed
b
y
Stef
an
id
is
et
a
l
.
[
9
]
.
T
h
e
c
o
n
ce
p
t
o
f
ca
r
r
y
k
illi
n
g
is
ap
p
lied
to
m
itig
ate
a
cr
itical
p
ath
d
elay
.
T
h
e
p
r
o
p
o
s
ed
ad
d
er
i
s
im
p
le
m
en
ted
in
a
f
in
ite
im
p
u
ls
e
r
esp
o
n
s
e
f
ilter
an
d
v
er
if
ied
f
o
r
s
ig
n
al
p
r
o
ce
s
s
in
g
ap
p
licatio
n
s
.
R
esu
lts
s
h
o
w
t
h
e
p
r
o
p
o
s
ed
ad
d
e
r
s
h
o
ws h
ig
h
er
ef
f
icien
cy
with
a
cc
ep
tab
le
n
o
is
e
lim
its
in
f
ilter
ap
p
licatio
n
.
Kav
an
d
et
a
l.
[
10
]
,
a
n
ew
c
o
m
p
r
ess
o
r
s
tr
u
ctu
r
e
is
p
r
o
p
o
s
ed
b
y
th
e
a
u
th
o
r
f
o
r
im
p
le
m
en
tin
g
a
n
ap
p
r
o
x
im
ate
m
u
ltip
lier
.
T
h
e
p
r
o
p
o
s
ed
co
m
p
r
ess
o
r
is
a
p
p
lied
in
v
ec
to
r
m
er
g
in
g
ad
d
er
s
tag
es
in
th
e
m
u
ltip
lier
f
o
r
f
in
al
ad
d
itio
n
ca
lcu
latio
n
.
T
h
e
n
u
m
b
er
o
f
s
lice
an
d
lo
g
ic
co
u
n
t
s
is
v
er
y
l
ow
in
co
m
p
ar
is
o
n
with
o
t
h
er
co
m
p
r
ess
o
r
s
tr
u
ctu
r
es.
T
h
e
h
y
b
r
id
ad
d
e
r
f
o
r
lo
w
p
o
wer
ap
p
licatio
n
is
in
tr
o
d
u
ce
d
b
y
Seo
an
d
Kim
[1
1
]
.
T
h
e
h
y
b
r
id
ad
d
e
r
in
clu
d
es
b
o
th
ac
c
u
r
ate
a
n
d
in
ac
cu
r
ate
ad
d
er
s
to
co
m
p
u
te
f
i
n
al
ad
d
itio
n
r
esu
lts
.
T
h
e
ac
cu
r
ate
ad
d
e
r
p
r
o
d
u
ce
s
ex
ac
t
r
esu
lt
s
with
o
u
t
an
y
tr
u
n
ca
tio
n
s
.
I
n
th
e
in
ac
cu
r
ate
ad
d
er
p
ar
t,
th
e
ad
d
er
s
with
a
m
in
im
u
m
n
u
m
b
er
o
f
g
ates
ar
e
u
s
ed
f
o
r
s
u
m
ca
lcu
la
tio
n
.
J
h
a
et
a
l
.
[1
2
]
p
r
o
p
o
s
ed
a
n
ac
cu
r
ac
y
co
n
f
ig
u
r
ab
le
ap
p
r
o
x
im
ate
ad
d
er
f
o
r
er
r
o
r
-
t
o
ler
an
t
ap
p
licatio
n
s
.
T
h
e
ac
cu
r
a
cy
le
v
el
o
f
th
e
a
d
d
er
cir
cu
it
ca
n
b
e
co
n
f
ig
u
r
ed
b
ased
o
n
th
e
ter
m
s
th
at
ar
e
u
s
ed
f
o
r
s
u
m
ca
lcu
latio
n
.
I
n
a
d
d
itio
n
,
th
e
co
r
r
ec
tio
n
lo
g
ic
is
in
tr
o
d
u
ce
d
to
r
ed
u
ce
an
ap
p
r
o
x
im
atio
n
er
r
o
r
.
Z
h
an
g
et
a
l
.
[1
3
]
p
r
o
p
o
s
ed
a
th
r
ee
f
o
ld
a
p
p
r
o
x
im
ate
m
u
lti
p
lier
f
o
r
lo
s
s
y
ap
p
licatio
n
s
.
I
t
in
v
o
lv
es
co
m
p
r
ess
o
r
s
,
co
r
r
ec
tio
n
u
n
its
an
d
f
ix
e
d
ap
p
r
o
x
im
atio
n
s
.
