I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
11
,
No
.
6
,
Dec
em
b
er
2
0
2
1
,
p
p
.
4
7
9
4
~
4
8
0
9
I
SS
N:
2
0
8
8
-
8
7
0
8
,
DOI
:
1
0
.
1
1
5
9
1
/
ijece
.
v
1
1
i
6
.
pp
4
7
9
4
-
4
8
0
9
4794
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
FP
G
A im
plemen
t
a
tion o
f
LDP
C so
ft
-
d
ecisio
n decode
rs ba
sed
DCSK
f
o
r sp
read
spectr
um a
pplica
tions
F
a
dh
il S.
H
a
s
a
n
1
,
M
a
hm
o
o
d F
.
M
o
s
leh
2
,
Ay
a
H
.
Abdu
lha
m
ee
d
3
1,
3
De
p
a
rtme
n
t
o
f
C
o
m
p
u
ter E
n
g
i
n
e
e
rin
g
Tec
h
n
iq
u
e
s,
M
i
d
d
le T
e
c
h
n
ica
l
Un
iv
e
rsity
,
Ba
g
h
d
a
d
,
Ira
q
2
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
Al
-
M
u
sta
n
sir
iy
a
h
U
n
iv
e
rsit
y
,
Ba
g
h
d
a
d
,
Ira
q
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
2
3
, 2
0
2
0
R
ev
is
ed
Ap
r
2
3
,
2
0
21
Acc
ep
ted
Ma
y
1
9
,
2
0
21
S
p
re
a
d
s
p
e
c
tru
m
(S
S
)
c
o
m
m
u
n
i
c
a
ti
o
n
s
h
a
v
e
a
tt
ra
c
ted
in
tere
st
b
e
c
a
u
se
o
f
th
e
ir
c
h
a
n
n
e
l
a
tt
e
n
u
a
ti
o
n
imm
u
n
i
ty
a
n
d
lo
w
in
terc
e
p
t
p
o
ten
ti
a
l.
A
p
a
rt
fr
o
m
so
m
e
e
x
tra
fe
a
tu
re
s
su
c
h
a
s
b
a
sic
tran
sc
e
iv
e
r
stru
c
tu
re
s,
c
h
a
o
ti
c
c
o
m
m
u
n
ica
ti
o
n
wo
u
ld
b
e
th
e
a
n
a
lo
g
a
lt
e
rn
a
ti
v
e
to
d
i
g
it
a
l
S
S
sy
ste
m
s.
Diffe
re
n
ti
a
l
c
h
a
o
s
sh
ift
k
e
y
i
n
g
(
DCSK)
sy
ste
m
s,
n
o
n
-
p
e
rio
d
ic
a
n
d
ra
n
d
o
m
c
h
a
ra
c
teristics
a
m
o
n
g
c
h
a
o
s
c
a
rri
e
rs
a
s
we
ll
a
s
th
e
ir
in
tera
c
ti
o
n
wit
h
so
ft
d
a
ta
a
re
d
e
sig
n
e
d
b
a
se
d
o
n
l
o
w
-
d
e
n
si
ty
p
a
rit
y
-
c
h
e
c
k
(LDP
C)
c
o
d
e
s
in
th
is
b
rief.
Be
c
a
u
se
o
f
sim
p
le
stru
c
t
u
re
,
a
n
d
g
l
o
rio
u
s
a
b
i
li
ty
to
c
o
r
r
e
c
t
e
r
r
o
r
s
.
U
s
i
n
g
t
h
e
X
i
l
i
n
x
k
i
n
t
e
x
7
F
P
G
A
d
e
v
e
l
o
p
m
e
n
t
k
i
t
,
w
e
i
n
v
e
s
t
i
g
a
t
e
t
h
e
h
a
r
d
w
a
r
e
p
e
r
f
o
r
m
a
n
c
e
a
n
d
r
e
s
o
u
r
c
e
r
e
q
u
i
r
e
m
e
n
t
t
e
n
d
e
n
c
i
e
s
o
f
t
h
e
D
C
S
K
c
o
m
m
u
n
ica
ti
o
n
sy
s
tem
b
a
se
d
o
n
LD
P
C
d
e
c
o
d
in
g
a
l
g
o
rit
h
m
s
(
P
ro
b
.
Do
m
a
in
,
Lo
g
D
o
m
a
in
a
n
d
M
in
-
S
u
m
)
o
v
e
r
AWG
N
c
h
a
n
n
e
l.
T
h
e
re
su
lt
s
in
d
ica
te
th
a
t
th
e
p
r
o
p
o
se
d
sy
st
e
m
m
o
d
e
l
h
a
s
su
b
sta
n
ti
a
l
imp
r
o
v
e
m
e
n
ts
in
th
e
p
e
rfo
rm
a
n
c
e
o
f
th
e
b
it
e
rr
o
r
ra
te
(BER)
a
n
d
th
e
re
a
l
-
ti
m
e
p
ro
c
e
ss
.
Th
e
M
in
-
S
u
m
d
e
c
o
d
e
r
h
a
s
re
lativ
e
ly
fe
we
r
F
P
G
A
re
s
o
u
rc
e
s th
a
n
t
h
e
o
t
h
e
r
d
e
c
o
d
e
rs.
Th
e
imp
lem
e
n
ted
sy
ste
m
will
a
c
h
iev
e
1
0
-
4
BER
e
fficie
n
c
y
with
5
d
B
a
ss
o
c
ia
te E
b
/N
o
a
s a
c
o
d
i
n
g
g
a
in
.
K
ey
w
o
r
d
s
:
DC
SK
Har
d
war
e
C
o
-
s
im
u
latio
n
L
DPC
So
f
t d
ec
is
io
n
d
ec
o
d
er
Xilin
x
SG
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Fad
h
il S.
Hasan
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
Al
Mu
s
tan
s
ir
iy
ah
Un
iv
er
s
ity
B
ag
h
d
ad
,
I
r
aq
E
m
ail:
f
ad
el_
s
ah
ib
@
u
o
m
u
s
ta
n
s
ir
iy
ah
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
B
ein
g
wid
e
-
b
an
d
,
ch
ao
tic
s
ig
n
als
ar
e
well
s
u
ited
f
o
r
co
m
m
u
n
icatio
n
with
th
e
s
p
r
ea
d
-
s
p
ec
tr
u
m
[
1
]
.
Am
o
n
g
th
e
p
r
o
p
o
s
ed
d
ig
ital
s
ch
em
es,
th
e
m
o
s
t
co
m
p
r
eh
e
n
s
iv
e
r
esear
ch
was
o
n
ch
ao
s
s
h
if
t
k
ey
in
g
(
C
SK)
an
d
d
if
f
er
en
tial
C
SK
(
DC
SK)
[
2
]
.
