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.
15
,
No
.
2
,
A
p
r
il
20
25
,
p
p
.
1
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5
4
~
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7
7
3
I
SS
N:
2
0
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8
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8
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,
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1
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1
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v
15
i
2
.
p
p
1
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4
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1
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7
3
1754
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Efficien
cy
of chan
nel codes
for dif
fe
rent
fading
mo
del
s in 5G
enha
nced mo
bile
bro
a
dba
nd scena
rio
M
ik
ha
il K
hm
elev
s
k
y
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,
G
enn
a
dy
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a
za
k
o
v
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e
p
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t
me
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t
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o
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En
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o
s
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v
i
a
t
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st
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e
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t
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n
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l
R
e
sea
r
c
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n
i
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si
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,
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o
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w
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ss
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icle
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nfo
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S
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RAC
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ticle
his
to
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y:
R
ec
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Ma
y
2
0
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2
0
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4
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ev
is
ed
Sep
1
8
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2
0
2
4
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ep
ted
Oct
1
,
2
0
2
4
In
u
r
b
a
n
e
n
v
i
r
o
n
m
e
n
ts
,
5
th
g
e
n
e
ra
t
io
n
(
5
G
)
si
g
n
a
ls
a
re
s
u
b
jec
t
t
o
in
t
e
rfe
re
n
c
e
,
m
u
lt
ip
le
p
ro
p
a
g
a
ti
o
n
a
n
d
th
e
rm
a
l
n
o
ise
,
re
su
lt
i
n
g
in
a
sig
n
ifi
c
a
n
t
a
m
o
u
n
t
o
f
e
rro
rs.
In
th
is
re
g
a
rd
,
c
h
a
n
n
e
l
c
o
d
in
g
is
a
p
p
li
e
d
,
wh
ich
a
ll
o
ws
to
i
n
c
re
a
se
th
e
re
li
a
b
il
it
y
o
f
th
e
tran
sm
it
te
d
m
e
ss
a
g
e
.
Th
is
wo
rk
f
o
c
u
se
s
o
n
c
o
m
p
a
rin
g
t
h
e
p
e
rfo
rm
a
n
c
e
o
f
lo
w
-
d
e
n
sity
p
a
rit
y
c
h
e
c
k
(LDP
C)
a
n
d
p
o
l
a
r
c
o
d
e
s
sta
n
d
a
rd
ize
d
b
y
t
h
e
3
rd
g
e
n
e
ra
ti
o
n
p
a
rtn
e
rsh
ip
p
r
o
jec
t
(
3
G
P
P
)
fo
r
a
p
p
li
c
a
ti
o
n
in
5
G
n
e
two
rk
s
in
p
h
y
sic
a
l
d
o
wn
li
n
k
sh
a
re
d
c
h
a
n
n
e
l
(P
DS
CH)
u
n
d
e
r
m
u
lt
ip
a
t
h
p
r
o
p
a
g
a
ti
o
n
c
o
n
d
i
ti
o
n
s
in
e
n
h
a
n
c
e
d
m
o
b
il
e
b
r
o
a
d
b
a
n
d
(e
M
BB)
sc
e
n
a
rio
.
Th
e
p
e
rfo
rm
a
n
c
e
o
f
th
e
c
o
d
e
s
u
n
d
e
r
stu
d
y
wa
s
in
v
e
stig
a
ted
c
o
n
sid
e
ri
n
g
a
ll
sig
n
a
l
p
ro
c
e
ss
in
g
o
p
e
ra
ti
o
n
s
im
p
lem
e
n
ted
in
h
a
rd
w
a
re
in
5
G
c
h
a
n
n
e
ls.
We
u
se
d
c
lu
ste
re
d
d
e
la
y
li
n
e
(CDL)
a
n
d
tap
p
e
d
d
e
lay
l
i
n
e
(TDL
)
m
o
d
e
ls
a
s
p
ro
p
a
g
a
ti
o
n
c
h
a
n
n
e
l
m
o
d
e
ls.
C
h
a
n
n
e
l
c
o
n
fi
g
u
ra
ti
o
n
a
n
d
se
lec
ti
o
n
o
f
sig
n
a
l
p
a
ra
m
e
ters
we
re
b
a
se
d
o
n
th
e
a
n
a
ly
sis
o
f
c
o
m
m
e
rc
ially
lau
n
c
h
e
d
5
G
n
e
two
rk
s.
On
e
o
f
th
e
sim
u
l
a
ti
o
n
s
re
su
lt
s
we
o
b
se
r
v
e
d
wa
s
th
e
h
i
g
h
sig
n
a
l
-
to
-
n
o
ise
ra
ti
o
(S
NR)
re
q
u
i
re
d
to
tran
sm
it
th
e
sig
n
a
l
wh
i
le
e
n
su
rin
g
a
g
iv
e
n
b
lo
c
k
e
rro
r
ra
te
(BL
ER).
P
o
lar
c
o
d
e
s
d
e
m
o
n
stra
ted
b
o
th
a
g
a
in
in
c
o
d
in
g
o
v
e
r
LDP
C
c
o
d
e
s
a
n
d
a
lo
ss
in
d
e
c
o
d
i
n
g
d
e
lay
o
f
t
h
e
re
c
e
i
v
e
d
sig
n
a
l
d
u
e
t
o
a
m
o
re
c
o
m
p
le
x
d
e
c
o
d
in
g
a
lg
o
rit
h
m
.
K
ey
w
o
r
d
s
:
B
lo
ck
er
r
o
r
r
ate
C
R
C
-
aid
ed
p
o
lar
co
d
es
Qu
asi cy
clic
lo
w
d
en
s
ity
p
ar
it
y
ch
ec
k
co
d
es
C
lu
s
ter
ed
d
elay
lin
e
T
ap
p
ed
d
elay
lin
e
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
:
Gen
n
ad
y
Kaz
ak
o
v
Dep
ar
tm
en
t o
f
T
h
eo
r
etica
l Rad
io
E
n
g
i
n
ee
r
in
g
,
Mo
s
co
w
Av
i
atio
n
I
n
s
titu
te
(
Natio
n
al
R
esear
ch
Un
iv
er
s
ity
)
Vo
lo
k
o
lam
s
k
o
e
Sh
o
s
s
e
4
,
1
2
5
9
9
3
Mo
s
co
w,
R
u
s
s
ia
E
m
ail: je
e2
@
m
ail.
r
u
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
5
th
g
e
n
er
atio
n
n
ew
r
ad
io
(
5
G
NR
)
tech
n
o
lo
g
y
is
r
ap
id
l
y
ev
o
lv
in
g
an
d
im
p
r
o
v
in
g
its
b
an
d
wid
th
,
en
er
g
y
ef
f
icien
c
y
an
d
f
lex
ib
i
lity
in
o
r
d
er
to
p
r
o
v
id
e
u
s
er
s
with
a
lar
g
er
s
et
o
f
s
er
v
ices
an
d
ap
p
licatio
n
s
.
I
n
ter
n
atio
n
al
T
elec
o
m
m
u
n
icat
io
n
Un
io
n
(
I
T
U)
r
ec
o
m
m
en
d
a
tio
n
M.
2
0
8
3
[
1
]
h
as
d
e
f
in
ed
th
r
ee
5
G
ap
p
licatio
n
s
ce
n
ar
io
s
:
en
h
an
ce
d
m
o
b
ile
b
r
o
ad
b
an
d
(
eM
B
B
)
,
m
ass
iv
e
m
ac
h
in
e
ty
p
e
c
o
m
m
u
n
icatio
n
s
(
m
MT
C
)
an
d
u
ltra
-
r
eliab
le
an
d
lo
w
laten
c
y
co
m
m
u
n
icatio
n
s
(
UR
L
L
C
)
.
T
h
u
s
,
f
o
r
eM
B
B
,
th
e
im
p
o
r
tan
t
m
etr
ic
is
th
e
u
ltima
te
tr
an
s
m
is
s
io
n
s
p
ee
d
;
UR
L
L
C
r
eq
u
ir
es
lo
w
laten
cy
(
less
th
an
1
m
s
)
a
n
d
ex
t
r
em
ely
h
ig
h
r
eliab
ilit
y
(
9
9
.
9
9
9
%);
m
MT
C
em
p
h
asizes
h
ig
h
co
n
n
ec
tiv
ity
d
en
s
ity
an
d
d
ev
ice
en
e
r
g
y
e
f
f
icien
cy
.
I
n
th
e
cu
r
r
e
n
t
p
h
ase
o
f
5
G
d
e
p
lo
y
m
e
n
t,
th
e
f
o
cu
s
is
o
n
t
h
e
eM
B
B
u
s
ag
e
s
ce
n
ar
io
.
Hig
h
-
s
p
ee
d
an
d
h
ig
h
-
q
u
ality
m
u
ltime
d
ia
s
er
v
ices
lik
e
v
ir
tu
al
r
ea
lity
(
VR
)
,
au
g
m
en
ted
r
ea
lity
(
AR
)
,
h
ig
h
-
r
eso
lu
tio
n
v
id
e
o
ar
e
av
ailab
le
to
u
s
er
s
th
r
o
u
g
h
t
h
e
eM
B
B
s
er
v
ices.
T
h
e
eM
B
B
s
ce
n
ar
io
s
h
o
u
ld
s
u
p
p
o
r
t
a
wid
e
r
a
n
g
e
o
f
co
d
e
r
ates,
d
if
f
er
e
n
t
co
d
e
len
g
th
s
an
d
m
o
d
u
latio
n
o
r
d
er
s
.
C
o
m
p
ar
ed
to
4
th
g
e
n
er
atio
n
lo
n
g
-
ter
m
ev
o
lu
tio
n
(
4
G
L
T
E
)
,
th
e
d
is
tin
ctiv
e
f
ea
tu
r
e
o
f
5
G
NR
is
th
e
u
s
e
o
f
two
n
ew
er
r
o
r
-
co
r
r
ec
tin
g
ch
an
n
el
co
d
es.
L
o
w
-
d
en
s
ity
p
ar
ity
ch
ec
k
(
L
DPC
)
co
d
es
h
av
e
r
ep
lace
d
t
u
r
b
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
E
fficien
cy
o
f c
h
a
n
n
el
co
d
es fo
r
d
iffer
en
t fa
d
in
g
mo
d
els in
5
G
en
h
a
n
ce
d
…
(
Gen
n
a
d
y
K
a
z
a
ko
v
)
1755
co
d
es
in
u
s
er
d
ata
ch
a
n
n
els
a
n
d
p
o
lar
co
d
es
h
av
e
r
ep
lace
d
tail
-
b
itin
g
co
n
v
o
lu
tio
n
al
c
o
d
e
s
(
T
B
C
C
)
in
co
n
tr
o
l
ch
an
n
els
to
im
p
r
o
v
e
d
ata
r
ate
an
d
p
r
o
v
id
e
ac
ce
p
tab
le
e
r
r
o
r
co
r
r
ec
tio
n
p
e
r
f
o
r
m
an
ce
[
2
]
.
L
DPC
,
tu
r
b
o
c
o
d
es
an
d
p
o
la
r
co
d
es
h
a
v
e
s
im
ilar
ch
an
n
el
p
er
f
o
r
m
an
ce
f
o
r
d
ata
in
ten
s
iv
e
ap
p
licatio
n
s
,
w
h
ile
L
DPC
is
le
s
s
co
m
p
lex
to
im
p
lem
en
t.
T
h
e
s
y
s
tem
's
p
er
f
o
r
m
an
ce
is
im
p
r
o
v
ed
o
v
er
o
t
h
er
m
o
d
e
r
n
ch
an
n
el
co
d
es
(
T
B
C
C
an
d
tu
r
b
o
c
o
d
es)
wh
en
c
o
m
b
in
i
n
g
cy
clic
r
ed
u
n
d
an
cy
ch
ec
k
(
C
R
C
)
co
d
es
with
p
o
lar
co
d
es
th
at
ar
e
d
ec
o
d
e
d
u
s
in
g
th
e
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
lis
t
(
SC
L
)
alg
o
r
ith
m
.
Nev
e
r
th
el
ess
,
p
o
lar
co
d
in
g
is
less
ef
f
icien
t
th
an
L
DPC
f
o
r
h
ig
h
d
ata
r
ates.
T
h
e
m
ain
g
o
al
o
f
th
is
wo
r
k
was
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
elec
ted
ch
a
n
n
el
c
o
d
es
u
n
d
e
r
p
h
y
s
ical
d
o
wn
lin
k
s
h
a
r
ed
ch
an
n
el
(
PDSC
H)
s
ig
n
al
an
d
en
v
ir
o
n
m
en
tal
p
ar
am
eter
s
ap
p
r
o
x
im
atin
g
th
o
s
e
r
ea
lized
b
y
t
h
e
lead
in
g
o
p
e
r
ato
r
s
o
f
5
G
c
o
m
m
u
n
icatio
n
n
etwo
r
k
s
.
Fro
m
th
is
,
it
is
p
o
s
s
ib
le
to
d
er
iv
e
esti
m
atio
n
s
o
f
th
e
s
ig
n
al
-
to
-
n
o
is
e
r
atio
(
SNR
)
v
alu
es
th
at
a
r
e
m
o
r
e
lik
ely
to
b
e
ex
p
e
r
ien
ce
d
b
y
u
s
er
s
f
r
o
m
5
G
s
y
s
tem
s
.
A
s
co
m
p
ar
ed
to
th
e
s
ig
n
al
p
ar
am
eter
s
th
at
h
av
e
b
ee
n
ar
b
itra
r
ily
estab
lis
h
ed
b
y
o
t
h
er
r
esear
ch
er
s
.
T
h
is
p
ap
er
p
r
esen
ts
an
ev
alu
atio
n
o
f
th
e
p
er
f
o
r
m
a
n
ce
o
f
p
o
la
r
an
d
L
DPC
co
d
es
in
a
PDSC
H
ch
an
n
el
f
o
r
s
ev
er
al
in
f
o
r
m
atio
n
b
lo
c
k
s
izes.