T
h
e
co
r
r
ec
tio
n
u
n
it
v
ar
ies
th
e
co
r
r
ec
tio
n
b
its
b
ase
d
o
n
th
e
co
m
p
r
ess
o
r
er
r
o
r
lev
e
ls
.
R
e
s
u
lts
o
n
im
ag
e
p
r
o
ce
s
s
i
n
g
p
u
r
p
o
s
e
s
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
m
u
ltip
lier
ac
h
iev
es m
in
im
u
m
a
r
ea
d
elay
p
r
o
d
u
ct
with
h
ig
h
e
r
s
ig
n
al
-
to
-
n
o
is
e
r
atio
(
SNR
)
v
alu
es.
C
h
en
et
a
l
.
[1
4
]
p
r
o
p
o
s
ed
a
m
o
d
if
ied
b
o
o
t
h
en
c
o
d
er
f
o
r
ap
p
r
o
x
im
ate
c
o
m
p
u
tin
g
.
T
h
e
e
n
c
o
d
in
g
b
its
in
th
e
b
o
o
th
ta
b
le
ar
e
ap
p
r
o
x
i
m
ated
to
p
er
f
o
r
m
s
elec
tiv
e
tr
u
n
ca
tio
n
.
T
h
e
p
r
o
p
o
s
ed
m
u
ltip
l
ier
is
ap
p
lied
in
th
e
m
ac
h
in
e
lear
n
in
g
alg
o
r
ith
m
f
o
r
ef
f
icien
cy
e
v
alu
atio
n
.
Da
R
o
s
a
e
t
a
l
.
[1
5
]
p
r
o
p
o
s
ed
a
p
ar
allel
ad
d
er
u
s
in
g
th
e
co
n
ce
p
t
o
f
ca
r
r
y
p
r
o
p
ag
atio
n
an
d
ca
r
r
y
g
en
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
ad
d
er
is
u
s
ed
to
d
esig
n
ap
p
r
o
x
im
ate
co
n
v
o
lu
tio
n
al
n
eu
r
al
n
etw
o
r
k
a
r
ch
itectu
r
e
f
o
r
p
atter
n
r
ec
o
g
n
itio
n
.
B
y
u
s
in
g
th
e
p
r
o
p
o
s
ed
ad
d
er
,
t
h
e
n
u
m
b
er
o
f
ad
d
e
r
co
s
t
r
e
q
u
i
r
em
en
t
s
is
r
ed
u
ce
d
co
n
s
id
er
ab
ly
.
I
n
th
eir
s
tu
d
y
,
C
h
u
et
a
l
.
[1
6
]
p
r
esen
ted
a
n
ap
p
r
o
x
im
ate
a
d
d
er
u
s
in
g
q
u
an
tu
m
-
d
o
t
ce
llu
lar
au
to
m
ata
tech
n
o
lo
g
y
.
T
h
e
m
a
jo
r
ity
o
f
lo
g
ic
m
in
im
izatio
n
i
s
u
tili
ze
d
to
d
esig
n
a
n
a
p
p
r
o
x
im
ate
cir
cu
it.
T
h
e
p
r
o
p
o
s
ed
ad
d
e
r
was
an
aly
s
ed
i
n
ter
m
s
o
f
th
e
n
u
m
b
er
o
f
d
o
ts
,
p
o
wer
an
d
d
elay
r
eq
u
ir
em
en
t
s
.
San
tiag
o
et
a
l
.
[1
7
]
p
r
o
p
o
s
ed
a
ca
r
r
y
-
awa
r
e
ap
p
r
o
x
im
ate
ad
d
er
f
o
r
m
u
lti
-
b
it
ad
d
itio
n
.
T
h
e
elim
in
atio
n
o
f
th
e
least
s
ig
n
i
f
ican
t
b
it
is
ca
r
r
ie
d
o
u
t
b
ase
d
o
n
th
e
n
u
m
b
er
o
f
o
n
e
s
p
r
esen
t
in
th
e
in
p
u
t
o
p
er
an
d
s
.
I
n
im
ag
e
co
m
p
r
ess
io
n
ap
p
licatio
n
s
,
th
e
p
r
o
p
o
s
ed
ad
d
er
s
h
o
ws
a
h
ig
h
e
r
ac
c
u
r
a
cy
lev
el
t
h
an
o
th
er
ad
d
er
s
.
Z
h
an
g
et
a
l.
[1
8
]
,
th
e
au
th
o
r
p
r
o
p
o
s
ed
a
n
ew
ap
p
r
o
ac
h
f
o
r
p
a
r
tial
p
r
o
d
u
ct
g
en
er
atio
n
i
n
b
o
o
th
m
u
ltip
lier
.