T
h
e
f
o
r
m
er
was
o
r
ig
in
ally
in
tr
o
d
u
ce
d
f
o
r
s
u
ch
a
co
h
e
r
en
t
i
m
p
lem
en
tatio
n
[
3
]
,
r
eq
u
ir
in
g
s
y
n
ch
r
o
n
ized
r
ep
lic
as
o
f
th
e
ch
ao
tic
b
ase
f
u
n
ctio
n
s
at
th
e
r
ec
eiv
er
.
T
h
is
r
eq
u
ir
e
m
en
t
h
as
s
till
n
o
t
b
ee
n
p
r
o
v
ed
p
r
ac
tical,
th
o
u
g
h
.
On
th
e
o
th
er
h
an
d
,
t
h
e
DC
SK
s
ch
em
e
r
ep
r
esen
ts
a
r
ath
er
m
o
r
e
r
o
b
u
s
t
n
o
n
-
co
h
er
en
t
s
ch
em
e
[
4
]
i
n
wh
ic
h
th
e
r
ec
eiv
er
d
o
es
n
o
t
n
ee
d
th
e
ex
ac
t
in
f
o
r
m
atio
n
o
f
ch
a
o
tic
b
asis
f
u
n
ctio
n
s
.
R
ath
er
th
e
two
s
ig
n
al
s
am
p
le
s
wer
e
co
r
r
elate
d
as
well
a
s
th
e
r
esu
lt
o
f
th
e
co
r
r
elatio
n
i
s
co
m
p
ar
ed
with
a
th
r
esh
o
ld
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
d
ig
ital
co
m
m
u
n
icatio
n
s
y
s
tem
s
b
ased
o
n
ch
ao
s
u
n
d
er
an
ad
d
itiv
e
w
h
i
te
g
au
s
s
ian
n
o
is
e
(
AW
GN)
en
v
ir
o
n
m
en
t
h
as b
ee
n
s
tu
d
ied
th
o
r
o
u
g
h
ly
[
5
]
-
[
8
]
.
L
o
w
-
d
en
s
ity
p
ar
ity
-
ch
ec
k
(
L
DPC
)
i
s
o
n
e
o
f
th
e
m
o
s
t
e
f
f
ec
tiv
e
tech
n
iq
u
es
am
o
n
g
s
t
th
e
er
r
o
r
co
r
r
ec
tio
n
c
o
d
es.
L
DPC
co
d
e
s
h
av
e
g
ain
ed
a
lo
t
o
f
atten
tio
n
r
ec
en
tly
s
in
ce
th
ey
ca
n
a
ch
iev
e
ex
ce
p
tio
n
al
p
er
f
o
r
m
an
ce
clo
s
e
to
th
e
Sh
an
n
o
n
lim
it
o
v
er
th
e
b
in
ar
y
s
y
m
m
etr
ic
ch
an
n
el
(
B
SC
)
an
d
als
o
th
e
ad
d
itiv
e
wh
ite
g
au
s
s
ian
n
o
is
e
(
AW
GN)
ch
an
n
el
[
9
]
.
Dec
o
d
i
n
g
a
n
L
DPC
co
d
e
allo
ws
f
o
r
a
h
ig
h
d
e
g
r
ee
o
f
p
ar
allelis
m
,
m
ak
in
g
it
id
ea
lly
s
u
ited
f
o
r
h
ig
h
d
ata
r
ate
ap
p
licati
o
n
s
in
clu
d
in
g
wid
e
-
b
an
d
wir
eless
m
u
ltime
d
ia
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:
2
0
8
8
-
8
7
0
8
F
P
GA
imp
leme
n
ta
tio
n
o
f LDP
C
s
o
ft
-
d
ec
is
io
n
d
ec
o
d
ers
b
a
s
ed
DC
S
K
fo
r
s
p
r
ea
d
…
(
F
a
d
h
il
S
.
Ha
s
a
n
)
4795
co
m
m
u
n
icatio
n
s
an
d
m
ag
n
e
tic
s
to
r
ag
e
s
y
s
tem
s
.
T
h
e
p
ar
ity
ch
ec
k
m
atr
ix
'
s
lo
w
-
d
en
s
ity
n
atu
r
e
th
u
s
co
n
tr
ib
u
tes
to
b
o
th
g
r
ea
t d
is
tan
ce
p
r
o
p
e
r
ties
an
d
th
e
r
elativ
ely
l
o
w
co
m
p
lex
ity
o
f
its
d
ec
o
d
in
g
alg
o
r
ith
m
[
1
0
]
,
[
1
1
]
.
Mo
r
eo
v
er
,
th
e
ex
ce
s
s
iv
e
n
o
is
e
d
er
iv
es
f
r
o
m
a
wid
e
s
ca
le
o
f
m
o
b
ile
c
o
m
m
u
n
icatio
n
,
th
e
b
i
t
er
r
o
r
r
ate
(
B
E
R
)
is
ac
ce
p
tab
le
in
m
o
d
er
n
co
m
m
u
n
icatio
n
with
an
ev
e
n
m
o
r
e
h
i
g
h
-
s
p
ee
d
d
ata
r
ate.
Hen
ce
,
s
u
p
p
o
r
t
f
o
r
th
e
DC
SK
co
m
m
u
n
icatio
n
s
y
s
tem
th
r
o
u
g
h
L
DPC
co
d
es
b
ec
o
m
es
ess
en
tial
to
m
itig
ate
t
h
e
h
ig
h
er
r
o
r
[
1
2
]
.
T
h
e
f
ield
p
r
o
g
r
am
m
a
b
le
g
ate
ar
r
ay
(
FP
GA)
is
u
s
ed
to
ev
alu
ate
a
s
y
s
tem
th
at
in
clu
d
ed
ea
ch
DC
SK
an
d
L
DP
C
co
d
es in
a
r
ea
l
-
tim
e
en
v
ir
o
n
m
en
t.
Gallag
er
'
s
s
u
g
g
ested
b
asi
c
d
ec
o
d
in
g
alg
o
r
ith
m
f
o
r
L
D
P
C
c
o
d
e
s
i
n
1
9
6
2
w
a
s
s
o
f
t
d
e
c
i
s
i
o
n
s
s
u
c
h
a
s
t
h
e
s
u
m
-
p
r
o
d
u
c
t
a
l
g
o
r
i
t
h
m
(
S
P
A
)
a
n
d
h
a
r
d
d
e
c
i
s
i
o
n
s
u
c
h
a
s
t
h
e
b
i
t
f
l
i
p
p
i
n
g
(
B
F)
[
1
3
]
.