W
e
wo
u
ld
lik
e
to
em
p
h
asize
th
at
th
is
s
tu
d
y
o
f
s
elec
ted
co
d
es
h
as
b
ee
n
p
er
f
o
r
m
ed
co
n
s
id
er
i
n
g
all
s
ig
n
al
p
r
o
ce
s
s
in
g
o
p
er
atio
n
s
p
er
f
o
r
m
ed
in
5
G
p
h
y
s
ical
ch
an
n
el
s
.
I
n
o
u
r
wo
r
k
,
we
u
s
ed
m
u
ltip
ath
p
r
o
p
ag
atio
n
ch
an
n
el
m
o
d
els
s
u
ch
as
tap
p
e
d
d
elay
lin
e
(
T
DL
)
an
d
clu
s
ter
e
d
d
elay
lin
e
(
C
DL
)
.
T
h
e
ap
p
licatio
n
o
f
th
ese
m
o
d
els
allo
ws
u
s
to
o
b
tain
SNR
esti
m
ates
clo
s
er
to
th
e
r
ea
l
o
n
e
s
th
an
wh
en
u
s
in
g
R
ice/Re
illy
ch
an
n
els.
T
DL
-
A
an
d
C
DL
-
A
ch
a
n
n
els
wer
e
u
s
ed
in
th
e
ca
s
e
o
f
lin
e
o
f
s
ig
h
t
(
L
OS)
,
T
DL
-
D
a
n
d
C
DL
-
D
in
th
e
ca
s
e
o
f
n
o
n
-
lin
e
-
of
-
s
ig
h
t
(
NL
OS)
.
T
h
e
co
m
p
ar
is
o
n
was
m
ad
e
o
n
t
h
e
tar
g
et
p
ar
am
eter
o
f
b
lo
ck
er
r
o
r
r
ate
(
B
L
E
R
)
f
r
o
m
t
h
e
s
y
m
b
o
l SNR
.
I
n
r
ec
en
t
y
ea
r
s
,
m
an
y
o
b
s
er
v
e
d
a
s
h
ar
p
in
cr
ea
s
e
in
r
esear
ch
d
ev
o
ted
to
th
e
s
tu
d
y
o
f
th
e
ef
f
ec
tiv
en
ess
o
f
L
DPC
an
d
p
o
lar
co
d
es,
a
s
well
as
th
e
s
ea
r
ch
f
o
r
ef
f
i
cien
t
en
co
d
e
r
s
an
d
d
ec
o
d
e
r
s
th
at
ca
n
p
r
o
v
id
e
a
co
m
p
r
o
m
is
e
b
etwe
en
th
e
r
e
q
u
ir
ed
h
ig
h
p
er
f
o
r
m
an
ce
an
d
th
r
o
u
g
h
p
u
t
a
n
d
l
o
w
h
ar
d
war
e
c
o
m
p
lex
ity
,
c
o
s
t
an
d
p
o
wer
co
n
s
u
m
p
tio
n
.
Fo
r
ex
a
m
p
le,
Hu
i
et
a
l.
[
3
]
d
escr
ib
es L
DPC
an
d
p
o
lar
co
d
es a
d
o
p
ted
b
y
th
e
s
tan
d
ar
d
an
d
5
G
NR
,
th
e
p
ec
u
liar
ities
o
f
th
eir
ap
p
licatio
n
.
T
h
e
p
e
r
f
o
r
m
an
ce
ad
v
an
tag
es
o
f
th
e
n
ewly
ap
p
lied
co
d
es
ar
e
co
m
p
ar
ed
with
t
h
e
ch
ar
ac
ter
i
s
tics
o
f
th
e
co
d
es
u
s
ed
in
th
e
lo
n
g
-
ter
m
e
v
o
lu
tio
n
(
LTE
)
.
A
co
m
p
r
eh
e
n
s
iv
e
r
ev
iew
o
f
th
e
m
ain
c
h
an
n
el
c
o
d
es
ad
o
p
ted
s
in
ce
th
e
th
ir
d
g
en
er
atio
n
o
f
m
o
b
ile
co
m
m
u
n
i
ca
tio
n
s
is
p
r
esen
ted
in
th
e
b
o
o
k
[
4
]
,
w
h
er
e
th
e
r
es
u
lts
o
f
th
e
s
tu
d
y
o
f
th
eir
a
p
p
li
ca
tio
n
p
er
f
o
r
m
a
n
ce
ar
e
also
p
r
esen
ted
.
R
ich
ar
d
s
o
n
an
d
Ku
d
ek
ar
[
5
]
r
ev
iewe
d
th
e
ch
an
n
el
co
d
e
r
eq
u
ir
em
en
ts
f
o
r
5
G
NR
.
I
n
n
o
v
atio
n
s
in
L
DPC
co
d
es
th
at
f
u
lf
il
th
e
r
eq
u
ir
e
m
en
ts
o
f
5
G
NR
ar
e
p
r
esen
ted
an
d
ex
p
lain
ed
.
E
f
f
icien
cy
o
f
ch
an
n
el
c
o
d
es
a
p
p
licatio
n
is
an
aly
ze
d
in
[
6
]
,
wh
er
e
d
ep
en
d
en
ce
s
o
f
b
l
o
ck
tr
an
s
m
is
s
io
n
er
r
o
r
p
r
o
b
a
b
ilit
ies
o
n
s
y
m
b
o
l
s
ig
n
al
-
to
-
n
o
is
e
r
atio
ar
e
p
r
e
s
en
ted
f
o
r
a
n
u
m
b
e
r
o
f
s
ets
o
f
co
d
i
n
g
m
eth
o
d
s
(
tu
r
b
o
co
d
es,
p
o
lar
co
d
es
a
n
d
L
DPC
)
an
d
c
o
d
e
-
m
o
d
u
lati
o
n
s
ch
em
es
at
a
v
er
ag
e
co
d
e
wo
r
d
len
g
th
(
a
b
o
u
t
th
o
u
s
an
d
s
o
f
b
its
)
.
Č
ar
ap
ić
et
a
l
.
[
7
]
co
n
d
u
cted
co
m
p
ar
ed
s
im
u
latio
n
s
tu
d
ies
o
n
th
e
u
s
e
o
f
L
DPC
an
d
p
o
lar
co
d
es
f
o
r
m
ess
ag
e
tr
an
s
m
is
s
io
n
th
r
o
u
g
h
v
ar
io
u
s
ch
an
n
el
m
o
d
els
lik
e
th
e
ad
d
itiv
e
w
h
ite
Gau
s
s
ian
n
o
is
e
(
AW
GN)
ch
an
n
el,
R
ice
an
d
R
ay
leig
h
m
o
d
els.
T
h
e
s
im
u
latio
n
r
esu
lts
r
ef
lect
th
e
ch
ar
ac
ter
is
tics
o
f
L
DP
C
an
d
p
o
lar
c
o
d
es
in
th
e
ca
s
e
o
f
ch
a
n
n
el
m
o
d
els:
AW
GN
ch
an
n
el
with
o
u
t
f
ad
in
g
an
d
AW
GN
ch
an
n
el
with
f
ad
in
g
.
I
n
[
8
]
,
an
o
v
er
v
iew
o
f
th
e
co
d
in
g
/d
ec
o
d
i
n
g
p
r
o
ce
s
s
in
5
G
N
R
is
g
iv
en
an
d
a
c
o
m
p
ar
is
o
n
o
f
th
e
ap
p
lie
d
co
d
es
is
m
ad
e
th
r
o
u
g
h
b
it
er
r
o
r
r
ate
(
B
E
R
)
an
d
B
L
E
R
p
er
f
o
r
m
an
ce
.
T
ah
ir
et
a
l
.
[
9
]
e
x
am
in
es
h
o
w
co
n
v
o
lu
tio
n
al
co
d
es,
tu
r
b
o
c
o
d
es,
L
DPC
co
d
es,
an
d
p
o
lar
co
d
es
p
er
f
o
r
m
in
ter
m
s
o
f
b
it
er
r
o
r
r
ate
f
o
r
m
u
ltip
le
ap
p
licatio
n
s
ce
n
ar
io
s
with
v
ar
y
in
g
i
n
f
o
r
m
atio
n
b
lo
ck
len
g
th
s
an
d
co
d
e
r
ates.
C
o
m
p
ar
ativ
e
an
aly
s
i
s
o
f
p
er
f
o
r
m
an
ce
o
f
ad
v
an
ce
d
tu
r
b
o
c
o
d
es
with
lis
t
d
ec
o
d
in
g
a
n
d
p
o
lar
co
d
es
with
s
u
p
p
o
r
t
o
f
C
R
C
co
d
es
wi
th
lis
t
d
ec
o
d
in
g
u
n
d
er
AW
GN
co
n
d
itio
n
s
f
o
r
s
h
o
r
t
b
lo
ck
s
o
f
in
f
o
r
m
atio
n
at
lo
w
co
d
e
r
ates u
s
in
g
B
L
E
R
as a
m
ea
s
u
r
e
o
f
ef
f
icien
cy
is
p
r
esen
ted
in
[
1
0
]
.
C
u
c
et
a
l
.
[
1
1
]
p
er
f
o
r
m
e
d
a
co
m
p
a
r
ativ
e
a
n
aly
s
is
o
f
L
DPC
an
d
p
o
lar
co
d
es in
ter
m
s
o
f
th
eir
p
er
f
o
r
m
an
ce
,
d
ef
in
ed
b
y
a
n
aly
zin
g
B
E
R
v
er
s
u
s
SNR
in
AW
GN
ch
an
n
el.
T
h
e
task
o
f
m
an
y
wo
r
k
s
was
to
ev
alu
ate
a
n
d
c
o
m
p
ar
e
th
e
ef
f
ec
tiv
en
ess
o
f
u
s
in
g
o
n
e
o
r
m
o
r
e
co
d
in
g
tech
n
o
lo
g
ies
in
th
e
co
m
m
u
n
ic
atio
n
s
y
s
tem
o
f
a
ce
r
tain
ty
p
e
o
r
s
tan
d
ar
d
.
Fo
r
ex
am
p
le,
El
-
E
b
b
asy
et
a
l
.
[
1
2
]
co
n
s
id
er
ed
th
e
p
o
s
s
ib
ilit
y
o
f
u
s
in
g
p
o
lar
co
d
es
with
SC
L
d
ec
o
d
er
s
in
d
ig
ital
v
id
eo
b
r
o
ad
ca
s
tin
g
(
DVB)
s
y
s
tem
s
,
co
m
p
ar
ed
th
e
ef
f
icie
n
cy
o
f
p
o
lar
co
d
es
a
n
d
L
DPC
co
d
es
in
te
r
m
s
o
f
B
E
R
,
en
co
d
er
/d
ec
o
d
er
d
elay
an
d
th
r
o
u
g
h
p
u
t.
T
h
e
B
L
E
R
m
etr
ic
was
u
s
ed
in
[
1
3
]
to
ev
alu
ate
d
if
f
er
en
t
ch
an
n
el
co
d
in
g
m
eth
o
d
s
th
at
ca
n
b
e
im
p
lem
en
ted
in
I
n
s
titu
te
o
f
E
l
ec
tr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
s
(
I
E
E
E
)
s
tan
d
ar
d
8
0
2
.
1
1
b
.
Am
o
n
g
th
e
m
er
its
o
f
th
e
w
o
r
k
ar
e
b
o
th
t
h
e
co
n
s
id
er
atio
n
o
f
ac
tu
al
co
d
in
g
tech
n
iq
u
es
u
s
ed
i
n
o
th
e
r
s
tan
d
ar
d
s
(
5
G
NR
p
o
lar
co
d
e
an
d
L
T
E
tu
r
b
o
co
d
es)
an
d
th
e
co
m
p
a
r
is
o
n
o
f
ef
f
icien
cy
b
ased
o
n
s
im
u
latio
n
r
es
u
lts
u
n
d
er
d
i
f
f
er
en
t
p
r
o
p
a
g
atio
n
ch
a
n
n
el
m
o
d
els.
T
h
e
au
th
o
r
s
o
f
a
lar
g
e
n
u
m
b
er
o
f
ar
ticles
d
ev
o
ted
to
th
e
p
ec
u
liar
ities
an
d
ef
f
icien
cy
o
f
ch
an
n
el
co
d
in
g
ap
p
licatio
n
in
5
G
N
R
n
etwo
r
k
s
d
well
o
n
a
s
p
ec
if
ic
s
ce
n
ar
io
o
r
ap
p
licatio
n
ar
ea
.
Fo
r
ex
am
p
le,
C
h
atzo
u
lis
et
a
l.
[
1
4
]
s
tu
d
ie
d
an
d
ev
al
u
ated
th
e
ef
f
ec
tiv
e
n
ess
o
f
5
G
NR
tu
r
b
o
c
o
d
es,
p
o
la
r
co
d
es
a
n
d
L
DPC
co
d
es
o
n
th
e
q
u
ality
o
f
s
er
v
i
ce
(
Qo
S)
u
n
d
er
th
e
e
n
v
ir
o
n
m
en
t
p
ar
am
eter
s
ch
ar
ac
ter
is
tic
o
f
th
e
v
eh
icle
-
to
-
ev
er
y
th
in
g
(
V2
X)
c
o
m
m
u
n
ica
tio
n
s
y
s
tem
.
T
h
u
s
,
in
a
d
d
itio
n
to
ev
alu
atin
g
a
n
u
m
b
er
o
f
c
o
d
in
g
s
ch
em
es
an
d
m
o
d
elin
g
s
ce
n
ar
io
s
b
ased
o
n
t
h
e
f
r
a
m
e
er
r
o
r
r
ate
(
FER)
p
ar
am
eter
(
s
im
ilar
to
B
L
E
R
)
,
th
e
r
esear
ch
er
s
s
tu
d
ie
d
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
7
5
4
-
1
7
7
3
1756
a
s
et
o
f
o
th
er
p
ar
am
eter
s
(
m
in
im
u
m
r
eq
u
ir
e
d
SNR
,
an
d
tr
an
s
m
it
p
o
wer
)
n
ec
ess
ar
y
to
r
ea
lize
Qo
S
o
f
a
ce
r
tain
q
u
ality
.