I
t
ap
p
lies
m
ac
h
in
e
lear
n
in
g
alg
o
r
ith
m
s
to
p
r
o
d
u
ce
a
p
ar
tial
p
r
o
d
u
ct.
T
h
e
p
r
o
p
o
s
ed
m
u
ltip
lier
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
E
fficien
t d
esig
n
o
f a
p
p
r
o
xima
te
ca
r
r
y
-
b
a
s
ed
s
u
m
ca
lcu
la
tin
g
fu
ll a
d
d
ers
…
(
B
a
d
ig
a
n
c
h
ela
S
h
iva
K
u
ma
r
)
1191
test
ed
in
f
ee
d
-
f
o
r
war
d
n
eu
r
al
n
etwo
r
k
im
p
lem
e
n
tatio
n
s
.
T
h
e
d
u
al
er
r
o
r
c
o
r
r
ec
tio
n
m
ec
h
a
n
is
m
is
p
r
o
p
o
s
ed
b
y
Aiza
z
an
d
Kh
ar
e
[1
9
]
f
o
r
-
b
o
o
t
h
m
u
ltip
lier
d
esig
n
.
T
h
e
er
r
o
r
co
r
r
ec
tio
n
m
ec
h
an
is
m
u
s
es
k
-
m
ap
s
im
p
lific
atio
n
to
r
ed
u
ce
th
e
n
u
m
b
e
r
o
f
g
ate
r
eq
u
ir
em
en
ts
.
I
m
p
lem
en
tatio
n
r
esu
lts
o
n
im
ag
e
p
r
o
ce
s
s
in
g
a
p
p
licatio
n
s
h
o
w
t
h
e
p
r
o
p
o
s
ed
m
u
ltip
lier
ac
h
ie
v
e
s
9
4
.
3
6
% a
cc
u
r
ac
y
with
an
er
r
o
r
r
ate
o
f
0
.
0
2
%.
T
h
e
co
n
ce
p
t
o
f
m
ac
h
in
e
lear
n
in
g
is
ap
p
lied
in
ap
p
r
o
x
im
ate
co
m
p
u
tin
g
b
y
L
iu
et
a
l
.
[
20
]
.
T
h
e
ap
p
r
o
x
im
atin
g
g
ate
s
o
r
b
lo
ck
s
in
a
cir
cu
it
ar
e
i
d
en
tif
ied
with
lear
n
in
g
m
o
d
els
t
o
g
et
a
m
in
im
u
m
ap
p
r
o
x
im
atio
n
er
r
o
r
w
h
en
r
e
m
o
v
ed
.
T
h
e
ad
d
itio
n
al
e
f
f
o
r
t
o
r
c
o
m
p
u
tatio
n
al
r
eso
u
r
ce
s
ar
e
u
tili
ze
d
f
o
r
lear
n
i
n
g
m
o
d
els.
I
n
th
eir
s
tu
d
y
,
R
o
y
et
a
l
.
[2
1
]
p
r
o
p
o
s
ed
a
h
y
b
r
id
ad
d
er
w
h
ich
in
clu
d
es
th
e
ap
p
r
o
x
im
ate
le
ast
s
ig
n
if
ican
t
b
it
p
ar
t
an
d
th
e
ac
cu
r
ate
m
o
s
t
s
ig
n
if
ican
t
b
it
p
a
r
t.
I
n
th
e
ap
p
r
o
x
im
ate
p
a
r
t,
th
e
tr
u
n
ca
tio
n
with
a
co
r
r
ec
tio
n
m
ec
h
an
is
m
is
in
t
r
o
d
u
ce
d
to
r
ed
u
ce
th
e
o
v
er
all
ar
ea
d
ela
y
p
r
o
d
u
ct.
T
h
e
ca
r
r
y
c
h
ain
d
iv
is
io
n
m
ec
h
an
is
m
is
u
s
ed
b
y
E
b
r
ah
i
m
i
-
Aza
n
d
ar
y
a
n
i
et
a
l
.
[2
2
]
f
o
r
lo
w
-
p
o
wer
ad
d
er
d
esig
n
.
B
as
ed
o
n
o
p
er
a
n
d
b
its
,
th
e
ca
r
r
y
ch
ai
n
is
d
iv
id
ed
in
to
d
if
f
er
en
t
len
g
th
s
to
r
ed
u
ce
o
v
er
all
cr
itical
d
elay
.