SP
A
r
eq
u
ir
es
m
o
r
e
s
tep
s
to
ad
d
iti
o
n
an
d
m
u
ltip
licatio
n
w
h
ich
en
ab
les
im
p
lem
en
tatio
n
i
n
th
e
ca
s
e
o
f
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
with
FP
GA
d
u
e
to
th
e
s
im
p
licity
o
f
t
h
is
o
p
er
atio
n
.
A
cr
u
cial
t
r
ad
e
-
o
f
f
b
e
twee
n
'
co
m
p
lex
ity
'
an
d
'
ef
f
icien
cy
'
is
n
ee
d
e
d
in
it
er
ativ
e
d
ec
o
d
in
g
.
I
n
th
is
p
ap
er
,
we
p
r
o
p
o
s
e
a
m
o
d
el
o
f
a
c
o
m
m
u
n
icatio
n
s
y
s
tem
in
clu
d
in
g
a
DC
SK
as
a
m
o
d
u
l
atio
n
tech
n
iq
u
e
s
u
p
p
o
r
te
d
b
y
t
h
r
ee
SP
A
(
Pro
b
.
Do
m
ain
,
L
o
g
Do
m
ain
a
n
d
Mi
n
-
Su
m
wh
ich
is
d
esig
n
e
d
to
r
e
d
u
ce
h
a
r
d
war
e
c
o
m
p
lex
ity
)
t
o
im
p
r
o
v
e
t
h
e
s
y
s
tem
p
e
r
f
o
r
m
a
n
c
e
.
T
h
e
p
r
o
p
o
s
e
d
s
y
s
t
e
m
w
i
l
l
b
e
i
m
p
l
e
m
e
n
t
e
d
u
s
i
n
g
a
n
F
P
G
A
K
i
n
t
e
x
7
d
e
v
e
l
o
p
m
e
n
t
k
i
t
i
n
t
e
g
r
a
t
e
d
w
i
t
h
V
i
v
a
d
o
2
0
1
7
.
4
s
o
f
twar
e.
2.
DCSK
WI
T
H
L
DP
C
E
NCO
DE
D
CO
M
M
UN
I
CA
T
I
O
N
SYST
E
M
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
d
iag
r
am
is
s
h
o
wn
in
Fig
u
r
e
1
th
at
in
c
lu
d
ed
a
b
i
n
ar
y
d
ata
s
o
u
r
ce
t
h
at
will
b
e
en
co
d
ed
th
r
o
u
g
h
th
e
L
DPC
b
lo
ck
with
a
co
d
e
r
ate
o
f
0
.
5
.
T
h
e
co
d
ewo
r
d
is
s
en
t
to
a
D
C
SK
m
o
d
u
lato
r
th
at
u
s
es
a
ch
ao
tic
ca
r
r
ier
f
o
r
s
p
r
ea
d
th
e
d
ig
ital
s
ig
n
al
ac
r
o
s
s
a
wid
e
f
r
e
q
u
en
c
y
b
an
d
to
ac
h
iev
e
a
m
o
d
u
lated
s
ig
n
a
l
with
s
u
ch
a
s
p
r
ea
d
in
g
f
ac
to
r
v
alu
e
eq
u
al
to
1
6
.
AW
GN
n
o
is
e
is
in
d
icate
d
with
th
e
m
o
d
u
lated
s
ig
n
al
wh
ich
is
m
o
s
tly
u
s
ed
f
o
r
th
e
e
x
p
er
im
e
n
tal
ap
p
licatio
n
s
f
o
r
s
im
p
licity
.
No
n
-
c
o
h
er
e
n
t
d
e
m
o
d
u
l
a
t
i
o
n
w
i
l
l
t
h
e
n
b
e
a
d
a
p
t
e
d
o
n
t
h
e
r
e
c
e
i
v
e
r
s
i
d
e
t
o
r
e
c
o
v
e
r
t
h
e
r
e
c
e
i
v
e
d
c
o
d
e
-
w
o
r
d
,
t
h
a
t
w
i
l
l
b
e
d
e
c
o
d
e
d
t
o
r
e
g
e
n
e
r
a
t
e
t
h
e
o
r
i
g
i
n
a
l
in
f
o
r
m
atio
n
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
th
e
s
y
s
tem
m
o
d
el
3.
H
ARDWA
R
E
CO
M
M
UN
I
C
AT
I
O
N
S
YS
T
E
M
DE
SI
G
N
As
m
en
tio
n
ed
in
s
ec
tio
n
2
th
e
s
y
s
tem
co
n
s
is
ts
o
f
th
r
ee
m
ain
p
ar
ts
:
tr
an
s
m
itter
,
ch
a
n
n
el
a
n
d
r
ec
eiv
er
.
A
tr
an
s
m
itter
s
ec
tio
n
is
estab
l
is
h
ed
b
y
th
e
s
u
b
s
eq
u
en
t,
L
o
g
i
s
tic
-
m
ap
as
in
p
u
t
ch
a
o
tic
d
ata
g
en
er
ato
r
,
L
DPC
en
co
d
er
b
y
u
s
in
g
th
e
s
y
s
tem
a
tic
f
o
r
m
o
f
H
m
atr
ix
a
n
d
co
m
p
u
tin
g
th
e
p
a
r
ity
ch
ec
k
e
q
u
ati
o
n
f
o
r
ea
c
h
r
o
w
o
f
th
is
m
atr
ix
an
d
DC
SK
m
o
d
u
l
ato
r
.
T
h
e
r
ec
eiv
er
is
estab
lis
h
ed
b
y
th
e
s
u
b
s
eq
u
en
t,
AW
GN
n
o
is
e,
DC
SK
d
e
-
m
o
d
u
lato
r
an
d
L
DPC
d
ec
o
d
e
r
with
th
r
ee
ty
p
es
o
f
d
ec
o
d
er
alg
o
r
ith
m
s
s
u
ch
as;
Pro
b
.
Do
m
ain
,
L
o
g
D
o
m
ain
an
d
Min
-
Su
m
alg
o
r
ith
m
s
.
T
h
e
s
y
s
tem
m
o
d
el
will
b
e
im
p
l
em
en
te
d
u
s
in
g
Xilin
x
SG
as
s
h
o
wn
in
Fig
u
r
e
2
,
ea
ch
b
lo
c
k
is
d
esig
n
ed
with
s
p
ec
if
ic
p
ar
am
eter
s
to
m
atc
h
th
e
o
v
er
all
s
y
s
tem
im
p
lem
en
tatio
n
as
will
b
e
ex
p
lain
ed
in
d
etail
in
d
iv
id
u
all
y
.