I
n
th
e
p
ap
er
[
1
5
]
,
b
ased
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
b
lo
c
k
e
r
r
o
r
r
ate
(
B
L
E
R
)
a
n
d
c
o
m
p
u
tatio
n
al
co
m
p
lex
ity
,
th
e
ef
f
ec
ti
v
en
ess
o
f
a
n
u
m
b
er
o
f
ch
an
n
el
co
d
in
g
s
ch
em
es
(
tu
r
b
o
,
L
DPC
co
d
es,
p
o
lar
an
d
co
n
v
o
l
u
tio
n
al
co
d
es)
f
o
r
UR
L
L
C
s
ce
n
ar
io
in
5
G
NR
is
in
v
e
s
tig
ated
.
I
n
[
1
6
]
,
a
s
tu
d
y
o
f
p
o
lar
co
d
e
in
eM
B
B
5
G
NR
s
ce
n
ar
io
was
ca
r
r
ied
o
u
t
f
o
r
b
o
th
Up
lin
k
an
d
d
o
w
n
lin
k
co
n
tr
o
l
in
f
o
r
m
atio
n
(
UC
I
an
d
DC
I
)
s
ig
n
als
an
d
b
r
o
a
d
ca
s
t
ch
an
n
el,
in
a
tr
an
s
m
is
s
io
n
ch
an
n
el
with
AW
G
N.
T
h
e
r
esu
lts
o
b
tain
ed
wer
e
p
r
esen
ted
u
s
in
g
th
e
B
E
R
p
ar
am
eter
.
A
s
im
ilar
s
tu
d
y
was
co
n
d
u
cted
in
[
1
7
]
,
wh
er
e
in
th
e
ca
s
e
o
f
a
5
G
NR
d
o
wn
lin
k
lin
e
s
y
s
tem
f
o
r
d
if
f
er
e
n
t
q
u
a
d
r
atu
r
e
am
p
li
tu
d
e
m
o
d
u
latio
n
(
QAM
)
s
ch
e
m
es,
th
e
ef
f
ec
ti
v
en
ess
o
f
a
p
p
l
y
in
g
th
e
o
r
t
h
o
g
o
n
al
tim
e
f
r
eq
u
en
c
y
s
p
ac
e
(
OT
F
S)
wav
ef
o
r
m
to
th
e
o
r
t
h
o
g
o
n
al
f
r
eq
u
en
cy
-
d
iv
is
io
n
m
u
l
tip
lex
in
g
(
OFDM)
wav
ef
o
r
m
was
co
m
p
ar
ed
f
o
r
T
DL
an
d
C
DL
ch
an
n
el
p
r
o
p
ag
atio
n
m
o
d
els
co
n
s
id
er
i
n
g
th
e
ap
p
licatio
n
o
f
m
in
im
u
m
m
ea
n
s
q
u
ar
e
e
r
r
o
r
(
MM
SE)
an
d
d
ec
is
io
n
f
ee
d
b
ac
k
eq
u
alize
r
s
(
DFE)
.
C
u
c
et
a
l
.
[
1
8
]
p
r
esen
ted
s
im
u
latio
n
r
esu
lts
in
t
h
e
f
o
r
m
o
f
a
n
u
m
b
er
o
f
B
E
R
ch
ar
ac
ter
is
tics
r
elate
d
t
o
tu
r
b
o
co
d
es,
L
DPC
co
d
es
an
d
p
o
lar
co
d
es
in
a
ch
an
n
el
with
ad
d
itiv
e
wh
ite
Gau
s
s
ian
n
o
is
e
in
th
e
p
r
esen
ce
o
f
in
ter
-
s
y
m
b
o
l
in
ter
f
er
en
ce
.
Se
v
er
al
ty
p
es
o
f
eq
u
alize
r
s
(
ze
r
o
-
f
o
r
ci
n
g
an
d
MM
SE)
h
av
e
b
ee
n
ap
p
lied
at
th
e
r
ec
eiv
in
g
en
d
to
elim
in
ate
th
e
n
eg
ativ
e
ef
f
ec
ts
o
f
in
ter
f
er
en
c
e.
A
n
u
m
b
er
o
f
s
tu
d
ies
[
1
9
]
–
[
2
1
]
wer
e
d
e
v
o
ted
to
co
m
p
ar
in
g
an
d
an
aly
zin
g
th
e
ef
f
icien
cy
o
f
ch
an
n
el
c
o
d
es
(
tu
r
b
o
co
d
es,
p
o
lar
c
o
d
es
a
n
d
o
th
e
r
s
)
,
m
ain
ly
th
r
o
u
g
h
th
e
B
E
R
an
d
B
L
E
R
ch
ar
ac
ter
is
tics
.
I
n
Sh
ao
e
t
a
l
.
[
2
2
]
r
ef
lecte
d
m
an
y
asp
ec
ts
af
f
ec
tin
g
th
e
im
p
lem
en
tatio
n
co
m
p
le
x
ity
o
f
tu
r
b
o
d
ec
o
d
er
s
,
L
DPC
a
n
d
p
o
lar
d
ec
o
d
er
s
.
L
ater
,
th
e
th
r
o
u
g
h
p
u
t,
er
r
o
r
co
r
r
ec
tio
n
ca
p
a
b
ilit
y
,
f
lex
ib
ilit
y
,
ar
ea
ef
f
icien
cy
an
d
en
er
g
y
ef
f
icien
cy
o
f
im
p
lem
en
tat
io
n
o
n
ap
p
licatio
n
-
s
p
ec
if
ic
in
teg
r
ated
cir
cu
it
(
ASI
C
)
wer
e
co
m
p
ar
e
d
.
A
d
etailed
an
aly
s
is
o
f
th
e
f
ea
t
u
r
es
o
f
p
o
lar
co
d
es
a
p
p
licatio
n
in
5
G
NR
is
p
r
esen
ted
in
[
2
3
]
.
Usi
n
g
B
L
E
R
an
d
f
alse
-
alar
m
-
r
ate
(
FAR
)
ch
ar
ac
ter
is
tics
,
th
e
co
r
r
ec
tiv
e
ab
ilit
y
was
ev
alu
ated
an
d
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
p
o
lar
c
o
d
es
was
co
m
p
ar
ed
with
L
DPC
co
d
es.
B
elh
ad
j
an
d
Ab
d
elm
o
u
n
aim
[
2
4
]
ex
am
in
ed
th
e
er
r
o
r
co
r
r
ec
tio
n
p
er
f
o
r
m
an
ce
o
f
p
o
lar
a
n
d
L
DPC
co
d
e
co
d
i
n
g
s
ch
em
es
wh
e
n
tr
a
n
s
m
itti
n
g
s
h
o
r
t
an
d
m
ed
iu
m
in
f
o
r
m
atio
n
b
lo
c
k
s
b
y
em
p
lo
y
in
g
B
L
E
R
an
d
B
E
R
m
etr
ics.
Kh
an
et
a
l
.
[
2
5
]
in
v
esti
g
ate
d
L
DPC
an
d
p
o
lar
co
d
es
in
ter
m
s
o
f
th
e
f
r
a
m
e
er
r
o
r
r
ate
(
FER)
p
ar
am
eter
,
wh
ich
is
ess
en
tially
th
e
s
a
m
e
as
B
L
E
R
,
wh
en
tr
an
s
m
itti
n
g
s
h
o
r
t
an
d
m
ed
iu
m
len
g
th
m
ess
ag
es,
co
n
s
id
er
e
d
m
u
ltip
le
d
ec
o
d
in
g
im
p
lem
e
n
tatio
n
s
ch
em
es
an
d
co
m
p
ar
ed
th
e
er
r
o
r
c
o
r
r
ec
tio
n
p
er
f
o
r
m
an
ce
o
v
er
th
e
ch
an
n
el
with
AW
GN.
I
n
m
an
y
o
f
th
e
wo
r
k
s
lis
ted
ab
o
v
e,
th
e
s
tu
d
y
o
f
th
e
ap
p
lica
tio
n
o
f
ce
r
tain
co
d
es
was
ca
r
r
ied
o
u
t
in
th
e
co
n
d
itio
n
s
o
f
t
h
e
AW
GN
ch
an
n
el
o
n
ly
,
with
o
u
t
tak
i
n
g
in
to
ac
co
u
n
t
m
u
ltip
ath
ef
f
ec
ts
.
I
n
n
u
m
er
o
u
s
p
u
b
licatio
n
s
,
th
e
e
f
f
icien
cy
o
f
co
d
es
ap
p
licatio
n
was
m
ad
e
th
r
o
u
g
h
th
e
p
ar
am
eter
o
f
B
E
R
,
in
co
m
p
ar
is
o
n
with
wh
ich
s
u
ch
a
p
ar
am
eter
,
as
B
L
E
R
,
ca
n
h
a
v
e
m
o
r
e
v
a
lu
e,
b
ec
au
s
e
b
its
o
n
th
e
r
ec
eiv
in
g
s
id
e
a
r
e
also
d
ec
o
d
ed
b
y
b
lo
ck
s
.
T
h
e
r
esear
ch
p
r
esen
ted
in
t
h
is
p
ap
er
,
p
ar
t
icu
lar
ly
th
e
ca
lcu
latio
n
a
n
d
s
el
ec
tio
n
o
f
th
e
b
asic
p
ar
am
eter
s
o
f
th
e
PDSC
H
s
ig
n
al
an
d
th
e
s
ize
o
f
th
e
t
r
an
s
m
itted
b
lo
ck
s
,
was
co
n
d
u
cted
with
r
ef
er
en
ce
to
t
h
e
r
ea
lized
5
G
NR
n
etwo
r
k
s
,
alth
o
u
g
h
with
a
n
u
m
b
e
r
o
f
ass
u
m
p
tio
n
s
.
An
o
th
e
r
im
p
o
r
tan
t d
if
f
er
en
ce
o
f
th
is
wo
r
k
is
th
at
th
e
ev
alu
atio
n
o
f
th
e
e
f
f
icien
cy
o
f
p
o
lar
a
n
d
L
DPC
co
d
es
was
ca
r
r
ied
o
u
t
with
th
e
ap
p
licatio
n
o
f
all
s
tan
d
ar
d
ized
i
n
ter
leav
in
g
o
p
e
r
atio
n
s
an
d
C
R
C
ad
d
itio
n
,
p
er
f
o
r
m
e
d
at
th
e
lev
el
o
f
th
e
tr
an
s
m
is
s
io
n
lin
e
co
n
n
ec
tio
n
o
n
th
e
ex
am
p
le
o
f
a
PDSC
H
s
ig
n
al.
I
n
th
is
s
tu
d
y
,
th
e
T
DL
an
d
C
DL
m
u
l
tip
ath
p
r
o
p
ag
atio
n
m
o
d
els
r
ec
o
m
m
en
d
e
d
b
y
3
rd
g
en
er
atio
n
p
ar
tn
e
r
s
h
ip
p
r
o
ject
(
3
GPP)
in
tech
n
ical
r
ep
o
r
t
(
T
R
)
3
8
.
9
0
1
[
2
6
]
wer
e
ap
p
lied
to
ac
c
o
u
n
t f
o
r
th
e
ef
f
e
cts o
f
f
ad
in
g
in
th
e
tr
a
n
s
m
is
s
i
o
n
ch
a
n
n
el,
in
a
d
d
itio
n
t
o
AW
GN.
T
h
e
r
em
ain
d
er
o
f
th
is
p
a
p
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws.
Sectio
n
2
p
r
esen
ts
a
b
r
ief
d
escr
ip
tio
n
o
f
L
DPC
an
d
p
o
lar
co
d
es
an
d
t
h
e
co
d
in
g
s
ch
em
es
u
s
ed
i
n
5
G
NR
c
h
an
n
els.
Sectio
n
3
d
escr
ib
es
t
h
e
m
etr
ics
u
s
ed
to
ev
alu
ate
th
e
co
d
in
g
ef
f
icien
c
y
.
Sectio
n
4
is
d
ev
o
te
d
to
th
e
d
escr
ip
tio
n
o
f
th
e
5
G
NR
p
r
o
p
a
g
atio
n
c
h
an
n
e
l
m
o
d
els.
T
h
e
m
eth
o
d
o
lo
g
y
o
f
th
e
s
tu
d
y
an
d
th
e
ca
lcu
lati
o
n
s
o
f
th
e
p
a
r
am
eter
s
r
eq
u
ir
ed
to
p
er
f
o
r
m
th
e
m
o
d
elin
g
ar
e
p
r
esen
ted
i
n
d
etail
in
s
ec
tio
n
5
,
wh
ile
s
ec
t
io
n
6
p
r
esen
ts
th
e
m
ain
r
esu
lts
o
f
th
e
s
tu
d
y
.
A
d
is
cu
s
s
io
n
o
f
th
e
r
esu
lts
an
d
c
o
n
clu
d
in
g
co
m
m
en
ts
ar
e
f
o
r
m
u
lated
in
s
ec
tio
n
7
.
2.
CO
DING
SCH
E
M
E
S AP
P
L
I
E
D
I
N
5
G
NR
T
h
e
d
ata
lin
k
lay
er
o
f
5
G
NR
3
GPP
s
tan
d
ar
d
s
in
clu
d
es
th
e
u
s
e
o
f
L
DPC
co
d
es
f
o
r
d
o
wn
l
in
k
s
h
ar
ed
ch
an
n
el
(
DL
-
SC
H)
an
d
u
p
li
n
k
s
h
ar
e
d
ch
a
n
n
el
(
UL
-
SC
H)
,
wh
ich
h
av
e
co
r
r
esp
o
n
d
i
n
g
p
h
y
s
ical
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2
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r
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el
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n
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n
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er
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PDS
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ical
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e
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d
u
latio
n
tech
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f
o
r
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ical
Evaluation Warning : The document was created with Spire.PDF for Python.
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f
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2
.
1
.
L
DP
C
co
des
L
DPC
co
d
es
wer
e
f
ir
s
t
p
r
ese
n
ted
b
y
Gallag
er
[
2
7
]
,
b
u
t
th
ey
wer
e
n
o
t
u
s
ed
in
th
eir
tim
e
an
d
wer
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f
o
r
g
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tte
n
f
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alm
o
s
t
4
0
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ea
r
s
.