L
ik
ewise,
th
e
n
ew
s
tr
ateg
y
is
p
r
o
p
o
s
ed
b
y
Fru
s
taci
et
a
l
.
[2
3
]
f
o
r
ap
p
r
o
x
im
ate
ad
d
er
an
d
m
u
ltip
lier
d
esig
n
.
Similar
way
,
th
e
W
u
et
a
l
.
[2
4
]
d
er
iv
ed
n
ew
m
etr
ics f
o
r
ass
ess
in
g
th
e
p
e
r
f
o
r
m
an
ce
o
f
ap
p
r
o
x
im
ate
cir
cu
its
.
W
u
et
a
l.
[
2
4
]
,
th
e
a
u
th
o
r
s
in
t
r
o
d
u
ce
a
r
ev
er
s
e
ca
r
r
y
co
n
ce
p
t
f
o
r
m
u
lti
-
b
it
ad
d
e
r
d
esig
n
.
T
h
e
ca
r
r
y
is
g
en
er
ated
f
r
o
m
t
h
e
m
o
s
t
s
ig
n
if
ican
t
b
it
to
th
e
least
s
ig
n
if
ican
t
b
it
to
r
ed
u
ce
a
n
ap
p
r
o
x
im
atio
n
er
r
o
r
.
T
h
e
p
r
o
p
o
s
ed
ad
d
e
r
is
im
p
lem
en
te
d
in
DC
T
ar
ch
itectu
r
e
f
o
r
d
o
m
ain
co
n
v
e
r
s
io
n
ap
p
licatio
n
s
.
Alan
an
d
Hen
k
el
[2
5
]
p
r
o
p
o
s
ed
an
ap
p
r
o
x
im
ate
ca
r
r
y
lo
o
k
ad
d
er
b
y
m
o
d
if
y
i
n
g
th
e
ca
r
r
y
p
r
ed
ictio
n
ter
m
.
B
y
in
teg
r
atin
g
a
m
u
ltip
lex
er
,
th
e
ad
d
er
ca
n
b
e
c
o
n
f
i
g
u
r
ed
to
eith
er
ap
p
r
o
x
im
ate
o
r
ac
cu
r
ate
m
o
d
es.
Sch
lach
ter
et
a
l
.
[2
6
]
in
tr
o
d
u
ce
a
p
r
u
n
in
g
tech
n
i
q
u
e
f
o
r
a
p
p
r
o
x
im
ate
cir
cu
it
d
esig
n
.
I
n
th
e
p
r
u
n
in
g
p
r
o
ce
s
s
,
th
e
lo
g
ical
g
ates
ar
e
s
elec
t
iv
ely
r
em
o
v
ed
b
ased
o
n
th
e
er
r
o
r
lev
el.
T
h
e
f
in
al
g
ate
-
lev
el
n
etlis
t
i
s
cr
ea
ted
af
ter
th
e
p
r
u
n
in
g
p
r
o
ce
s
s
.
T
s
ai
et
a
l
.
[2
7
]
p
r
o
p
o
s
ed
a
m
e
m
o
r
y
-
b
ased
ap
p
r
o
x
im
atio
n
te
ch
n
iq
u
e
f
o
r
ad
d
er
an
d
m
u
ltip
lier
d
esig
n
.
Th
e
ad
d
itio
n
an
d
m
u
ltip
licatio
n
ter
m
s
ar
e
s
to
r
e
d
in
th
e
lo
o
k
-
u
p
tab
le
t
o
r
e
d
u
ce
c
o
m
p
u
tatio
n
co
s
t
s
.
C
o
m
p
ar
ed
to
tr
u
n
ca
tio
n
s
ch
em
es,
th
e
m
em
o
r
y
-
b
ased
a
p
p
r
o
ac
h
s
h
o
ws
m
in
im
u
m
ap
p
r
o
x
im
atio
n
er
r
o
r
s
.
L
ik
ewise,
d
if
f
er
en
t a
d
d
er
s
ar
e
p
r
o
p
o
s
ed
f
o
r
d
if
f
e
r
en
t im
ag
e
-
p
r
o
ce
s
s
in
g
ap
p
licatio
n
s
[
2
8
].
3.
P
RO
P
O
SE
D
SYS
T
E
M
I
n
th
is
wo
r
k
,
a
n
ew
ap
p
r
o
x
i
m
ate
ad
d
er
is
p
r
o
p
o
s
ed
b
ased
o
n
g
ate
-
lev
el
m
o
d
if
icatio
n
s
.