I
t
is
wo
r
th
to
m
en
tio
n
th
at
all
th
e
th
r
ee
d
ec
o
d
er
alg
o
r
ith
m
s
h
av
e
th
e
s
am
e
d
esig
n
ar
ch
itectu
r
e
e
x
ce
p
t th
e
p
ar
t d
ea
l w
ith
d
ec
o
d
er
b
lo
ck
.
3
.
1
.
L
DP
C
enco
der
T
h
e
B
er
n
o
u
lli
r
an
d
o
m
b
in
a
r
y
n
u
m
b
er
g
en
er
ated
m
ess
ag
e
wo
r
d
with
a
len
g
th
o
f
k
=1
0
was
f
ed
to
th
e
L
DPC
b
lo
ck
th
r
o
u
g
h
g
atew
ay
b
lo
ck
to
o
b
tain
a
co
d
e
w
o
r
d
with
a
len
g
th
o
f
n
=
2
0
at
th
e
o
u
tp
u
t
o
f
a
ce
r
tain
b
lo
ck
.
T
h
er
e
is
a
s
er
ial
to
p
ar
a
llel
b
lo
ck
with
in
th
e
L
DPC
en
co
d
er
b
lo
ck
s
h
o
wn
in
F
i
g
u
r
e
3
w
h
i
c
h
w
i
l
l
b
e
u
s
e
d
t
o
c
o
n
v
e
r
t
a
g
r
o
u
p
o
f
s
a
m
p
l
e
s
s
e
r
i
a
l
l
y
p
r
e
s
e
n
t
e
d
a
t
t
h
e
i
n
p
u
t
t
o
s
i
n
g
l
e
s
a
m
p
l
e
s
p
r
e
s
e
n
t
a
t
t
h
e
o
u
tp
u
t
is
s
h
o
wn
in
Fig
u
r
e
4
.
In
th
is
p
ap
e
r
,
we
h
av
e
=
10
as
m
en
tio
n
ed
p
r
ev
io
u
s
ly
r
ep
r
esen
ted
b
y
1
−
10
in
(
1
)
w
h
ile
11
−
20
r
ep
r
esen
ted
th
e
r
ed
u
n
d
an
c
y
b
i
ts
(
=
−
)
[
1
4
]
.
=
[
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
]
(
1
)
T
h
e
p
ar
ity
b
its
ar
e
in
co
r
p
o
r
a
ted
u
s
in
g
(
2
)
an
d
(
3
)
wh
ich
r
ef
lect
th
e
f
ir
s
t
an
d
s
ec
o
n
d
p
ar
ity
b
its
co
r
r
esp
o
n
d
s
r
esp
ec
tiv
ely
to
f
i
r
s
t
an
d
s
ec
o
n
d
r
o
ws
o
f
th
e
(
4
)
m
atr
ix
.
T
h
e
r
e
m
ain
in
g
p
ar
ity
is
g
en
er
ated
in
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
7
9
4
-
4
8
0
9
4796
s
am
e
m
eth
o
d
th
at
t
h
e
r
est
o
f
s
u
ch
m
atr
ix
r
o
ws
r
e
p
r
esen
t
[
1
5
]
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
h
ar
d
war
e
im
p
lem
en
tatio
n
o
f
th
ese
e
q
u
at
io
n
s
th
at
ar
e
im
p
lem
en
ted
u
s
i
n
g
1
0
XOR
g
ates
to
g
en
er
ate
1
0
p
a
r
ity
ch
ec
k
b
its
,
b
ased
o
n
th
e
in
p
u
t
m
ess
ag
e.
11
=
3
⊕
6
⊕
9
(
2
)
12
=
5
⊕
6
⊕
7
⊕
8
(
3
)
=
[
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
]
(
4
)
No
w,
th
e
2
0
-
b
it
co
d
e
-
wo
r
d
is
s
u
p
p
lied
to
co
n
ca
t
b
lo
c
k
,
co
n
ca
ten
atin
g
two
o
r
m
o
r
e
b
its
o
f
in
p
u
ts
to
g
et
a
s
y
m
b
o
l
o
f
t
h
ese
b
its
in
th
e
o
u
tp
u
t.
E
v
e
n
tu
ally
,
th
e
p
ar
allel
to
s
er
ial
b
l
o
ck
in
d
u
ce
s
th
e
c
o
d
e
w
o
r
d
as
o
u
tp
u
t
b
lo
c
k
.
S
o
th
at
ea
ch
s
a
m
p
le
p
r
o
v
id
ed
in
th
is
b
lo
c
k
'
s
in
p
u
t
b
ec
am
e
m
u
ltip
le
s
am
p
les
d
is
p
lay
ed
s
er
ially
in
th
e
o
u
t
p
u
t.
Fig
u
r
e
2
.
XSG
o
f
t
h
e
s
y
s
tem
m
o
d
el
F
ig
u
r
e
3
.
L
DPC
e
n
co
d
e
r
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:
2
0
8
8
-
8
7
0
8
F
P
GA
imp
leme
n
ta
tio
n
o
f LDP
C
s
o
ft
-
d
ec
is
io
n
d
ec
o
d
ers
b
a
s
ed
DC
S
K
fo
r
s
p
r
ea
d
…
(
F
a
d
h
il
S
.
Ha
s
a
n
)
4797
Fig
u
r
e
4
.
S2
P
b
l
o
ck
Fig
u
r
e
5
.
T
h
e
h
ar
d
war
e
o
f
e
n
c
o
d
er
3
.
2
.
DCSK
m
o
du
la
t
o
r
T
h
e
co
d
e
-
wo
r
d
g
e
n
er
ated
b
y
L
DPC
wa
s
f
ed
to
a
Xilin
x
SG
DC
SK
m
o
d
u
lato
r
d
esig
n
ed
.
T
h
r
o
u
g
h
o
u
t
th
e
DC
SK
m
o
d
u
lato
r
,
ea
ch
b
it
Si
is
ex
p
r
ess
ed
b
y
2
s
ets
o
f
β
-
p
er
io
d
ch
ao
tic
s
ig
n
al
s
am
p
les
wh
er
e
2
β
r
ef
er
s
to
th
e
s
p
r
ea
d
in
g
f
ac
t
o
r
with
s
u
ch
an
in
teg
er
n
u
m
b
er
.