Du
e
to
th
e
ad
v
an
ce
m
en
t
o
f
c
o
m
p
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ter
tech
n
o
lo
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d
n
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m
m
u
n
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L
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d
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o
m
e
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FEC)
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d
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s
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o
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th
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r
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p
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r
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r
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c
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tio
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t
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r
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an
d
h
i
g
h
p
ar
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m
in
d
ec
o
d
in
g
im
p
le
m
en
tatio
n
.
R
ec
en
tly
,
L
DPC
co
d
es
h
av
e
b
ee
n
u
s
ed
in
m
an
y
m
o
d
er
n
telec
o
m
m
u
n
icatio
n
tech
n
o
lo
g
ies,
s
u
ch
as
DVB
-
S2
,
DVB
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T
2
,
DVB
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C
2
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I
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3
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,
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1
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1
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e.
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d
es
d
em
o
n
s
tr
ate
h
i
g
h
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f
f
icie
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ter
m
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o
f
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it
er
r
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r
p
r
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b
a
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ilit
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wh
ich
is
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e
r
y
clo
s
e
to
th
e
Sh
an
n
o
n
lim
it (
0
.
6
-
0
.
8
d
B
lo
s
s
f
o
r
lo
n
g
er
m
ess
ag
e
len
g
th
s
)
.
L
DPC
co
d
es
ar
e
lin
ea
r
b
lo
ck
co
d
es
(
,
)
d
ef
in
e
d
b
y
m
ea
n
s
o
f
p
ar
ity
ch
ec
k
m
atr
ix
(
PC
M)
ch
ar
ac
ter
ized
b
y
r
elativ
ely
s
m
all
n
u
m
b
er
o
f
‘
1
’
in
r
o
ws an
d
co
lu
m
n
s
.
Sp
ar
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ity
o
f
‘
1
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r
o
v
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es lo
w
co
m
p
lex
ity
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f
c
o
d
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g
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d
d
ec
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d
i
n
g
.
An
e
x
am
p
le
o
f
th
e
m
atr
ix
(
2
,
4
)
(
2
is
th
e
n
u
m
b
er
o
f
‘
1
’
(
j
)
in
ea
c
h
co
lu
m
n
,
4
is
th
e
n
u
m
b
er
o
f
‘
1
’
(
k
)
in
ea
c
h
r
o
w)
o
f
a
r
e
g
u
lar
L
DPC
co
d
e
is
g
iv
en
:
=
[
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
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1
0
0
0
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0
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0
1
0
0
0
0
1
1
0
0
]
(
1
)
I
t
is
o
f
ten
co
n
v
en
ien
t
to
r
e
p
r
e
s
en
t
L
DPC
co
d
es
u
s
in
g
a
b
ip
ar
tite
g
r
ap
h
o
r
T
a
n
n
er
g
r
ap
h
[
2
8
]
.
I
t
co
n
tain
s
two
ty
p
es
o
f
n
o
d
es:
ch
ec
k
n
o
d
es
(
C
N)
co
r
r
esp
o
n
d
in
g
to
th
e
r
o
w
s
o
f
th
e
m
atr
ix
H
,
an
d
v
ar
iab
l
e
n
o
d
es
(
VN)
o
r
b
it
n
o
d
es
co
r
r
esp
o
n
d
in
g
to
th
e
c
o
lu
m
n
s
o
f
an
d
b
its
o
f
th
e
co
d
ewo
r
d
.
C
h
ec
k
n
o
d
e
j
is
co
n
n
ec
ted
to
v
ar
iab
le
nod
e
if
an
d
o
n
ly
if
th
e
elem
e
n
t
ℎ
in
is
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to
‘
1
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.
Fo
r
ex
a
m
p
le,
th
e
T
an
n
er
g
r
ap
h
o
f
th
e
m
atr
ix
i
s
s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
R
ep
r
esen
tatio
n
o
f
th
e
p
ar
ity
ch
ec
k
m
atr
ix
H
as a
ta
n
n
er
g
r
ap
h
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
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m
p
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g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
7
5
4
-
1
7
7
3
1758
Am
o
n
g
L
DPC
co
d
es
th
er
e
a
r
e
r
eg
u
lar
a
n
d
ir
r
eg
u
lar
co
d
es.
T
h
e
v
er
if
icatio
n
m
atr
ix
o
f
th
e
f
o
r
m
er
is
ch
ar
ac
ter
ized
b
y
th
e
f
ac
t
t
h
at
all
co
lu
m
n
s
an
d
r
o
ws
c
o
n
tain
th
e
s
am
e
n
u
m
b
er
o
f
‘
1
’
j
an
d
k
,
r
esp
ec
tiv
ely
.
I
n
ir
r
eg
u
lar
L
DPC
co
d
es
th
is
p
r
o
p
er
ty
is
n
o
t
o
b
s
er
v
ed
.
Fo
r
ir
r
eg
u
lar
L
DPC
co
d
e,
we
ca
n
s
ay
th
at
th
e
a
v
er
ag
e
n
u
m
b
er
o
f
‘
1
’
in
a
r
o
w
an
d
t
h
e
av
er
ag
e
n
u
m
b
er
o
f
‘
1
’
in
a
co
lu
m
n
ar
e
s
m
all
co
m
p
ar
e
d
to
th
e
n
u
m
b
er
o
f
co
lu
m
n
s
a
n
d
th
e
n
u
m
b
er
o
f
r
o
ws.
C
o
m
p
ar
ed
to
r
eg
u
lar
L
DPC
,
ir
r
eg
u
lar
L
DPC
h
as
m
o
r
e
d
esig
n
f
lex
i
b
ilit
y
an
d
o
p
tim
izatio
n
p
o
s
s
ib
ilit
ies.
5
G
NR
,
lik
e
m
an
y
telec
o
m
m
u
n
icatio
n
s
tan
d
ar
d
s
(
I
E
E
E
8
0
2
.
1
6
,
I
E
E
E
8
0
2
.
1
1
,
an
d
DVB
-
S2
)
,
u
tili
ze
s
a
f
o
r
m
o
f
ir
r
e
g
u
lar
L
DPC
co
d
es
s
u
ch
as
q
u
asi
-
cy
clic
L
DPC
(
QC
-
L
DPC
)
[
2
9
]
.
T
h
e
f
o
llo
win
g
tech
n
ical
ad
v
an
tag
e
s
o
f
QC
-
L
DP
C
ca
n
b
e
n
o
ted
:
i)
R
elativ
ely
lo
w
er
r
o
r
r
ate,
s
u
itab
le
f
o
r
s
y
s
tem
s
with
h
ig
h
r
eliab
ilit
y
;
ii)
De
co
d
in
g
is
h
ig
h
ly
p
a
r
allelize
d
,
wh
ich
e
n
s
u
r
es
f
ast
d
ec
o
d
in
g
an
d
h
ig
h
d
ata
th
r
o
u
g
h
p
u
t
;
iii)
QC
-
L
DPC
co
d
es
ar
e
r
elativ
ely
f
lex
i
b
le
a
n
d
ca
n
b
e
co
n
s
tr
u
cted
with
m
u
ltip
le
co
d
e
r
ates,
n
u
m
er
o
u
s
o
f
b
lo
ck
len
g
th
s
,
a
n
d
s
ev
er
al
b
lo
ck
s
izes
[
3
0
]
.
T
h
ese
ar
e
im
p
o
r
tan
t
in
th
e
c
o
n
s
tr
u
ctio
n
o
f
m
o
d
e
r
n
m
o
b
ile
an
d
wir
eless
co
m
m
u
n
i
ca
tio
n
s
y
s
tem
s
;
an
d
iv
)
T
h
e
d
ec
o
d
in
g
co
m
p
lex
ity
d
ec
r
e
ases
as
th
e
co
d
in
g
r
ate
in
cr
ea
s
es,
wh
ich
s
atis
f
ies th
e
r
eq
u
ir
em
en
t
o
f
h
i
g
h
p
ea
k
d
ata
r
ate.
T
h
e
d
ec
o
d
in
g
p
r
o
ce
s
s
o
f
L
DP
C
co
d
es
is
b
ased
o
n
an
iter
ativ
e
s
ch
em
e
b
etwe
en
b
it
n
o
d
es
a
n
d
c
o
n
tr
o
l
n
o
d
es
in
a
T
a
n
n
er
g
r
ap
h
.
T
h
e
d
ec
o
d
in
g
s
ch
em
e
f
o
r
L
DP
C
co
d
es
is
k
n
o
wn
as
m
ess
ag
e
p
ass
in
g
alg
o
r
ith
m
(
MPA)
,
wh
ich
iter
ativ
ely
p
ass
es m
ess
ag
es b
ac
k
an
d
f
o
r
th
b
e
twee
n
b
it n
o
d
es a
n
d
co
n
t
r
o
l n
o
d
es u
n
til a
r
esu
lt is
ac
h
iev
ed
(
o
r
th
e
p
r
o
ce
s
s
is
s
t
o
p
p
ed
)
.
T
h
er
e
ar
e
two
b
asic
ap
p
r
o
ac
h
es
f
o
r
d
ec
o
d
in
g
L
D
PC
co
d
es:
d
ec
o
d
in
g
with
“
h
ar
d
”
(
b
it
-
f
lip
p
in
g
alg
o
r
ith
m
)
an
d
“
s
o
f
t
”
d
ec
is
io
n
s
(
s
u
m
-
p
r
o
d
u
ct,
m
in
-
s
u
m
alg
o
r
ith
m
s
)
.
Dec
o
d
er
s
with
s
o
f
t
d
ec
is
io
n
s
ar
e
m
o
r
e
e
f
f
icie
n
t,
b
ec
a
u
s
e
th
ey
r
ec
ei
v
e
m
o
r
e
in
f
o
r
m
atio
n
,
b
u
t
at
th
e
s
am
e
ti
m
e,
th
e
y
ar
e
m
o
r
e
d
if
f
icu
lt to
im
p
lem
e
n
t.
T
h
e
b
it
-
f
lip
p
in
g
al
g
o
r
ith
m
is
a
MPA
with
h
ar
d
d
ec
is
io
n
s
f
o
r
L
DPC
co
d
es
[
3
1
]
–
[
3
3
]
.
E
ac
h
r
ec
eiv
ed
b
it
is
p
r
o
ce
s
s
ed
b
y
th
e
d
etec
to
r
,
wh
ich
m
ak
es
a
b
in
a
r
y
d
ec
is
io
n
an
d
tr
an
s
m
its
it
to
th
e
d
ec
o
d
er
.
Fo
r
th
e
b
it
-
f
lip
p
in
g
alg
o
r
ith
m
,
t
h
e
m
ess
ag
es
tr
an
s
m
itted
alo
n
g
th
e
e
d
g
es
o
f
th
e
T
an
n
e
r
g
r
a
p
h
ar
e
b
in
ar
y
:
a
v
ar
iab
le
n
o
d
e
s
en
d
s
a
m
es
s
ag
e
d
ec
lar
in
g
wh
eth
er
it
is
a
o
n
e
o
r
a
ze
r
o
.
Nex
t,
ea
ch
ch
ec
k
n
o
d
e
p
er
f
o
r
m
s
a
p
ar
ity
ch
ec
k
o
n
its
ass
o
ciate
d
v
ar
iab
le
n
o
d
es
an
d
th
en
s
en
d
s
a
m
ess
ag
e
to
ea
c
h
b
it
-
f
lip
p
i
n
g
n
o
d
e
ass
o
ciate
d
with
it,
d
ec
lar
in
g
wh
at
v
alu
e
t
h
e
b
it
h
as
b
ased
o
n
th
e
i
n
f
o
r
m
atio
n
a
v
ailab
le
to
th
at
ch
ec
k
n
o
d
e.
I
f
o
n
e
(
o
r
m
o
r
e)
v
a
r
iab
le
n
o
d
es
f
ail
th
e
p
ar
ity
ch
ec
k
th
e
g
r
ea
test
n
u
m
b
er
o
f
tim
es,
th
o
s
e
n
o
d
es
ch
an
g
e
(
f
lip
)
th
eir
c
u
r
r
en
t
v
alu
es.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
all
p
ar
ity
ch
e
ck
eq
u
atio
n
s
ar
e
s
atis
f
ied
,
o
r
u
n
til
th
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
iter
atio
n
s
h
as
b
ee
n
p
er
f
o
r
m
ed
.
Alth
o
u
g
h
b
it
-
f
lip
p
i
n
g
alg
o
r
ith
m
is
ea
s
y
to
im
p
lem
en
t,
it
is
n
o
t
as
ef
f
icien
t
as
o
th
er
alg
o
r
i
th
m
s
,
lik
e
th
e
s
u
m
-
p
r
o
d
u
ct
alg
o
r
ith
m
.
T
h
is
alg
o
r
ith
m
,
also
o
f
ten
r
e
f
er
r
ed
to
as
th
e
b
elief
p
r
o
p
a
g
atio
n
(
B
P)
alg
o
r
ith
m
,
is
MPA
with
s
o
f
t
s
o
lu
tio
n
s
[
3
4
]
–
[
3
8
]
.
I
t
is
s
im
ilar
to
th
e
b
it
-
f
lip
p
in
g
alg
o
r
ith
m
,
b
u
t
th
e
d
i
f
f
er
en
ce
is
th
at
th
e
m
ess
ag
es
r
ep
r
esen
tin
g
ea
ch
d
ec
is
io
n
ar
e
n
o
w
p
r
o
b
ab
ilis
tic
r
ath
er
th
an
d
is
cr
ete
(
o
r
b
in
ar
y
:
‘
0
’
an
d
‘
1
’
)
.
W
h
ile
b
it
-
f
lip
p
in
g
d
ec
o
d
i
n
g
m
a
k
es
an
in
itial
h
ar
d
d
ec
is
io
n
o
n
t
h
e
r
ec
eiv
ed
b
its
as
in
p
u
t
d
at
a,
th
e
s
u
m
-
p
r
o
d
u
ct
alg
o
r
ith
m
is
a
s
o
f
t
d
ec
is
io
n
alg
o
r
ith
m
th
at
tak
es
th
e
p
r
o
b
ab
ilit
y
o
f
ea
ch
r
ec
eiv
ed
b
it
as
in
p
u
t
d
ata.