T
h
e
m
ajo
r
p
o
wer
-
h
u
n
g
r
y
s
o
u
r
ce
o
f
ad
d
e
r
elem
en
t
s
is
XOR
g
ate
o
p
er
atio
n
s
.
T
h
is
wo
r
k
m
o
d
if
ies
s
u
m
ter
m
ca
lcu
latio
n
b
ased
o
n
ca
r
r
y
ter
m
b
y
elim
in
atin
g
th
e
XOR
o
p
er
ati
o
n
.
T
h
e
B
o
o
lean
f
u
n
ctio
n
f
o
r
th
e
co
n
v
en
tio
n
al
f
u
ll
a
d
d
er
is
s
tated
as f
o
llo
ws:
Su
m
=
a
XOR b
XOR c;
(
1
)
C
ar
r
y
=
(
a
AND
b
)
OR
(
b
AN
D
c)
OR
(
c
AND
a)
;
(
2
)
T
h
e
ex
p
r
ess
io
n
f
o
r
th
e
p
r
o
p
o
s
ed
ad
d
er
is
as f
o
llo
ws:
C
ar
r
y
=
(
a
AND
b
)
OR
(
b
AN
D
c)
OR
(
c
AND
a)
;
(
3
)
Su
m
=
NOT
(
C
ar
r
y
AND
b
)
;
(
4
)
T
h
e
s
u
m
ter
m
is
d
er
iv
e
d
f
r
o
m
th
e
ca
r
r
y
.
B
y
n
eg
atin
g
th
e
lo
g
ical
AND
o
f
th
e
ca
r
r
y
-
o
u
t
a
n
d
in
p
u
t
b
it
A,
th
e
s
u
m
is
ca
lcu
lated
in
a
s
t
r
aig
h
tf
o
r
wa
r
d
m
an
n
er
with
o
u
t
th
e
n
ee
d
f
o
r
XOR g
ates.
T
h
is
m
eth
o
d
in
tr
o
d
u
ce
s
a
co
n
tr
o
lled
ap
p
r
o
x
im
atio
n
in
t
o
th
e
s
u
m
ca
lc
u
latio
n
.
T
h
e
s
tr
u
ctu
r
e
o
f
co
n
v
en
tio
n
al
an
d
p
r
o
p
o
s
ed
f
u
ll
ad
d
e
r
is
s
h
o
wn
in
Fig
u
r
e
1
,
Fig
u
r
es
1
(
a
)
an
d
1
(
b
)
.
T
h
e
f
u
n
ctio
n
ality
o
f
th
e
o
r
i
g
in
al
an
d
p
r
o
p
o
s
ed
f
u
ll
ad
d
er
is
g
iv
en
i
n
T
ab
le
1
.
T
ab
le
1
.
T
r
u
th
tab
le
o
f
p
r
o
p
o
s
ed
ad
d
er
A
B
C
in
S
u
m
C
a
r
r
y
C
a
r
r
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a
p
p
0
0
0
0
0
1
0
0
1
1
0
1
0
1
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1
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1
1
0
1
1
1
0
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1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
Evaluation Warning : The document was created with Spire.PDF for Python.
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c
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co
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tr
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o
r
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ate
is
ac
ce
p
tab
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in
m
an
y
a
p
p
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p
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licatio
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s
wh
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r
e
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ac
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a
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(
a)
(
b
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Fig
u
r
e
1
.
S
tr
u
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f
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v
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a
d
d
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d
(
b
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p
r
o
p
o
s
ed
ad
d
er
Ap
p
r
o
x
im
ate
ad
d
er
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b
ased
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is
cr
ete
co
s
in
e
tr
an
s
f
o
r
m
s
,
i
n
im
ag
e
p
r
o
ce
s
s
in
g
,
th
e
DC
T
is
w
id
ely
u
s
ed
f
o
r
im
ag
e
co
m
p
r
ess
io
n
ap
p
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s
s
u
ch
as
J
PEG.
T
h
e
D
C
T
tr
an
s
f
o
r
m
s
s
p
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d
o
m
ain
d
ata
in
to
f
r
eq
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en
c
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d
o
m
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ata
to
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t
a
s
ig
n
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t
co
e
f
f
icien
t
th
at
ca
n
b
e
co
m
p
r
ess
ed
ef
f
ec
tiv
ely
.
T
h
e
ap
p
r
o
x
im
ate
ad
d
er
s
ar
e
u
s
ed
in
DC
T
to
r
e
d
u
ce
p
o
wer
co
n
s
u
m
p
tio
n
,
ar
ea
,
an
d
d
e
lay
.