T
h
e
f
ir
s
t
an
d
t
h
e
s
ec
o
n
d
s
ets
r
esp
ec
tiv
ely
r
e
p
r
esen
ted
t
h
e
s
eg
m
en
t
o
f
r
ef
er
e
n
ce
an
d
th
e
s
eg
m
en
t
o
f
d
ata.
Sam
p
les
f
r
o
m
th
e
d
ata
s
eg
m
en
t
ar
e
e
q
u
al
to
th
e
r
ef
er
en
ce
s
eg
m
en
t
f
o
r
tr
an
s
m
is
s
io
n
+1
,
an
d
an
in
v
er
te
d
v
ar
ian
t
o
f
a
r
e
f
er
en
ce
s
eg
m
en
t
is
b
ein
g
u
s
ed
f
o
r
tr
an
s
m
is
s
io
n
o
f
b
it
-
1
.
T
h
e
tr
an
s
m
itter
e
k
'
s
o
u
t
p
u
t d
u
r
in
g
th
e
i
th
b
it p
er
io
d
is
[
1
6
]
-
[
1
8
]
.
Fig
u
r
e
6
Sh
o
ws th
e
Xilin
x
SG b
lo
ck
o
f
DC
SK m
o
d
u
latio
n
s
y
s
tem
with
eq
u
al
t
o
8
.
=
{
1
<
≤
−
<
≤
2
(
5
)
B
o
th
C
h
ao
s
g
en
er
ato
r
an
d
m
ap
p
in
g
b
lo
ck
s
ar
e
s
h
o
wn
r
esp
ec
tiv
ely
in
Fig
u
r
es
7
an
d
8
.
C
h
eb
y
s
h
ev
p
o
ly
n
o
m
ial
f
u
n
ctio
n
(
C
PF
)
o
f
o
r
d
er
two
as
in
(
6
)
is
s
elec
ted
as
a
c
h
ao
tic
g
e
n
er
ato
r
with
s
u
ch
an
in
itial
co
n
d
itio
n
v
alu
e
o
f
0
.
1
to
b
e
im
p
lem
en
ted
s
im
p
ly
u
s
in
g
a
m
u
ltip
lex
er
,
m
u
ltip
lier
a
n
d
a
d
d
e
r
b
lo
ck
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
7
9
4
-
4
8
0
9
4798
+
1
=
1
−
2
2
(
6
)
T
h
e
m
ap
p
in
g
b
lo
ck
co
n
s
is
ts
o
f
a
R
OM
to
in
d
icate
eith
er
in
p
u
t
{0
}
o
r
in
p
u
t
{1
}
ac
co
r
d
in
g
to
th
e
in
itial
R
OM
v
ec
to
r
v
alu
e
[
-
1
,
1
]
.
Dela
y
wa
s
co
n
n
ec
ted
s
o
th
e
R
OM
b
l
o
c
k
en
ab
lin
g
p
in
ca
n
m
ask
all
s
e
r
ial
b
its
b
ef
o
r
e
th
ey
b
ec
o
m
e
r
ea
d
y
f
o
r
th
e
m
ap
o
p
e
r
atio
n
.
Fig
u
r
e
6
.
Xilin
x
SG d
esig
n
o
f
DC
SK
m
o
d
u
lato
r
Fig
u
r
e
7
.
T
h
e
ch
a
o
s
-
g
en
er
ato
r
b
lo
ck
Fig
u
r
e
8
.
Ma
p
p
in
g
{+
1
,
-
1
}
b
l
o
ck
3.
3
.
Cha
nn
el
I
f
th
e
m
o
d
u
lated
s
ig
n
al
is
tr
an
s
m
itted
o
v
er
a
ch
an
n
el,
n
o
is
e
in
th
e
ch
an
n
el
r
e
p
r
esen
ted
b
y
ad
d
itiv
e
wh
ite
g
au
s
s
ian
n
o
is
e
(
AW
GN
)
,
,
ca
n
co
r
r
u
p
t
it.
Su
ch
n
o
is
e
ch
ar
ac
ter
ized
b
y
a
wid
e
f
r
eq
u
en
cy
s
p
ec
tr
u
m
,
wh
ich
is
s
tatis
t
ically
r
an
d
o
m
r
ad
io
n
o
is
e.
T
h
e
h
ar
d
war
e
-
im
p
lem
en
ted
f
o
r
th
ese
ch
a
n
n
els
is
illu
s
tr
ated
with
s
ee
d
v
alu
e
5
1
2
in
Fig
u
r
e
9
.
Fig
u
r
e
9
.
AW
GN
ch
an
n
el
b
lo
ck
3.
4
.
DCSK
d
em
o
du
la
t
io
n
T
o
co
n
v
er
t
th
e
1
6
s
er
ial
to
p
ar
allel
s
am
p
les,
th
e
o
b
tain
ed
s
ig
n
al
p
ass
es
to
an
S2
P
b
lo
c
k
to
d
e
-
s
p
r
ea
d
with
in
a
s
in
g
le
b
it.
Fig
u
r
e
1
0
illu
s
tr
ates
th
e
d
etails
o
f
th
e
Xilin
x
SG
S2
P b
lo
ck
co
n
s
is
tin
g
o
f
1
6
latch
es
an
d
its
co
r
r
esp
o
n
d
in
g
d
elay
b
l
o
ck
s
.
S2
P
'
s
1
6
o
u
tp
u
t sam
p
les ar
e
lin
k
ed
to
a
co
r
r
elato
r
,
in
wh
ich
th
e
r
ef
er
en
ce
s
am
p
les
as
well
as
th
e
co
r
r
es
p
o
n
d
in
g
in
f
o
r
m
atio
n
s
am
p
les
wer
e
co
r
r
elate
d
u
s
in
g
m
u
lti
p
lier
s
.
i
th
co
r
r
elato
r
o
u
tp
u
t is th
e
v
a
r
iab
le
i
th
d
ec
is
io
n
,
D
i
[
1
9
]
.
=
∑
+
=
1
(
7
)
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:
2
0
8
8
-
8
7
0
8
F
P
GA
imp
leme
n
ta
tio
n
o
f LDP
C
s
o
ft
-
d
ec
is
io
n
d
ec
o
d
ers
b
a
s
ed
DC
S
K
fo
r
s
p
r
ea
d
…
(
F
a
d
h
il
S
.
Ha
s
a
n
)
4799
T
h
e
i
th
b
it is
d
em
o
d
u
lated
u
s
in
g
a
ze
r
o
th
r
esh
o
ld
,
m
ea
s
u
r
in
g
th
e
s
ig
n
o
f
th
e
f
in
al
co
r
r
elato
r
o
u
tp
u
t.