T
h
e
p
r
o
b
a
b
ilit
ies
o
f
th
e
r
ec
eiv
ed
in
p
u
t
b
its
ar
e
ca
lled
a
p
r
io
r
i
p
r
o
b
ab
ilit
ies,
an
d
th
e
b
it
p
r
o
b
a
b
ilit
ies
r
etu
r
n
ed
b
y
th
e
d
ec
o
d
e
r
ar
e
ca
lled
p
o
s
ter
io
r
p
r
o
b
ab
ilit
ies.
I
n
th
e
c
ase
o
f
s
u
m
-
p
r
o
d
u
ct
d
ec
o
d
i
n
g
alg
o
r
ith
m
,
th
ese
p
r
o
b
a
b
ilit
ies ar
e
ex
p
r
ess
ed
th
r
o
u
g
h
l
o
g
lik
elih
o
o
d
r
atio
s
(
L
L
R
)
[
3
8
]
.
=
ln
Pr
(
=
+
1
)
Pr
(
=
−
1
)
=
ln
1
−
(
2
)
T
h
e
ad
v
a
n
tag
e
o
f
th
e
lo
g
ar
ith
m
ic
r
ep
r
esen
tatio
n
o
f
th
e
p
r
o
b
ab
ilit
ies
is
th
at,
in
ca
s
e
it
is
n
ec
ess
ar
y
to
m
u
ltip
ly
th
e
p
r
o
b
ab
ilit
ies,
it
will
b
e
s
u
f
f
icien
t
t
o
ad
d
th
e
L
L
R
s
,
wh
ich
will
r
ed
u
ce
th
e
co
m
p
le
x
ity
o
f
th
e
d
ec
o
d
er
im
p
lem
e
n
tatio
n
.
I
n
B
P
alg
o
r
ith
m
,
iter
ativ
ely
tr
an
s
m
itted
m
ess
ag
es
b
etwe
en
n
o
d
es
r
ep
r
esen
t
th
e
b
elief
lev
el
o
f
th
e
ac
ce
p
ted
co
d
ewo
r
d
s
.
E
ac
h
v
ar
ia
b
le
n
o
d
e
tr
a
n
s
m
its
a
m
ess
ag
e
to
ea
ch
co
n
tr
o
l
n
o
d
e
co
n
n
ec
ted
to
it.
E
ac
h
co
n
tr
o
l
n
o
d
e
tr
an
s
m
its
a
m
ess
ag
e
to
e
ac
h
b
it
n
o
d
e
c
o
n
n
ec
ted
to
th
at
n
o
d
e.
T
h
e
g
o
al
o
f
th
is
alg
o
r
ith
m
is
to
co
m
p
u
te
th
e
m
ax
im
u
m
a
p
o
s
ter
io
r
i
p
r
o
b
ab
ilit
y
(
MA
P)
f
o
r
ea
ch
b
i
t
o
f
th
e
co
d
ewo
r
d
{
=
1
∣
}
,
wh
ich
is
th
e
p
r
o
b
ab
ilit
y
th
a
t
th
e
-
th
b
it
o
f
th
e
co
d
ew
o
r
d
is
eq
u
al
to
o
n
e
p
r
o
v
id
ed
th
a
t
all
p
ar
ity
ch
ec
k
co
n
s
tr
ain
ts
ar
e
s
atis
f
ied
in
ev
en
t
N.
T
h
e
f
in
al
v
alu
e
o
f
th
e
d
ec
o
d
ed
b
it
is
d
eter
m
in
ed
b
y
co
m
p
ar
in
g
th
e
s
u
m
o
f
th
e
L
L
R
o
f
th
is
b
it with
th
e
th
r
esh
o
ld
v
alu
e
(
ze
r
o
)
.
T
h
e
s
u
m
-
p
r
o
d
u
ct
alg
o
r
ith
m
[
3
9
]
,
w
h
ich
u
s
es
a
p
r
o
b
ab
ilis
tic
ap
p
r
o
ac
h
t
o
d
ec
o
d
in
g
p
r
o
b
l
em
s
,
h
as
a
b
etter
co
r
r
ec
tiv
e
ab
ilit
y
co
m
p
ar
ed
to
b
it
-
f
lip
p
i
n
g
.
Ho
we
v
er
,
at
its
u
s
e
th
e
co
m
p
u
tatio
n
al
co
s
ts
in
cr
ea
s
e,
ca
u
s
ed
b
y
n
ec
ess
ity
to
u
s
e
c
o
m
p
lex
f
u
n
ctio
n
s
o
f
h
y
p
er
b
o
lic
tan
g
en
t
ℎ
an
d
ar
ctan
g
e
n
t
ℎ
−
1
to
f
o
r
m
m
ess
ag
es
f
r
o
m
c
h
ec
k
n
o
d
es
to
b
it
-
f
lip
p
in
g
n
o
d
es.
T
h
er
e
f
o
r
e,
f
o
r
h
ar
d
wa
r
e
im
p
lem
e
n
t
atio
n
,
th
e
m
in
-
s
u
m
d
ec
o
d
in
g
alg
o
r
ith
m
,
wh
ich
u
s
es
an
ap
p
r
o
x
im
ate
co
m
p
u
tatio
n
o
f
th
e
ch
ec
k
m
ess
ag
es
t
o
th
e
b
it
n
o
d
es,
is
wid
ely
u
s
ed
.
T
h
u
s
,
i
n
s
tead
o
f
co
m
p
u
tin
g
th
e
p
r
o
d
u
ct
o
f
th
e
ℎ
an
d
ℎ
−
1
,
an
d
o
p
er
atio
n
s
ar
e
u
s
ed
,
b
ec
au
s
e
o
f
wh
ich
th
e
d
ec
o
d
er
is
s
im
p
ler
in
im
p
lem
e
n
tatio
n
an
d
f
aster
in
p
r
o
ce
s
s
in
g
tim
e.
I
n
ad
d
itio
n
,
th
er
e
is
n
o
n
ee
d
to
m
ea
s
u
r
e
t
h
e
n
o
is
e
v
ar
ia
n
ce
v
alu
e
2
,
wh
ich
in
th
e
s
u
m
-
p
r
o
d
u
ct
al
g
o
r
it
h
m
is
in
clu
d
ed
in
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
-
8
7
0
8
E
fficien
cy
o
f c
h
a
n
n
el
co
d
es fo
r
d
iffer
en
t fa
d
in
g
mo
d
els in
5
G
en
h
a
n
ce
d
…
(
Gen
n
a
d
y
K
a
z
a
ko
v
)
1759
th
e
L
L
R
ca
lcu
latio
n
f
o
r
m
u
la
as
a
s
ca
lin
g
f
ac
to
r
.
Fo
r
th
e
s
e
ad
v
an
tag
es,
th
e
m
in
-
s
u
m
d
ec
o
d
in
g
alg
o
r
ith
m
tu
r
n
ed
o
u
t to
b
e
m
o
r
e
p
r
e
f
er
ab
le
in
p
r
ac
tical
im
p
lem
en
tatio
n
s
.
T
h
e
n
u
m
b
e
r
o
f
co
m
p
u
tatio
n
al
o
p
er
atio
n
s
p
er
iter
atio
n
f
o
r
th
e
s
u
m
-
p
r
o
d
u
ct
alg
o
r
ith
m
co
m
p
ar
ed
to
th
e
b
it
-
f
lip
p
in
g
an
d
m
in
-
s
u
m
alg
o
r
ith
m
s
ar
e
ap
p
r
o
x
im
ately
8
an
d
3
tim
es
g
r
ea
ter
,
r
esp
ec
t
iv
ely
.
At
th
e
s
am
e
tim
e,
d
u
e
to
t
h
e
s
im
p
lific
atio
n
o
f
ca
lcu
latio
n
s
,
th
e
ef
f
icie
n
cy
o
f
th
e
m
in
-
s
u
m
alg
o
r
ith
m
r
elativ
e
to
th
e
s
u
m
-
p
r
o
d
u
ct
alg
o
r
ith
m
is
r
ed
u
ce
d
b
y
ab
o
u
t
0
.
2
-
0
.
5
d
B
.
Ho
wev
er
,
th
is
lo
s
s
ca
n
b
e
r
ed
u
ce
d
b
y
s
o
m
e
m
o
d
if
icatio
n
s
o
f
th
e
m
in
-
s
u
m
alg
o
r
ith
m
,
s
u
ch
as
th
e
m
in
-
s
u
m
n
o
r
m
ali
ze
d
an
d
m
in
-
s
u
m
o
f
f
s
et
alg
o
r
ith
m
[
3
9
]
–
[
4
1
]
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
t
h
e
3
GPP
tech
n
ical
s
p
ec
if
icatio
n
(
T
S)
3
8
.
2
1
2
[
2
]
d
o
es
n
o
t
im
p
o
s
e
s
tr
ict
r
eq
u
ir
em
e
n
ts
f
o
r
th
e
u
s
e
o
f
a
p
ar
ticu
lar
L
DPC
d
ec
o
d
in
g
alg
o
r
ith
m
in
an
y
o
f
th
e
ch
an
n
els,
leav
in
g
it
to
t
h
e
d
is
cr
etio
n
o
f
th
e
s
y
s
tem
d
esig
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er
.
I
n
th
is
p
ap
er
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we
d
ec
id
e
d
to
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o
c
u
s
o
n
th
e
B
P
alg
o
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ith
m
as
th
e
m
o
s
t
d
e
v
elo
p
ed
a
n
d
wid
el
y
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s
ed
.
2
.
2
.
L
DP
C
co
des
in 5
G
NR
As
alr
ea
d
y
m
en
tio
n
e
d
,
q
u
asi
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cy
clic
lo
w
-
d
e
n
s
ity
p
ar
ity
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ch
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k
(
QC
-
L
DPC
)
co
d
es
h
av
e
b
ee
n
s
elec
ted
f
o
r
u
s
e
in
5
G
NR
.
T
h
e
L
DP
C
co
d
in
g
ch
ain
is
s
h
o
wn
in
Fig
u
r
e
2
an
d
in
clu
d
es
co
d
e
b
lo
ck
s
eg
m
en
tatio
n
,
ad
d
itio
n
o
f
C
R
C
co
d
e,
L
DP
C
en
co
d
in
g
,
r
ate
m
atch
in
g
an
d
s
y
s
tem
atic
b
it
in
ter
leav
in
g
[
2
]
.
B
y
s
eg
m
en
tin
g
co
d
e
b
l
o
ck
s
,
lar
g
e
tr
an
s
p
o
r
t
b
lo
ck
s
ca
n
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e
d
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i
d
ed
i
n
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u
ltip
le
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m
aller
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s
th
a
t
ca
n
b
e
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r
o
ce
s
s
ed
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icien
tly
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p
a
r
allel
b
y
th
e
L
DPC
en
co
d
er
/d
ec
o
d
er
.
Fig
u
r
e
2
.
L
DPC
co
d
in
g
ch
ain
in
5
G
NR
T
h
e
tr
an
s
p
o
r
t
b
lo
ck
is
m
o
d
if
i
ed
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y
a
d
d
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g
C
R
C
b
its
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e
s
am
e
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o
r
d
o
wn
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k
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u
p
lin
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es
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eir
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r
r
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i
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SC
H
an
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UL
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SC
H
ch
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I
f
th
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n
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o
r
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ize
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B
S)
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r
r
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o
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d
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g
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th
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ce
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in
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o
r
m
atio
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y
m
b
o
ls
A
ex
ce
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s
3
8
2
4
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its
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a
2
4
-
b
it
C
R
C
f
o
r
m
ed
b
y
th
e
f
o
llo
win
g
g
en
er
atin
g
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o
ly
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o
m
ial
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ed
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th
e
en
d
o
f
th
e
tr
an
s
p
o
r
t
b
lo
ck
:
24
(
)
=
[
24
+
23
+
18
+
17
+
14
+
11
+
10
+
7
+
6
+
5
+
4
+
3
+
+
1
]
.
I
n
o
th
er
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a
1
6
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ased
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n
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g
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atin
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o
ly
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o
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ial
16
(
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is
ad
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t
h
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en
d
o
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wo
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ase
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m
atr
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ely
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G1
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d
B
G2
[
5
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,
[
4
2
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,
wer
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in
tr
o
d
u
ce
d
in
t
h
e
T
S
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.
2
1
2
[
2
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to
m
ain
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ca
lab
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n
d
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m
p
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f
th
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th
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T
B
S
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th
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o
r
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h
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esh
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4
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its
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o
r
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G
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e
th
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esh
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ld
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8
4
0
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tr
an
s
p
o
r
t
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n
d
er
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o
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eg
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en
tatio
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y
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p
litt
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g
i
n
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ev
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al
c
o
d
e
b
lo
ck
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o
f
th
e
s
am
e
s
ize.
At
th
e
e
n
d
o
f
e
ac
h
co
d
e
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lo
c
k
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a
n
ad
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itio
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al
2
4
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R
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is
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ed
a
f
ter
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eg
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e
n
tatio
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o
b
tai
n
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s
in
g
th
e
g
e
n
er
atin
g
p
o
ly
n
o
m
ial
24
(
)
=
[
24
+
23
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+
5
+
+
1
]
.
R
ate
m
atch
in
g
p
er
f
o
r
m
ed
b
y
th
e
cir
cu
lar
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u
f
f
er
co
n
s
is
ts
o
f
ad
ju
s
tin
g
th
e
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d
ewo
r
d
len
g
t
h
(
i.e
.
,
th
e
n
u
m
b
er
o
f
co
d
e
d
b
its
at
th
e
o
u
tp
u
t
o
f
th
e
cir
cu
lar
b
u
f
f
er
)
ac
co
r
d
in
g
to
t
h
e
av
ailab
le
r
ad
io
r
eso
u
r
ce
s
o
f
th
e
ch
an
n
el.