T
h
e
DC
T
f
o
r
m
u
la
f
o
r
an
8
×
8
b
lo
c
k
is
:
(
,
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=
1
4
(
)
(
)
∑
∑
(
,
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c
os
[
(
2
+
1
)
16
7
=
0
]
c
os
[
(
2
+
1
)
16
7
=
0
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(
5
)
W
h
er
e
c(
u
)
an
d
c(
v
)
ar
e
th
e
n
o
r
m
aliza
tio
n
f
ac
to
r
s
.
I
n
itially
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th
e
im
ag
es
ar
e
co
n
v
er
ted
in
to
g
r
ay
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s
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le
im
ag
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s
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T
h
en
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th
e
e
n
tire
im
a
g
e
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d
iv
id
ed
in
to
8
×8
b
lo
c
k
s
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h
e
p
r
o
p
o
s
ed
a
p
p
r
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x
im
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d
er
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lied
in
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itio
n
al
s
tag
es o
f
DC
T
co
m
p
u
tatio
n
.
T
h
e
r
esu
lts
wer
e
v
er
i
f
ied
in
ter
m
s
o
f
SNR
r
ates.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
T
h
e
p
r
o
p
o
s
ed
ad
d
e
r
is
co
d
ed
in
v
er
ilo
g
HDL
an
d
e
x
ec
u
ted
u
s
in
g
th
e
Xilin
x
s
o
f
twar
e
en
v
ir
o
n
m
e
n
t.
T
h
e
p
r
o
p
o
s
ed
ad
d
er
with
v
a
r
y
in
g
b
it
s
izes
is
im
p
lem
en
te
d
in
t
h
e
Sp
ar
ta
n
3
E
FP
GA
f
am
ily
with
th
e
d
ev
ice
XC
3
S1
0
0
E
.
T
h
e
co
r
r
esp
o
n
d
in
g
R
T
L
s
ch
em
atic
an
d
g
ate
-
le
v
el
n
etlis
t a
r
e
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
v
is
u
aliza
tio
n
o
f
f
u
n
ctio
n
al
v
e
r
if
icatio
n
is
g
iv
en
in
Fig
u
r
e
3
.
Fo
r
a
f
air
c
o
m
p
ar
is
o
n
,
th
e
p
r
o
p
o
s
ed
ad
d
e
r
is
co
m
p
ar
ed
with
p
r
ev
io
u
s
ly
p
r
o
p
o
s
ed
ad
d
er
s
.
Fig
u
r
e
2
.
R
T
L
an
d
g
ate
lev
el
n
etlis
t o
f
ad
d
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
E
fficien
t d
esig
n
o
f a
p
p
r
o
xima
te
ca
r
r
y
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ed
s
u
m
ca
lcu
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tin
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ll a
d
d
ers
…
(
B
a
d
ig
a
n
c
h
ela
S
h
iva
K
u
ma
r
)
1193
Fig
u
r
e
3
.
Simu
lated
wa
v
ef
o
r
m
T
h
e
o
b
tain
ed
s
lice
an
d
L
UT
v
alu
es
f
o
r
v
ar
y
in
g
b
it
s
ize
s
a
r
e
g
iv
en
in
T
ab
le
2
.
T
h
e
s
lice
an
d
L
UT
v
alu
es
in
cr
ea
s
e
lin
ea
r
ly
with
in
cr
ea
s
in
g
b
it
s
izes.
T
h
e
p
r
o
p
o
s
ed
ad
d
er
s
h
o
ws
a
b
alan
ce
d
an
d
o
p
tim
ized
p
er
f
o
r
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an
ce
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ter
m
s
o
f
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ar
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eter
s
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en
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m
p
ar
e
d
to
o
th
er
a
d
d
er
s
.
T
h
e
m
ir
r
o
r
ap
p
r
o
x
im
ate
ad
d
er
p
r
o
p
o
s
ed
b
y
G
u
p
ta
et
a
l
.
[
2
9
]
s
h
o
ws
th
e
h
ig
h
est
d
elay
an
d
ar
ea
co
n
s
u
m
p
tio
n
.
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h
e
a
p
p
r
o
x
im
ate
ad
d
er
b
ased
o
n
th
e
m
aj
o
r
ity
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g
ic
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s
ed
b
y
W
.
L
iu
s
h
o
ws m
o
d
er
ate
p
e
r
f
o
r
m
a
n
ce
in
ter
m
s
o
f
ar
ea
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n
d
d
elay
.
T
h
e
R
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L
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iew
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t
o
f
th
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s
ed
DC
T
im
p
lem
en
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is
s
h
o
wn
i
n
Fig
u
r
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4
.