T
h
e
DC
SK
d
em
o
d
u
lato
r
Xilin
x
SG is sh
o
wn
in
Fig
u
r
e
11.
Fig
u
r
e
1
0
.
1
6
-
s
am
p
les S2
P b
lo
ck
s
at
th
e
d
em
o
d
u
lato
r
Fig
u
r
e
1
1
.
Xilin
x
SG D
C
SK d
em
o
d
u
lato
r
b
lo
ck
3.
5
.
Dec
o
ders
Pro
b
.
Do
m
ain
,
L
o
g
Do
m
ain
an
d
Min
-
Su
m
alg
o
r
ith
m
s
r
ep
r
esen
t
a
ty
p
e
o
f
s
o
f
t
d
ec
is
io
n
alg
o
r
ith
m
s
an
d
it
wo
r
k
s
b
y
p
ass
in
g
m
ess
ag
es
b
etwe
en
th
e
C
Ns
an
d
th
e
v
ar
iab
le
n
o
d
es
(
VNs).
I
t
is
u
s
ed
to
co
r
r
ec
t
th
e
r
ec
eiv
ed
b
its
to
o
b
tain
1
0
-
b
it
s
y
m
b
o
ls
wh
ich
will
r
ep
r
esen
t
t
h
e
o
r
ig
in
al
s
ig
n
al
a
f
ter
th
e
d
ec
o
d
in
g
p
r
o
ce
s
s
.
T
h
e
d
em
o
d
u
lated
b
its
ar
e
f
ir
s
tly
f
ed
to
th
e
S2
P
co
n
v
er
ter
b
lo
c
k
to
m
atch
ea
ch
o
th
er
with
in
SG
b
lo
ck
s
.
T
h
e
S2
P
will
b
e
u
s
ed
to
c
o
n
v
e
r
t
th
e
2
0
-
s
tr
ea
m
o
f
b
its
to
p
a
r
allel
b
i
ts
to
b
e
in
itialized
.
I
n
g
en
er
a
l,
th
ese
alg
o
r
ith
m
s
p
er
f
o
r
m
in
m
ain
th
r
ee
s
tep
s
.
−
I
n
itializatio
n
−
Ho
r
izo
n
tal
Step
−
Ver
tical
Step
an
d
Dec
o
d
in
g
/
E
s
tim
atio
n
T
h
e
s
tep
d
etails f
o
r
ea
ch
ty
p
e
o
f
th
ese
alg
o
r
ith
m
s
will b
e
d
escr
ib
ed
with
a
zo
o
m
-
in
v
iew
b
e
lo
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
7
9
4
-
4
8
0
9
4800
3
.
5
.
1
.
P
ro
b.
do
m
a
in deco
der
I
n
i
t
i
a
l
i
z
a
t
i
o
n
:
I
n
t
h
e
in
it
ializati
o
n
s
t
e
p
t
h
e
v
a
l
u
e
o
f
P
(
1
)
=
,
(
1
)
a
n
d
P
(
0
)
=
,
(
0
)
i
s
o
b
t
a
i
n
e
d
f
r
o
m
(
9
)
&
(
10
)
w
h
i
c
h
r
e
p
r
e
s
e
n
t
s
t
h
e
m
e
s
s
a
g
e
t
h
a
t
w
i
l
l
b
e
s
e
n
t
f
r
o
m
t
h
e
V
N
n
t
o
C
N
m
.
E
a
c
h
o
n
e
o
f
t
h
e
m
e
s
s
a
g
e
s
h
a
s
t
h
e
p
a
i
r
,
(
0
)
a
s
w
e
l
l
a
s
,
(
1
)
r
e
f
e
r
r
i
n
g
t
o
t
h
e
i
n
d
i
c
a
t
i
o
n
t
h
a
t
rx
h
a
s
b
e
e
n
o
n
e
o
r
ze
r
o
[
2
0
]
.
(
1
)
=
1
[
1
+
−
2
0
]
(
8
)
(
0
)
=
1
−
(
1
)
(
9
)
W
h
er
e
(
1
)
an
d
(
0
)
ar
e
th
e
p
o
s
ter
io
r
p
r
o
b
ab
ilit
ies
an
d
th
eir
v
alu
e
s
ca
n
b
e
f
o
u
n
d
b
ased
o
n
th
e
r
ec
eiv
ed
s
ig
n
al,
also
N
0
r
ep
r
esen
tin
g
n
o
is
e
v
ar
ian
ce
.
Ho
r
izo
n
tal
s
tep
:
T
h
e
h
o
r
izo
n
t
al
s
tep
ca
lcu
latio
n
is
cr
ea
ted
d
ep
en
d
i
n
g
o
n
th
e
n
u
m
b
e
r
o
f
1
s
o
v
er
all
co
lu
m
n
s
o
f
te
n
r
o
ws th
r
o
u
g
h
o
u
t th
e
m
atr
ix
(
11
)
-
(
13
)
.
=
∏
(
,
′
(
0
)
−
,
′
(
1
)
)
∈
,
′
≠
(
1
0
)
,
(
0
)
=
1
/
2
(
1
+
)
(
1
1
)
,
(
1
)
=
1
/
2
(
1
−
)
(
1
2
)
T
h
ese
v
ar
iab
le
n
o
d
e
h
as
b
ee
n
d
esig
n
ed
b
y
u
s
in
g
th
e
b
asic
ad
d
-
s
u
b
an
d
m
u
lt
Xilin
x
SG
b
lo
ck
s
to
ev
alu
ate
th
e
b
y
tak
in
g
th
e
p
r
o
d
u
ct
o
f
s
u
b
tr
ac
tio
n
,
′
(
1
)
also
,
′
(
0
)
ex
clu
d
in
g
b
it
′
,
,
(
0
)
as
well
a
s
,
(
1
)
wh
ich
r
e
p
r
esen
tin
g
th
e
p
r
o
b
ab
ilit
y
wh
ich
ch
ec
k
m
ca
n
b
e
d
esig
n
e
d
ea
s
ily
b
y
u
s
in
g
a
d
d
-
s
u
b
to
ad
d
o
r
s
u
b
o
n
e
f
r
o
m
v
alu
e
th
en
m
u
x
th
e
r
esu
lts
b
y
0
.
5
u
s
in
g
Xilin
x
SG
b
lo
c
k
.