I
n
5
G
NR
L
DPC
,
a
r
o
w
an
d
co
l
u
m
n
in
ter
lea
v
er
is
u
s
ed
to
in
ter
leav
e
ea
c
h
co
d
e
b
lo
ck
af
ter
t
h
e
r
ate
m
atch
er
.
T
h
e
p
u
r
p
o
s
e
o
f
in
ter
l
ea
v
in
g
is
to
p
r
o
tect
a
g
ain
s
t
p
a
ck
et
in
ter
f
er
e
n
ce
.
Af
ter
i
n
ter
le
av
in
g
,
th
e
o
r
i
g
in
al
lo
ca
lly
co
n
ce
n
tr
ate
d
in
ter
f
er
e
n
ce
is
d
is
tr
ib
u
ted
in
to
s
ep
ar
at
e
is
o
lated
in
ter
f
er
en
ce
.
Su
b
s
eq
u
en
tly
,
s
m
all
er
r
o
r
s
o
cc
u
r
r
in
g
d
u
r
in
g
d
ec
o
d
in
g
a
r
e
ea
s
ier
to
d
etec
t
an
d
co
r
r
ec
t.
T
h
e
in
ter
leav
er
im
p
r
o
v
es
p
er
f
o
r
m
an
ce
b
y
m
ak
in
g
s
y
s
tem
atic
b
its
m
o
r
e
r
eliab
le
th
an
p
ar
ity
b
its
f
o
r
in
itial
co
d
e
b
lo
ck
tr
a
n
s
m
is
s
io
n
.
Data
is
r
eo
r
d
er
e
d
b
ased
o
n
th
e
p
r
in
cip
le
o
f
lin
e
-
by
-
lin
e
w
r
itin
g
an
d
c
o
lu
m
n
-
by
-
co
lu
m
n
r
ea
d
in
g
.
2
.
3
.
P
o
la
r
co
des
T
h
e
b
asic
id
ea
o
f
p
o
lar
co
d
e
s
,
f
ir
s
t
in
tr
o
d
u
ce
d
b
y
Ar
i
k
an
in
[
4
3
]
,
u
n
d
er
ly
i
n
g
th
e
e
n
c
o
d
in
g
a
n
d
d
ec
o
d
in
g
alg
o
r
ith
m
s
o
f
p
o
lar
co
d
es
is
ch
a
n
n
el
p
o
lar
izat
io
n
.
C
h
an
n
el
p
o
la
r
izatio
n
is
th
e
o
p
er
atio
n
o
f
tr
an
s
f
o
r
m
in
g
a
c
o
m
m
u
n
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n
ch
an
n
el
in
to
in
d
ep
en
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e
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t
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o
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ies
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it
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v
ir
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al
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h
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n
els
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e
cr
ea
ted
b
etwe
en
in
p
u
t
an
d
o
u
tp
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t
b
its
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in
wh
ic
h
th
e
p
r
o
b
ab
ilit
y
o
f
er
r
o
r
d
u
r
i
n
g
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ata
tr
an
s
m
is
s
io
n
ten
d
s
to
‘
0
’
,
o
r
t
o
‘
1
’
as
th
e
len
g
th
o
f
th
e
in
f
o
r
m
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s
eq
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en
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cr
ea
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I
n
f
o
r
m
atio
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b
its
ar
e
tr
an
s
m
itted
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r
o
u
g
h
v
ir
tu
al
ch
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n
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h
av
in
g
l
o
w
er
r
o
r
p
r
o
b
a
b
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with
h
ig
h
th
r
o
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g
h
p
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t,
asy
m
p
to
tically
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ch
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g
th
e
Sh
a
n
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o
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it.
T
h
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s
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it
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tly
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it
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o
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g
h
m
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ch
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n
els
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o
s
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lo
w
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r
o
r
p
r
o
b
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.
C
h
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lled
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n
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s
m
is
s
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n
is
p
er
f
o
r
m
ed
o
v
e
r
th
em
.
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
7
5
4
-
1
7
7
3
1760
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h
e
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ased
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ik
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h
e
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k
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atr
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[
1
0
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1
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an
d
th
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d
en
o
t
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its
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-
th
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k
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eg
r
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[
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3
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.
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h
e
s
eq
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en
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ee
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s
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e
tr
an
s
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ich
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ca
lled
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o
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ep
r
esen
tatio
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,
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o
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tain
th
e
r
e
q
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ir
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t
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e
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r
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Fo
r
ex
am
p
le
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1
(
0
0
0
1
)
→
(
1
0
0
0
)
8
.
T
h
u
s
,
th
e
p
er
m
u
tatio
n
m
atr
i
x
m
u
s
t
b
e
in
t
r
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ce
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t
o
o
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t
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th
e
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r
r
esp
o
n
d
in
g
m
at
r
ix
.
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h
e
r
esu
ltin
g
g
en
er
atin
g
m
atr
ix
is
d
ef
in
ed
b
y
th
e
f
o
llo
win
g
e
x
p
r
ess
io
n
=
∗
2
⊗
.
T
o
p
er
f
o
r
m
th
e
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o
lar
izatio
n
o
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atio
n
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it
is
n
ec
ess
ar
y
to
p
er
f
o
r
m
a
tr
an
s
f
o
r
m
atio
n
o
f
th
e
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ca
lar
ch
an
n
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in
to
a
v
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ch
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n
el,
i
d
en
tify
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it
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e
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n
d
itio
n
al
p
r
o
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a
b
ilit
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en
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ity
f
u
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n
o
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e
o
u
tp
u
t
s
y
m
b
o
l
[
4
3
]
,
[
4
4
]
.
T
h
is
is
ac
h
iev
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y
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e
m
an
n
er
,
as p
r
esen
ted
in
Fig
u
r
e
3
.
Fig
u
r
e
3
.
R
ec
u
r
s
iv
e
m
et
h
o
d
o
f
co
d
e
v
ec
t
o
r
f
o
r
m
atio
n
T
h
e
id
ea
o
f
th
e
tr
ad
itio
n
al
d
e
co
d
in
g
alg
o
r
ith
m
f
o
r
p
o
lar
co
d
es
co
n
s
is
ts
in
s
eq
u
en
tial
esti
m
atio
n
o
f
in
f
o
r
m
atio
n
b
its
.
Su
ch
d
ec
o
d
i
n
g
alg
o
r
ith
m
is
k
n
o
wn
as
th
e
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
(
SC
)
alg
o
r
ith
m
[
4
3
]
.
T
h
e
d
is
ad
v
an
tag
e
o
f
th
is
alg
o
r
ith
m
co
n
s
is
ts
th
at
if
o
n
s
o
m
e
s
tep
o
f
d
ec
o
d
in
g
t
h
er
e
is
an
er
r
o
r
,
th
en
th
e
esti
m
atio
n
o
f
all
o
th
er
b
its
also
will
b
e
er
r
o
n
eo
u
s
.
B
esid
es,
ap
p
licatio
n
o
f
SC
alg
o
r
ith
m
lead
s
to
b
ig
d
ec
o
d
in
g
d
elay
s
.
Fo
r
a
co
d
ewo
r
d
o
f
len
g
t
h
,
th
e
to
tal
d
ec
o
d
i
n
g
d
elay
o
f
SC
alg
o
r
ith
m
is
eq
u
al
to
(
2
−
2
)
clo
ck
c
y
c
les,
is
a
s
er
io
u
s
p
r
o
b
lem
f
o
r
a
p
p
licatio
n
o
f
p
o
lar
c
o
d
es in
r
ea
l
-
tim
e
a
p
p
licatio
n
s
.
C
o
m
p
u
tatio
n
al
co
m
p
lex
ity
(
e
x
ec
u
tio
n
tim
e)
f
o
r
en
c
o
d
in
g
an
d
d
ec
o
d
i
n
g
o
p
er
atio
n
s
o
f
p
o
la
r
co
d
es
b
y
SC
alg
o
r
ith
m
ca
n
b
e
ex
p
r
ess
ed
as
(
)
,
wh
er
e
is
th
e
len
g
th
o
f
in
f
o
r
m
atio
n
s
eq
u
en
ce
,
th
e
am
o
u
n
t
o
f
m
em
o
r
y
r
eq
u
ir
ed
is
(
)
.
SC
d
ec
o
d
ed
p
o
lar
co
d
es
h
av
e
w
o
r
s
e
er
r
o
r
co
r
r
ec
tio
n
p
e
r
f
o
r
m
an
ce
at
f
in
ite
co
d
e
len
g
th
co
m
p
a
r
ed
to
m
o
d
e
r
n
c
h
an
n
el
co
d
es
s
u
ch
as
L
DPC
an
d
tu
r
b
o
c
o
d
es.
T
o
im
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
o
f
p
o
lar
co
d
es,
im
p
r
o
v
e
d
v
er
s
i
o
n
s
o
f
th
e
SC
alg
o
r
ith
m
,
s
u
ch
as
s
u
cc
ess
iv
e
ca
n
ce
llati
o
n
lis
t
(
SC
L
)
an
d
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
s
tack
(
SC
S),
h
av
e
b
ee
n
d
e
v
elo
p
e
d
,
wh
ich
p
er
f
o
r
m
m
u
ch
b
etter
th
an
th
e
SC
d
ec
o
d
in
g
alg
o
r
ith
m
,
alth
o
u
g
h
th
ey
h
av
e
h
ig
h
e
r
co
m
p
lex
ity
co
m
p
ar
e
d
to
SC
.
Fu
r
th
er
m
o
r
e,
C
R
C
co
d
es
ar
e
co
m
b
i
n
ed
with
p
o
lar
co
d
es
th
at
ar
e
d
ec
o
d
ed
u
s
in
g
th
e
SC
L
alg
o
r
ith
m
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
a
co
n
ca
ten
ated
s
y
s
tem
o
u
tp
er
f
o
r
m
s
o
th
e
r
cu
ttin
g
-
ed
g
e
ch
an
n
el
c
o
d
es.
On
e
o
f
way
s
to
o
v
er
c
o
m
e
d
ep
en
d
en
ce
o
n
esti
m
ates
o
f
p
r
ec
e
d
in
g
b
its
at
d
ec
o
d
in
g
o
f
p
o
la
r
co
d
e
is
to
u
s
e
o
f
SC
L
alg
o
r
ith
m
T
ala
-
Var
d
i
[
4
5
]
.
I
t
allo
ws
to
in
c
r
ea
s
e
ef
f
icien
cy
o
f
d
ec
o
d
in
g
o
f
p
o
lar
co
d
e
at
tr
an
s
m
is
s
io
n
o
f
s
m
all
an
d
m
e
d
iu
m
s
ize
m
ess
ag
es.
I
n
th
is
alg
o
r
ith
m
f
o
r
d
ec
o
d
in
g
o
f
i
n
p
u
t
b
its
o
n
e
b
y
o
n
e
b
est
d
ec
o
d
in
g
p
ath
s
ar
e
s
im
u
ltan
eo
u
s
ly
tr
ac
k
e
d
,
u
n
lik
e
S
C
d
ec
o
d
in
g
m
eth
o
d
,
in
wh
ic
h
o
n
ly
o
n
e
p
ath
is
tr
ac
k
ed
.
T
h
is
alg
o
r
ith
m
allo
w
s
to
r
ea
lize
d
ec
o
d
i
n
g
co
m
p
ar
ab
le
to
th
e
m
a
x
im
u
m
lik
elih
o
o
d
m
eth
o
d
alr
ea
d
y
f
o
r
a
s
m
all
lis
t
s
ize
(
=
16
)
.
T
h
e
co
m
p
lex
ity
o
f
th
e
SC
L
alg
o
r
ith
m
d
ep
en
d
s
o
n
th
e
s
ize
o
f
th
e
lis
t.
I
ts
tim
e
co
m
p
lex
ity
is
eq
u
al
t
o
(
)
,
an
d
its
m
em
o
r
y
co
m
p
le
x
ity
is
eq
u
al
t
o
(
)
.
An
im
p
r
o
v
ed
v
er
s
io
n
o
f
th
e
S
C
alg
o
r
ith
m
ca
lled
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
s
tack
(
SC
S)
is
p
r
o
p
o
s
ed
in
[
4
6
]
.
I
t
u
s
es
a
s
tack
f
o
r
s
to
r
a
g
e
an
d
d
eter
m
in
es
th
e
b
est
ca
n
d
id
ate
p
ath
b
y
o
p
tim
al
s
ea
r
ch
.
W
h
en
ev
er
th
e
b
est
p
ath
r
ea
ch
es
a
m
etr
ic
v
alu
e,
th
e
d
ec
o
d
in
g
o
p
e
r
atio
n
is
s
to
p
p
ed
an
d
a
d
ec
is
io
n
is
m
ad
e
ab
o
u
t
th
e
b
its
tr
an
s
m
itted
.
T
h
e
len
g
th
o
f
th
e
ca
n
d
id
ate
p
at
h
s
is
wh
at
d
is
tin
g
u
is
h
es
SC
L
f
r
o
m
SC
S.
C
an
d
id
ate
p
ath
s
in
th
e
SC
L
alg
o
r
ith
m
h
av
e
th
e
s
am
e
len
g
th
,
b
u
t
in
th
e
SC
S
alg
o
r
ith
m
,
th
ey
ca
n
v
ar
y
i
n
len
g
t
h
.
T
h
e
la
r
g
est
s
tack
v
alu
e
in
th
e
SC
S
d
ec
o
d
e
r
is
D
,
an
d
t
h
e
n
u
m
b
e
r
o
f
ex
p
an
d
in
g
p
ath
s
is
lim
ited
b
y
L
.
T
h
e
n
th
e
c
o
m
p
u
tatio
n
al
an
d
m
em
o
r
y
co
m
p
le
x
ity
f
o
r
SC
S
is
d
ef
in
ed
as
(
)
an
d
(
)
r
esp
ec
tiv
ely
.
T
h
e
p
ar
am
eter
L
is
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
-
8
7
0
8
E
fficien
cy
o
f c
h
a
n
n
el
co
d
es fo
r
d
iffer
en
t fa
d
in
g
mo
d
els in
5
G
en
h
a
n
ce
d
…
(
Gen
n
a
d
y
K
a
z
a
ko
v
)
1761
u
s
u
ally
tak
en
s
m
all
o
f
t
h
e
o
r
d
er
o
f
‘
8
’
,
D
s
h
o
u
l
d
b
e
o
f
th
e
o
r
d
e
r
o
f
th
e
co
d
e
len
g
t
h
N
.