T
h
e
v
is
u
aliza
tio
n
o
f
f
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ctio
n
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l
v
er
if
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n
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iv
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Fig
u
r
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5
.
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h
e
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o
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tain
ed
f
o
r
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m
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e
g
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in
T
a
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le
3
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2
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Per
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8
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ab
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3
.
FIR im
p
lem
en
tatio
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r
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lts
P
a
r
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me
t
e
r
D
C
T
w
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t
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ma
j
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r
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se
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a
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t
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6
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e
l
a
y
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5
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4
2
.
8
9
T
h
e
DC
T
with
th
e
m
ajo
r
ity
ad
d
er
u
s
es
6
8
7
s
lices.
I
n
co
n
tr
ast,
th
e
DC
T
with
th
e
p
r
o
p
o
s
ed
ad
d
er
s
h
o
ws
im
p
r
o
v
ed
ef
f
icien
cy
b
y
u
s
in
g
o
n
ly
4
5
3
s
lices.
T
h
e
p
r
o
p
o
s
ed
ad
d
e
r
ac
h
iev
es
a
1
2
%
r
ed
u
ctio
n
in
s
lice
u
s
ag
e.
T
h
e
DC
T
f
ilter
with
t
h
e
m
ajo
r
ity
ad
d
er
r
eq
u
ir
es
1
0
1
2
L
UT
s
.
O
n
th
e
o
th
er
h
a
n
d
,
th
e
DC
T
with
th
e
p
r
o
p
o
s
ed
ad
d
e
r
co
n
s
u
m
es
8
5
6
L
UT
s
.
T
h
e
p
r
o
p
o
s
ed
ad
d
er
ac
h
iev
es
a
1
5
%
r
ed
u
cti
o
n
in
L
UT
u
s
ag
e.
T
h
e
m
ajo
r
ity
o
f
ad
d
e
r
-
b
ased
DC
T
s
h
o
ws
a
d
elay
o
f
5
5
.
6
u
n
its
.
Ho
wev
er
,
th
e
p
r
o
p
o
s
ed
ad
d
er
-
b
ased
DC
T
n
o
tab
ly
o
u
tp
er
f
o
r
m
s
th
is
with
a
d
elay
o
f
o
n
ly
4
2
.
8
9
u
n
its
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
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3
,
Dec
em
b
er
20
2
5
:
1
1
8
9
-
1
1
9
8
1194
Fig
u
r
e
4
.
R
T
L
an
d
g
ate
lev
el
n
etlis
t o
f
DC
T
Fig
u
r
e
5
.
Simu
lated
wa
v
ef
o
r
m
A
p
ea
k
s
ig
n
al
-
to
-
n
o
is
e
r
atio
(
PS
NR
)
is
u
s
ed
as
a
m
etr
ic
f
o
r
th
e
p
er
f
o
r
m
an
ce
ass
ess
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en
t
to
co
m
p
ar
e
th
e
o
r
ig
in
al
im
a
g
e
ag
ai
n
s
t
th
e
ap
p
r
o
x
im
ate
o
n
e.
T
h
e
PS
NR
o
f
th
e
im
ag
e
is
r
e
p
r
esen
ted
in
d
B
ca
n
b
e
co
m
p
u
ted
as,
PS
NR
=
1
0
lo
g
10
(
(
MN
*
2
5
5
2
)
/(
∑
∑
[
P
(
i
,
j
)
−
P
′
(
i
,
j
)
]
N
−
1
n
=
0
M
−
1
m
=
0
2
)
(
6
)
T
h
e
ex
is
tin
g
an
d
t
h
e
p
r
o
p
o
s
e
d
ad
d
er
s
ar
e
im
p
lem
en
ted
in
im
ag
e
p
r
o
ce
s
s
in
g
ap
p
licatio
n
s
s
u
ch
as
s
m
o
o
th
en
in
g
an
d
s
h
a
r
p
en
in
g
o
f
th
e
im
ag
es.
T
h
e
im
p
lem
en
tat
io
n
r
esu
lts
ar
e
g
iv
e
n
in
T
ab
le
4
.
T
ab
le
4
.
PS
NR
co
m
p
ar
is
o
n
o
f
im
ag
e
A
p
p
l
i
c
a
t
i
o
n
D
C
T
B
e
n
c
h
mar
k
M
a
j
o
r
i
t
y
-
b
a
se
d
a
p
p
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x
i
m
a
t
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d
d
e
r
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Le
n
a
1
2
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1
3
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3
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f
f
a
n
y
6
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5
8
.