Fig
u
r
es
1
2
an
d
1
3
illu
s
tr
ate
th
e
f
ir
s
t r
o
w
co
m
p
u
tatio
n
s
ac
co
r
d
in
g
to
th
e
(
10
)
-
(
12
)
o
f
t
h
e
h
o
r
izo
n
tal
s
tep
.
Fig
u
r
e
1
2
.
Ho
r
izo
n
tal
s
tep
f
o
r
th
e
f
ir
s
t r
o
w
o
f
p
r
o
b
.
d
o
m
ain
d
ec
o
d
er
Fig
u
r
e
1
3
.
Deta
ils
o
f
th
e
b
lo
c
k
s
(
1
)
o
f
t
h
e
f
ir
s
t r
o
w
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:
2
0
8
8
-
8
7
0
8
F
P
GA
imp
leme
n
ta
tio
n
o
f LDP
C
s
o
ft
-
d
ec
is
io
n
d
ec
o
d
ers
b
a
s
ed
DC
S
K
fo
r
s
p
r
ea
d
…
(
F
a
d
h
il
S
.
Ha
s
a
n
)
4801
Ver
tical
s
tep
:
T
h
is
s
tep
's
ca
lcu
latio
n
s
ar
e
m
ea
s
u
r
e
d
b
y
th
e
n
u
m
b
er
o
f
1
s
f
o
r
ea
ch
r
o
w
o
f
s
u
ch
T
wen
ty
co
lu
m
n
s
as in
m
atr
ix
co
n
s
is
ten
t w
ith
th
e
(1
3
)
an
d
(
14
)
.
(
0
)
=
(
0
)
.
∏
,
=
1
(
0
)
(
1
3
)
(
1
)
=
(
1
)
.
∏
,
=
1
(
1
)
(
1
4
)
W
h
er
e
ki
n
(
0
)
an
d
ki
n
(
1
)
ar
e
s
ca
les
f
ac
to
r
s
wh
ich
ar
e
im
p
lem
e
n
ted
u
s
in
g
Mu
lt
Xilin
x
SG
b
lo
ck
s
.
A
ls
o
,
a
d
ec
is
io
n
f
o
r
ea
c
h
b
it is
m
ad
e
a
cc
o
r
d
in
g
to
(
15
)
.
ℎ
=
{
1
,
Qi
n
(
1
)
>
Qi
n
(
0
)
0
,
Qi
n
(
1
)
≤
Qi
n
(
0
)
.
(
1
5
)
T
h
e
Xilin
x
SG b
lo
ck
o
f
co
l
u
m
n
twelv
e
is
d
escr
ib
ed
in
Fig
u
r
e
1
4
.
Fig
u
r
e
1
4
.
Ver
tical
s
tep
(
co
lu
m
n
1
2
)
3
.
5
.
2
.
L
o
g
do
ma
in a
lg
o
rit
h
m
I
n
itializatio
n
:
I
n
L
o
g
Do
m
ain
d
ec
o
d
er
t
h
e
lo
g
-
lik
elih
o
o
d
r
a
tio
(
L
L
R
)
o
f
p
r
io
r
(
wh
ic
h
r
e
p
r
esen
ts
th
e
r
ec
eiv
in
g
m
ess
ag
es
f
r
o
m
th
e
ch
an
n
el)
an
d
p
o
s
ter
io
r
(
w
h
ich
r
ep
r
esen
ts
th
e
m
ed
ial
m
ess
ag
es
m
o
v
ed
b
etw
ee
n
C
Ns
an
d
VNs)
p
r
o
b
ab
ilit
y
is
u
s
ed
.
So
,
th
e
p
r
io
r
m
ess
ag
es
s
en
t
f
r
o
m
B
N
n
t
o
th
e
C
N
m
r
ep
r
esen
t
th
e
L
L
R
[
2
1
]
.
=
−
4
0
(
1
6
)
ℎ
,
=
(
)
(
1
7
)
,
=
|
|
(
1
8
)
T
h
is
p
r
o
ce
s
s
is
a
p
p
lied
t
o
2
0
r
ec
eiv
ed
b
its
s
er
ially
.
T
h
en
,
t
h
e
ab
s
o
lu
te
v
alu
e
an
d
s
ig
n
v
a
lu
e
(
will
ca
lcu
late
th
e
s
ig
n
v
alu
e
wh
eth
er
it
is
p
o
s
itiv
e
o
r
n
eg
ativ
e
o
r
eq
u
al
to
ze
r
o
)
will
b
e
ca
lcu
lated
f
o
r
ea
c
h
b
it.
T
h
e
im
p
lem
en
tatio
n
o
f
t
h
e
in
itializatio
n
b
lo
ck
is
d
o
n
e
b
y
u
s
in
g
Mu
lt,
Mu
x
an
d
r
elatio
n
al
Xil
in
x
SG
b
lo
ck
.
T
h
e
p
r
o
ce
s
s
o
f
in
itializatio
n
b
lo
c
k
an
d
th
e
s
ig
n
b
lo
ck
will b
e
d
ec
l
ar
ed
in
Fig
u
r
es 1
5
an
d
1
6
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
5
.
I
n
itializatio
n
p
r
o
ce
s
s
Fig
u
r
e
1
6
.
Deta
ils
o
f
Sig
n
b
lo
ck
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
7
9
4
-
4
8
0
9
4802
Ho
r
izo
n
tal
s
tep
:
T
h
e
c
o
m
p
u
tatio
n
s
o
f
th
e
h
o
r
iz
o
n
tal
s
tep
a
r
e
cr
ea
ted
d
ep
e
n
d
u
p
o
n
t
h
e
am
o
u
n
t
o
f
1
s
p
er
co
lu
m
n
o
f
ten
r
o
ws
th
r
o
u
g
h
o
u
t
t
h
e
m
atr
ix
.
T
o
C
o
m
p
u
tin
g
th
e
ex
tr
i
n
s
ic
m
ess
ag
es
f
o
r
ea
ch
s
et
o
f
b
its
co
n
n
ec
ted
t
o
C
N
m
b
y
ex
clu
d
i
n
g
th
e
b
it
′
th
e
eq
u
at
io
n
b
elo
w
will b
e
u
s
ed
.
,
=
l
og
(
,
+
1
,
−
1
)
(
1
9
)
W
h
er
e
,
r
e
p
r
esen
ts
th
e
p
r
o
b
a
b
ilit
y
th
at
p
a
r
ity
-
ch
ec
k
m
h
a
s
b
ee
n
ac
h
iev
ed
in
t
h
e
ca
s
e
wh
en
b
it
n
is
s
u
p
p
o
s
ed
to
b
e
a
1
f
o
r
t
h
e
L
L
R
.