No
te
th
at
th
e
r
ec
o
m
m
en
d
atio
n
T
S
3
8
.
2
1
2
[
2
]
s
u
g
g
ests
u
s
in
g
in
ch
an
n
els
with
p
o
lar
co
d
in
g
e
x
ac
tly
d
ec
o
d
in
g
alg
o
r
ith
m
C
R
C
-
aid
ed
SC
L
(
C
A
-
S
C
L
)
,
s
o
in
o
u
r
wo
r
k
we
ap
p
lied
it.
2
.
4
.
CRC
-
a
ided po
la
r
co
des
in 5
G
NR
Up
lin
k
an
d
d
o
wn
lin
k
co
n
tr
o
l
in
f
o
r
m
atio
n
(
UC
I
an
d
DC
I
)
is
b
ein
g
e
n
co
d
e
d
u
s
in
g
p
o
lar
co
d
es
as
th
e
co
d
in
g
s
ch
em
e
f
o
r
5
G
NR
[
1
]
.
DC
I
in
v
o
lv
es
co
n
ca
ten
atin
g
p
o
lar
co
d
es
with
d
is
tr
ib
u
ted
C
R
C
,
wh
ich
b
its
ar
e
d
er
iv
ed
b
y
in
ter
leav
i
n
g
b
its
b
etwe
en
th
e
C
R
C
en
co
d
er
an
d
th
e
p
o
lar
e
n
co
d
er
.
T
h
u
s
,
5
G
n
ew
r
ad
io
u
s
es
a
C
R
C
-
aid
ed
p
o
lar
co
d
in
g
s
ch
e
m
e
(
C
A
-
Po
lar
)
.
T
h
e
i
n
ter
leav
i
n
g
d
is
tr
ib
u
tes
th
e
C
R
C
b
its
in
s
u
ch
a
wa
y
th
at
th
e
C
R
C
b
it
i
s
p
o
s
itio
n
ed
b
y
th
e
last
b
it
n
ee
d
ed
to
co
m
p
u
te
it
[
4
7
]
.
T
h
er
e
f
o
r
e,
d
ec
o
d
in
g
co
m
p
lex
ity
ca
n
b
e
r
ed
u
ce
d
b
y
s
to
p
p
in
g
d
ec
o
d
i
n
g
ea
r
ly
wh
en
a
n
in
co
r
r
ec
t c
h
ec
k
is
d
etec
ted
[
4
8
]
,
[
4
9
]
.
T
h
e
im
p
licit
C
R
C
en
co
d
in
g
o
f
d
o
wn
lin
k
(
DC
I
o
r
B
C
H)
o
r
Up
lin
k
(
UC
I
)
m
ess
ag
e
b
its
d
i
ctate
s
th
e
u
s
e
o
f
C
R
C
-
aid
ed
s
er
ial
ca
n
ce
l
lis
t
(
C
A
-
SC
L
)
d
ec
o
d
in
g
[
5
0
]
as
a
d
ec
o
d
in
g
alg
o
r
ith
m
.
C
A
-
SC
L
d
ec
o
d
in
g
h
as
b
ee
n
k
n
o
w
n
to
o
u
tp
er
f
o
r
m
L
DPC
o
r
tu
r
b
o
co
d
es
[
5
1
]
,
lead
in
g
3
GPP
to
ad
o
p
t
p
o
lar
co
d
es
.
C
A
-
S
C
L
d
ec
o
d
in
g
will
ex
clu
d
e
p
ath
s
th
at
h
av
e
in
v
alid
C
R
C
s
wh
en
an
in
p
u
t
m
ess
ag
e
is
co
m
b
in
ed
with
o
n
e,
as
lo
n
g
as
at
lea
s
t
o
n
e
p
at
h
h
as
a
v
alid
C
R
C
.
T
h
e
C
A
-
SC
L
d
ec
o
d
er
p
er
f
o
r
m
s
b
etter
wh
en
th
is
o
p
e
r
atio
n
is
u
s
ed
in
th
e
f
in
al
p
ath
s
elec
tio
n
th
an
wh
en
it
is
u
s
ed
in
SC
L
d
ec
o
d
in
g
.
A
C
R
C
o
f
2
4
b
its
is
u
s
ed
f
o
r
th
e
d
o
wn
lin
k
,
wh
ile
C
R
C
s
o
f
6
an
d
1
1
b
its
ar
e
s
p
ec
if
ied
f
o
r
th
e
u
p
lin
k
,
wh
ich
v
ar
y
d
ep
e
n
d
in
g
o
n
th
e
v
alu
e
o
f
th
e
tr
an
s
m
itted
in
f
o
r
m
atio
n
b
lo
ck
len
g
th
.
T
h
e
Fig
u
r
e
s
4
(
a)
an
d
4
(
b
)
s
h
o
w
th
e
co
d
i
n
g
ch
ain
s
o
f
5
G
NR
p
o
lar
co
d
es
f
o
r
u
p
lin
k
a
n
d
d
o
wn
lin
k
[
2
]
.
So
m
e
o
f
th
e
lis
ted
o
p
er
atio
n
s
a
r
e
p
er
f
o
r
m
ed
o
n
ly
i
n
th
e
u
p
lin
k
o
r
d
o
wn
lin
k
.
T
h
e
m
ai
n
co
m
p
o
n
en
ts
o
f
th
e
co
d
in
g
ch
ai
n
s
ar
e
C
R
C
en
co
d
er
,
p
o
lar
c
o
d
in
g
an
d
r
ate
m
atch
in
g
.
(
a)
(
b
)
Fig
u
r
e
4
.
Po
lar
c
o
d
e
e
n
co
d
i
n
g
ch
ain
in
5
G
NR
f
o
r
(
a)
d
o
wn
li
n
k
an
d
(
b
)
u
p
lin
k
Seg
m
en
tatio
n
in
v
o
l
v
es
d
iv
id
in
g
th
e
o
r
ig
in
al
in
f
o
r
m
atio
n
b
lo
ck
in
to
s
ev
er
al
s
u
b
b
lo
c
k
s
b
ef
o
r
e
p
er
f
o
r
m
in
g
p
o
lar
co
d
in
g
f
o
r
e
ac
h
s
u
b
b
lo
c
k
.
Seg
m
e
n
tatio
n
i
s
o
n
ly
p
e
r
f
o
r
m
ed
i
n
Up
lin
k
d
u
r
in
g
UC
I
s
ig
n
alin
g
an
d
is
o
n
ly
r
eq
u
ir
e
d
wh
en
th
e
in
f
o
r
m
atio
n
b
lo
c
k
s
ize
ex
ce
e
d
s
a
ce
r
tain
len
g
th
an
d
s
u
f
f
ici
en
t
r
ad
io
r
eso
u
r
ce
s
h
av
e
b
ee
n
allo
ca
ted
.
T
h
e
C
R
C
p
ar
ity
b
its
ar
e
u
s
ed
f
o
r
er
r
o
r
co
r
r
ec
tio
n
at
th
e
en
d
o
f
SC
L
d
ec
o
d
in
g
to
elim
in
ate
d
ec
o
d
in
g
p
ath
s
in
t
h
e
lis
t
th
at
d
o
n
o
t
m
atch
th
e
C
R
C
an
d
to
s
elec
t
th
e
m
o
s
t
p
r
o
b
a
b
le
co
d
ew
o
r
d
.
Af
ter
th
at,
th
e
in
f
o
r
m
atio
n
s
eq
u
en
ce
is
p
o
lar
ized
f
o
r
a
g
iv
e
n
s
ize
co
d
e
=
2
.
Fo
r
all
in
f
o
r
m
atio
n
b
lo
ck
len
g
th
s
in
th
e
PDC
C
H
an
d
PB
C
H
ch
an
n
els,
a
2
4
-
b
it C
R
C
i
s
u
s
e
d
,
wh
ich
is
o
b
tain
ed
u
s
in
g
a
g
e
n
er
atin
g
p
o
ly
n
o
m
ial
C
RC
2
4
(
)
=
[
24
+
23
+
21
+
20
+
17
+
15
+
13
+
12
+
8
+
4
+
2
+
+
1
]
.
I
n
th
e
ca
s
e
o
f
a
PUC
C
H
ch
an
n
el
with
in
f
o
r
m
atio
n
b
lo
ck
le
n
g
th
A
∈
[
1
2
,
1
9
]
,
a
6
-
b
it
C
R
C
is
u
s
ed
,
wh
ich
is
o
b
tain
ed
u
s
in
g
a
g
en
e
r
atin
g
p
o
ly
n
o
m
ial
C
RC
6
(
)
=
[
6
+
5
+
1
]
.
I
f
th
e
in
f
o
r
m
atio
n
b
lo
ck
s
ize
A
∈
[
2
0
,
1
7
0
6
]
in
th
e
PUC
C
H
ch
an
n
el,
th
en
th
e
f
o
llo
win
g
is
u
s
ed
1
1
-
b
it
C
R
C
f
o
r
m
ed
b
y
a
g
e
n
er
atin
g
p
o
ly
n
o
m
ial
C
RC
1
1
(
)
=
[
11
+
10
+
9
+
5
+
1
]
.
C
R
C
b
it
in
ter
leav
in
g
is
a
co
m
p
o
n
e
n
t
o
f
th
e
co
d
in
g
ch
ain
th
at
is
p
er
f
o
r
m
e
d
o
n
l
y
in
d
o
wn
lin
k
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
C
R
C
in
ter
leav
er
is
to
d
is
tr
ib
u
te
t
h
e
C
R
C
b
its
with
in
a
b
lo
ck
m
o
r
e
e
v
en
ly
a
m
o
n
g
th
e
in
f
o
r
m
atio
n
al
an
d
f
r
o
ze
n
b
its
.
T
o
ca
lcu
late
th
e
v
alu
e
o
f
a
C
R
C
b
it,
it
i
s
n
ec
ess
ar
y
to
wait
f
o
r
th
e
in
f
o
r
m
atio
n
b
its
th
at
co
m
e
a
f
ter
a
g
iv
en
C
R
C
b
it,
as
th
e
C
R
C
in
ter
lea
v
er
is
d
esig
n
ed
to
d
ep
en
d
s
o
l
ely
o
n
th
e
p
r
ev
io
u
s
in
f
o
r
m
atio
n
b
its
d
u
r
in
g
SC
/S
C
L
d
ec
o
d
in
g
.
Dis
tr
ib
u
ted
C
R
C
b
its
m
ak
e
it
p
o
s
s
ib
le
to
co
n
d
u
ct
C
R
C
ch
ec
k
s
ea
r
lier
in
th
e
d
ec
o
d
in
g
p
r
o
ce
s
s
an
d
s
to
p
th
e
lis
t d
ec
o
d
in
g
p
r
o
ce
s
s
wh
en
all
ca
n
d
id
ate
p
ath
s
f
ail
C
R
C
ch
ec
k
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
7
5
4
-
1
7
7
3
1762
R
ate
m
atch
er
,
wh
ich
co
n
s
is
ts
o
f
a
s
u
b
b
lo
c
k
in
ter
leav
er
a
n
d
a
cir
cu
lar
b
u
f
f
er
,
is
task
ed
with
ad
ju
s
tin
g
th
e
co
d
ewo
r
d
len
g
th
in
ac
c
o
r
d
an
ce
with
th
e
av
ailab
le
r
ad
i
o
r
eso
u
r
ce
s
o
f
th
e
c
h
an
n
el.
B
ef
o
r
e
b
ein
g
in
s
er
ted
in
to
th
e
cir
cu
lar
b
u
f
f
er
,
th
e
s
u
b
b
lo
ck
in
te
r
leav
er
aim
s
to
g
r
o
u
p
th
e
co
d
ed
b
its
in
th
e
o
r
d
e
r
th
ey
ar
e
d
is
ca
r
d
e
d
o
r
r
ec
ei
v
ed
.
C
o
n
ca
ten
atin
g
th
e
b
its
o
f
ea
ch
en
co
d
ed
b
lo
ck
i
s
d
o
n
e
af
ter
t
h
e
r
ate
m
atch
er
,
an
d
th
e
o
u
tp
u
t
d
ata
is
s
en
t
f
o
r
f
u
r
th
er
p
r
o
ce
s
s
in
g
.
Af
ter
war
d
,
t
h
e
c
o
d
ed
b
its
ar
e
d
ed
icate
d
t
o
b
e
tr
a
n
s
m
itted
b
y
th
e
r
ate
m
atch
er
,
an
d
all
co
d
ed
b
lo
ck
s
ar
e
m
er
g
ed
to
g
eth
er
.
T
h
e
o
u
tp
u
t b
its
ar
e
s
en
t f
o
r
m
o
r
e
p
r
o
ce
s
s
in
g
.
C
h
an
n
el
in
ter
leav
er
is
im
p
lem
en
ted
t
o
r
e
d
u
ce
t
h
e
n
e
g
ativ
e
ef
f
ec
ts
o
f
f
ad
in
g
in
th
e
p
r
o
p
ag
atio
n
ch
a
n
n
el
a
n
d
r
eliab
ilit
y
d
if
f
er
e
n
ce
s
b
etwe
en
in
d
i
v
id
u
al
b
its
o
f
th
e
UC
I
s
ig
n
al
o
n
tr
an
s
m
is
s
io
n
e
f
f
icien
cy
.
A
tr
ian
g
u
lar
in
ter
le
av
er
is
u
s
ed
f
o
r
5
G
NR
p
o
lar
co
d
es with
a
l
in
e
-
by
-
lin
e
d
ec
r
ea
s
e
in
co
lu
m
n
co
u
n
t p
er
r
o
w.
W
h
en
u
s
in
g
h
ig
h
o
r
d
er
m
o
d
u
latio
n
,
th
e
ef
f
icien
cy
o
f
th
e
p
o
lar
NR
co
d
e
ca
n
b
e
g
r
ea
tly
im
p
r
o
v
e
d
b
y
th
is
in
ter
leav
er
.