0
H
o
u
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e
1
2
.
5
1
3
.
5
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a
mer
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ma
n
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1
4
.
4
M
o
o
n
s
u
r
f
a
c
e
1
0
.
6
1
0
.
8
P
e
p
p
e
r
s
13
15
Tu
l
i
p
s
1
1
.
5
1
4
.
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
E
fficien
t d
esig
n
o
f a
p
p
r
o
xima
te
ca
r
r
y
-
b
a
s
ed
s
u
m
ca
lcu
la
tin
g
fu
ll a
d
d
ers
…
(
B
a
d
ig
a
n
c
h
ela
S
h
iva
K
u
ma
r
)
1195
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
ad
d
er
is
co
m
p
ar
ed
a
g
ain
s
t
a
m
ajo
r
ity
-
b
ased
ap
p
r
o
x
i
m
ate
ad
d
er
.
Fo
r
th
e
L
en
a
im
ag
e,
t
h
e
m
aj
o
r
ity
-
b
ased
a
p
p
r
o
x
im
ate
ad
d
e
r
ac
h
iev
es
a
PS
NR
o
f
1
2
.
2
.
T
h
e
p
r
o
p
o
s
ed
a
d
d
er
s
co
r
es
h
ig
h
er
th
an
th
e
m
ajo
r
ity
-
b
ased
ad
d
e
r
ab
o
u
t
1
3
.
3
.
Simil
ar
ly
,
f
o
r
th
e
T
if
f
an
y
im
ag
e
,
th
e
p
r
o
p
o
s
ed
ad
d
er
im
p
r
o
v
es
th
e
PS
NR
f
r
o
m
6
.
5
to
8
.
0
.
Fo
r
th
e
Pep
p
er
s
im
ag
e,
th
e
PS
NR
in
cr
ea
s
es
s
ig
n
if
ica
n
tly
f
r
o
m
1
3
to
1
5
,
an
d
f
o
r
th
e
T
u
lip
s
im
a
g
e,
th
e
PS
NR
im
p
r
o
v
es
f
r
o
m
1
1
.
5
t
o
1
4
.
1
.
T
h
ese
r
esu
lts
in
d
icate
th
at
t
h
e
p
r
o
p
o
s
e
d
ad
d
er
co
n
s
is
ten
tly
p
r
o
v
id
es
b
etter
p
er
f
o
r
m
an
ce
ac
r
o
s
s
v
ar
io
u
s
im
ag
es
co
m
p
ar
ed
t
o
th
e
m
ajo
r
ity
-
b
ase
d
ap
p
r
o
x
im
ate
ad
d
er
.
T
h
e
im
p
r
o
v
em
en
ts
s
u
g
g
est
th
at
t
h
e
p
r
o
p
o
s
ed
d
esig
n
en
h
a
n
ce
s
er
r
o
r
r
esil
ien
ce
w
h
ile
m
ain
tain
in
g
o
r
ev
en
im
p
r
o
v
i
n
g
th
e
q
u
ality
o
f
th
e
p
r
o
c
ess
ed
im
ag
es,
d
em
o
n
s
tr
atin
g
its
ef
f
ec
tiv
en
ess
in
er
r
o
r
-
to
ler
an
t a
p
p
licatio
n
s
.
T
h
e
in
p
u
t a
n
d
co
r
r
esp
o
n
d
in
g
o
u
tp
u
t im
ag
es a
r
e
s
h
o
wn
in
Fig
u
r
e
6
.
Fig
u
r
e
6
.
I
n
p
u
t a
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a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
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3
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Dec
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1196
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Ven
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Un
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Au
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ah
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y
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as th
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DATA AV
AI
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eq
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est.
RE
F
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R
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NC
E
S
[
1
]
S
.
M
i
t
t
a
l
,
“
A
s
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.
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2
]
Q
.
Zh
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.
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n
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R
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8
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4
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4
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[
3
]
B.
S
a
k
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n
d
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.
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a
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ma
,
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r
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.
[
4
]
M
.
R
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,
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.
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m
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A
C
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PLAN
N
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7
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5
4
.
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4
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5
.
[
5
]
M
.
U
s
h
a
r
a
n
i
,
B
.
S
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k
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e
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.
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y
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g
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i
,
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c
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r
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t
y
,
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t
e
l
l
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g
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n
t
Au
t
o
m
a
t
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,
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.
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I
n
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f
&
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m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
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E
fficien
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1197
[
6
]
M
.
M
.
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.
d
a
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,
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.
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r
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n
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c
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7
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N
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