C
o
m
p
u
te
th
e
s
u
m
m
atio
n
o
f
,
ex
clu
d
in
g
th
e
b
it n
.
,
=
∑
,
′
n
∈
,
n
′
≠
n
(
2
0
)
T
h
en
co
m
p
u
te
,
:
,
=
l
og
(
,
+
1
,
−
1
)
(
2
1
)
Get
p
r
o
d
u
cts o
f
ℎ
,
ex
clu
d
in
g
t
h
e
b
it n
:
,
=
∏
ℎ
,
′
n
∈
,
n
′
≠
n
(
2
2
)
Fin
ally
,
co
m
p
u
te
,
,
=
,
×
,
(
2
3
)
T
o
r
e
d
u
ce
th
e
c
o
m
p
lex
ity
o
f
Xilin
x
SG
d
esig
n
r
elate
d
to
th
e
lo
g
ar
ith
m
(
l
o
g
)
p
r
o
ce
s
s
in
(
19
)
,
a
l
o
o
k
-
u
p
tab
le
is
p
r
o
p
o
s
ed
b
y
tak
in
g
th
e
v
alu
es
o
f
r
x
an
d
a
p
p
ly
in
g
(
19
)
as
s
h
o
wn
in
T
ab
le
1
.
Fig
u
r
e
1
7
s
h
o
ws
th
e
d
etails o
f
th
e
Xilin
x
SG d
esig
n
f
o
r
t
h
e
Pi
ca
lcu
latio
n
ac
co
r
d
in
g
to
(
19
)
f
o
r
ea
c
h
b
it e
q
u
al
t
o
o
n
e.
T
ab
le
1
.
L
o
o
k
-
u
p
tab
le
f
o
r
t
h
e
v
alu
es
o
f
Pi
V
a
l
u
e
o
f
b
e
t
a
i
j
V
a
l
u
e
o
f
P
i
0
≤
rx
<
0
.
5
0
0
.
5
≤
rx
<
1
1
.
4
0
6
8
1
≤
rx
<
1
.
5
0
.
7
7
1
9
4
1
.
5
≤
rx
<
2
0
.
4
5
3
8
9
2
.
5
≤
r
x
<
3
0
.
2
7
2
3
4
3
≤
rx
<
3
.
5
…
….
C
o
n
t
i
n
u
e
0
.
1
6
4
5
4
0
rx
>
3
1
0
Fig
u
r
e
1
7
.
T
h
e
P
i
p
r
o
ce
s
s
b
lo
ck
o
f
Xilin
x
SG
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:
2
0
8
8
-
8
7
0
8
F
P
GA
imp
leme
n
ta
tio
n
o
f LDP
C
s
o
ft
-
d
ec
is
io
n
d
ec
o
d
ers
b
a
s
ed
DC
S
K
fo
r
s
p
r
ea
d
…
(
F
a
d
h
il
S
.
Ha
s
a
n
)
4803
Fo
r
ex
am
p
le,
th
e
Xilin
x
SG
d
esig
n
f
o
r
t
h
e
f
ir
s
t
r
o
w
will
b
e
im
p
lem
en
ted
b
y
u
s
i
n
g
M
u
l
t
a
n
d
A
d
d
-
S
u
b
b
l
o
c
k
a
c
c
o
r
d
i
n
g
t
o
(
20
)
-
(
23
)
a
s
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
1
8
.
T
h
e
d
e
t
a
i
l
s
f
o
r
e
a
c
h
o
n
e
o
f
t
h
e
b
l
o
c
k
s
i
n
F
i
g
u
r
e
1
8
ca
n
b
e
d
ec
lar
ed
in
F
ig
u
r
es
1
9
-
2
1
.
Fu
r
th
er
m
o
r
e
,
to
r
ed
u
ce
th
e
co
m
p
lex
ity
o
f
Xilin
x
SG
d
esig
n
r
elate
d
to
th
e
lo
g
ar
ith
m
(
l
o
g
)
p
r
o
ce
s
s
ac
co
r
d
in
g
to
(
21
)
,
a
lo
o
k
-
u
p
tab
le
is
p
r
o
p
o
s
ed
as illu
s
tr
ated
in
Fig
u
r
e
2
0
a
n
d
T
a
b
le
2
.
Fig
u
r
e
1
8
.
Ho
r
izo
n
tal
s
tep
f
o
r
th
e
f
ir
s
t r
o
w
Fig
u
r
e
1
9
.
T
h
e
PiS
b
lo
ck
o
f
th
e
f
i
r
s
t r
o
w
Fig
u
r
e
2
0
.
T
h
e
PiS
p
r
o
ce
s
s
b
lo
ck
o
f
Xilin
x
SG
Fig
u
r
e
2
1
.
Pr
b
lo
ck
d
etails
T
ab
le
2
.
T
h
e
v
alu
e
o
f
PiS
V
a
l
u
e
s
o
f
S
P
V
a
l
u
e
s
o
f
P
i
S
1
≤
S
P
≤
2
.
9
9
9
0
.
4
1
9
5
3
≤
S
P
≤
5
0
.
0
4
6
5
5
.
5
≤
S
P
≤
9
0
.
0
0
2
5
0
.
1
≤
S
P
≤
0
.
9
9
9
9
1
.
5
7
3
1
0
.
0
1
≤
S
P
≤
0
.
0
9
9
9
3
.
3
6
0
3
0
.
0
0
1
≤
S
P
<
0
.
0
0
9
9
9
9
6
.
1
5
3
2
0
.
0
0
0
1
≤
S
P
≤
0
.
0
0
0
9
9
9
9
7
.
9
9
1
7
0
.
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
9
9
9
9
1
0
.
7
5
8
3
0
.
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
9
9
9
9
1
2
.
2
4
2
8
0
.
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
9
9
9
9
1
5
.
3
6
3
5
0
.
0
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
0
9
9
9
9
1
6
.
6
1
5
8
0
.
0
0
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
0
0
9
9
9
9
1
9
.
9
6
8
4
0
.
0
0
0
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
0
0
0
9
9
9
9
2
1
.
4
7
4
1
0
.
0
0
0
0
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
0
0
0
0
9
9
9
9
2
3
.
1
0
7
0
0
.
0
0
0
0
0
0
0
0
0
0
0
1
≤
S
P
≤
0
.
0
0
0
0
0
0
0
0
0
0
0
9
9
9
9
2
6
.
8
7
6
4
El
se
2
8
.
8
2
6
1
Evaluation Warning : The document was created with Spire.PDF for Python.