3.
СO
DING
P
E
RF
O
R
M
ANC
E
M
E
T
RIC
S
3
.
1
.
Relia
bil
it
y
B
E
R
an
d
B
L
E
R
ar
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
to
e
v
alu
ate
th
e
r
eliab
ilit
y
o
f
m
ess
ag
e
tr
an
s
m
is
s
io
n
in
d
ig
ital
co
m
m
u
n
icatio
n
s
y
s
tem
s
.
B
o
th
ar
e
im
p
o
r
tan
t
f
o
r
u
n
d
er
s
tan
d
in
g
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
o
f
a
co
m
m
u
n
icatio
n
s
y
s
tem
.
B
L
E
R
in
d
icate
s
th
e
q
u
ality
o
f
t
h
e
en
tire
tr
an
s
m
is
s
io
n
ch
an
n
el,
wh
ile
B
E
R
ca
n
o
n
ly
r
ef
lect
an
esti
m
ate
o
f
th
e
c
o
d
i
n
g
ef
f
icie
n
cy
.
T
h
er
ef
o
r
e,
B
L
E
R
is
th
e
p
ar
am
eter
th
at
m
u
s
t
b
e
ac
h
iev
ed
in
o
r
d
er
to
p
r
o
v
id
e
a
p
a
r
ticu
lar
s
er
v
ice.
B
E
R
i
s
th
e
r
atio
o
f
th
e
n
u
m
b
er
o
f
b
its
er
r
o
n
e
o
u
s
ly
r
ec
eiv
e
d
b
y
th
e
r
ec
eiv
e
r
to
th
e
to
tal
n
u
m
b
er
o
f
b
its
tr
an
s
m
itted
b
y
th
e
tr
an
s
m
itter
.
B
E
R
ca
n
b
e
d
iv
id
ed
in
to
two
ty
p
es
d
ep
en
d
in
g
o
n
h
o
w
it
is
m
ea
s
u
r
ed
.
T
h
e
f
ir
s
t
is
tr
an
s
p
o
r
t
B
E
R
,
wh
ich
is
th
e
r
atio
o
f
d
etec
ted
in
co
r
r
e
ct
b
its
b
ef
o
r
e
er
r
o
r
c
o
r
r
ec
tio
n
to
th
e
to
tal
n
u
m
b
er
o
f
b
its
tr
an
s
m
itted
(
in
clu
d
in
g
r
ed
u
n
d
an
t
co
d
e
b
its
)
.
T
h
e
s
ec
o
n
d
o
p
tio
n
is
th
e
in
f
o
r
m
atio
n
B
E
R
,
wh
ich
is
th
e
n
u
m
b
er
o
f
d
ec
o
d
e
d
b
its
r
em
ai
n
in
g
in
c
o
r
r
ec
t
af
te
r
er
r
o
r
co
r
r
e
ctio
n
d
iv
id
e
d
b
y
th
e
to
tal
n
u
m
b
er
o
f
d
ec
o
d
ed
b
its
(
u
s
ef
u
l in
f
o
r
m
atio
n
)
.
I
t is o
f
te
n
th
e
s
ec
o
n
d
v
ar
ian
t t
h
at
is
u
s
ed
.
T
h
e
B
L
E
R
p
ar
am
eter
,
in
s
o
m
e
ca
s
es
also
d
ef
in
e
d
as
f
r
am
e
er
r
o
r
r
ate
(
FER
)
,
is
d
ef
in
ed
as
th
e
r
atio
o
f
th
e
n
u
m
b
er
o
f
er
r
o
n
eo
u
s
b
lo
ck
s
r
ec
eiv
ed
to
th
e
to
tal
n
u
m
b
er
o
f
b
lo
c
k
s
s
en
t
:
=
(
3
)
A
s
in
g
le
b
it
er
r
o
r
in
th
e
en
ti
r
e
f
r
am
e
is
co
n
s
id
er
ed
a
f
r
a
m
e
er
r
o
r
;
ty
p
ically
,
th
e
f
r
am
e
is
d
is
ca
r
d
ed
an
d
a
r
etr
an
s
m
is
s
io
n
is
r
eq
u
ested
.
An
er
r
o
n
eo
u
s
b
l
o
ck
is
d
ef
in
ed
as
a
tr
an
s
p
o
r
t
b
lo
ck
wh
o
s
e
C
R
C
ch
ec
k
is
in
co
r
r
ec
t.
At
t
h
e
lin
k
lay
er
,
th
e
s
y
s
tem
ca
n
wo
r
k
o
n
ly
with
wh
o
le
m
ess
ag
e
f
r
am
es,
n
o
t
wi
th
in
d
iv
id
u
al
b
its
.
I
n
th
is
ca
s
e,
if
a
tr
an
s
m
is
s
io
n
er
r
o
r
o
cc
u
r
s
,
th
e
d
ata
ca
n
b
e
r
esto
r
ed
to
t
h
e
o
r
i
g
in
al
s
tate
d
u
e
t
o
th
e
ef
f
icien
c
y
o
f
th
e
d
ec
o
d
i
n
g
alg
o
r
ith
m
.
An
alter
n
ativ
e
p
ar
am
eter
f
o
r
ass
es
s
in
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
ap
p
licatio
n
o
f
an
i
n
ter
f
er
en
ce
-
r
esis
tan
t
co
d
e
ca
n
b
e
t
h
e
r
elati
v
e
ch
an
n
el
ca
p
a
city
,
wh
ich
is
d
ef
in
ed
as
th
e
r
atio
o
f
th
e
n
u
m
b
er
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th
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2
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n
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eq
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tim
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f
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m
itted
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m
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c
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W
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r
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m
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T
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p
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(
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I
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2088
-
8
7
0
8
E
fficien
cy
o
f c
h
a
n
n
el
co
d
es fo
r
d
iffer
en
t fa
d
in
g
mo
d
els in
5
G
en
h
a
n
ce
d
…
(
Gen
n
a
d
y
K
a
z
a
ko
v
)
1763
tr
an
s
m
is
s
io
n
tim
e
to
p
r
ev
en
t
b
u
f
f
er
o
v
e
r
f
lo
w.
L
et
r
ep
r
esen
t
th
e
b
lo
ck
tr
an
s
m
is
s
io
n
tim
e,
an
d
th
en
th
e
ex
p
r
ess
io
n
(
5
)
ca
n
b
e
r
ewr
itte
n
as:
≥
+
3
+
+
+
(
6
)
3
.
3
.
Co
m
pu
t
a
t
io
na
l c
o
m
plex
it
y
C
o
m
p
u
tatio
n
al
co
m
p
le
x
ity
is
also
a
v
er
y
im
p
o
r
tan
t
p
a
r
am
eter
o
f
d
ec
o
d
in
g
.
W
ith
o
u
t
li
m
itatio
n
o
f
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
,
m
ax
im
u
m
lik
elih
o
o
d
(
ML
)
d
ec
o
d
in
g
m
et
h
o
d
will
alwa
y
s
b
e
o
p
tim
al
in
ter
m
s
o
f
r
eliab
ilit
y
f
o
r
an
y
co
d
es.
Hen
c
e,
th
e
g
o
al
o
f
d
esig
n
in
g
a
d
ec
o
d
in
g
s
ch
em
e
is
to
ac
h
iev
e
d
ec
o
d
in
g
p
er
f
o
r
m
a
n
ce
clo
s
e
to
ML
with
a
r
ea
s
o
n
ab
l
e
lev
el
o
f
co
m
p
lex
ity
.
Dec
o
d
i
n
g
co
m
p
lex
ity
is
an
im
p
o
r
ta
n
t
d
elay
f
ac
to
r
,
s
in
ce
th
e
d
ec
o
d
i
n
g
tim
e
is
o
n
e
o
f
th
e
m
ain
p
ar
ts
o
f
th
e
to
tal
en
d
-
to
-
en
d
d
ela
y
.
a.
L
DPC
co
d
es
:
b
elief
-
p
r
o
p
a
g
atio
n
d
ec
o
d
in
g
alg
o
r
ith
m
I
n
th
e
B
P
alg
o
r
ith
m
,
th
e
d
ec
o
d
in
g
co
m
p
lex
ity
is
co
m
p
o
s
ed
o
f
th
e
n
u
m
b
er
o
f
ad
d
itio
n
o
p
e
r
atio
n
s
an
d
r
ef
er
en
ce
tab
le
ac
ce
s
s
o
p
er
ati
o
n
s
[
5
2
]
.
Fo
r
h
ar
d
war
e
im
p
le
m
en
tatio
n
,
tab
le
ac
ce
s
s
o
p
er
a
tio
n
s
ar
e
d
esira
b
le
b
ec
au
s
e
th
ey
ca
n
b
e
ac
co
m
p
lis
h
ed
with
a
s
m
all
am
o
u
n
t
o
f
m
em
o
r
y
in
th
e
f
o
r
m
o
f
an
ar
r
ay
in
d
e
x
in
g
o
p
er
atio
n
.
Me
m
o
r
y
r
ea
d
s
ca
n
tak
e
less
p
r
o
ce
s
s
in
g
tim
e
th
an
co
n
v
e
n
tio
n
al
o
p
er
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n
s
s
u
ch
as
m
u
ltip
licatio
n
,
ad
d
itio
n
,
an
d
s
o
f
o
r
th
.
T
h
e
c
o
m
p
lex
ity
o
f
a
d
d
in
g
an
d
ac
ce
s
s
in
g
th
e
tab
le
wh
ile
d
ec
o
d
in
g
ca
n
b
e
esti
m
ated
u
s
in
g
ex
p
r
ess
io
n
s
(
7
)
an
d
(
8
)
r
esp
ec
tiv
ely
:
×
Ο
(
2
×
×
+
×
(
2
×
−
1
)
)
(
7
)
∗
Ο
(
×
)
(
8
)
wh
e
r
e
is
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
d
e
c
o
d
in
g
it
er
ati
o
n
s
,
is
le
n
g
t
h
o
f
L
DPC
co
d
e
,
is
a
v
e
r
a
g
e
v
a
lu
e
o
f
th
e
v
a
r
i
ab
le
n
o
d
e
i
n
th
e
PC
M,
is
n
u
m
b
er
o
f
p
a
r
it
y
c
h
e
ck
b
its
,
is
a
v
e
r
a
g
e
v
al
u
e
o
f
c
h
ec
k
n
o
d
e
i
n
t
h
e
PC
M.
b.
Po
lar
co
d
es
:
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
lis
t a
lg
o
r
ith
m
I
n
th
e
ca
s
e
o
f
th
e
SC
L
d
ec
o
d
i
n
g
alg
o
r
ith
m
[
5
3
]
.
I
ts
co
m
p
lex
ity
is
esti
m
ated
as
(
9
)
:
Ο
(
∗
∗
2
)
(
9
)
wh
er
e
is
th
e
d
ep
th
o
f
t
h
e
s
u
cc
ess
iv
e
ca
n
ce
llatio
n
d
ec
o
d
in
g
lis
t,
is
p
o
lar
co
d
e
len
g
th
.
4.
P
RO
P
AG
AT
I
O
N
CH
ANN
E
L
M
O
D
E
L
S US
E
D
I
N
5
G
N
R
B
ef
o
r
e
d
esig
n
in
g
,
m
o
d
elin
g
a
n
d
p
lan
n
in
g
wir
eless
s
y
s
tem
s
,
it
is
n
ec
ess
ar
y
to
s
et
th
e
p
ar
am
eter
s
o
f
a
ch
an
n
el
p
r
o
p
ag
atio
n
m
o
d
el
.
T
h
ey
ca
n
p
r
o
v
id
e
in
f
o
r
m
atio
n
ab
o
u
t
th
e
f
u
tu
r
e
s
tr
u
ctu
r
e,
p
e
r
f
o
r
m
an
ce
,
ef
f
icien
cy
,
an
d
ac
c
u
r
ac
y
.
Mo
s
t
o
f
th
e
ab
o
v
e
-
m
en
tio
n
ed
w
o
r
k
s
o
n
ch
an
n
el
m
o
d
ellin
g
i
n
5
G
NR
u
s
ed
th
e
f
o
llo
win
g
m
o
d
els,
f
o
r
wh
ich
we
g
iv
e
a
b
r
ie
f
co
m
p
ar
is
o
n
b
e
lo
w.
4
.
1
.
Sto
cha
s
t
ic
Ra
y
leig
h
a
nd
rice
cha
nn
el
m
o
dels
Sto
ch
asti
c
ch
an
n
el
m
o
d
els
s
im
u
late
th
e
p
r
o
b
ab
ilit
y
d
en
s
ity
f
u
n
ctio
n
(
PDF)
o
f
th
e
c
h
an
n
el
im
p
u
ls
e
r
esp
o
n
s
e
(
o
r
e
q
u
iv
ale
n
t
f
u
n
cti
o
n
s
)
.
I
n
s
tead
o
f
ac
cu
r
ately
p
r
e
d
ictin
g
th
e
im
p
u
ls
e
r
esp
o
n
s
e
a
t
a
s
in
g
le
lo
ca
tio
n
,
th
ese
m
eth
o
d
s
aim
to
p
r
e
d
ict
th
e
PDF
ac
r
o
s
s
a
lar
g
e
ar
ea
.
Usi
n
g
s
to
ch
asti
c
m
o
d
els
is
m
o
r
e
co
m
m
o
n
f
o
r
s
y
s
tem
d
esig
n
an
d
co
m
p
ar
is
o
n
.
A
ch
an
n
el
with
R
ay
leig
h
f
a
d
in
g
o
cc
u
r
s
wh
en
th
er
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ar
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m
an
y
d
if
f
er
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t
s
ig
n
al
p
ath
s
b
et
wee
n
th
e
tr
an
s
m
itter
an
d
r
ec
eiv
er
,
n
o
n
e
o
f
wh
ich
is
d
o
m
in
an
t
(
th
e
ca
s
e
o
f
NL
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.
T
h
e
m
o
d
el
d
escr
ib
es
a
wo
r
s
t
-
ca
s
e
s
ce
n
ar
io
in
th
e
s
en
s
e
th
at
th
e
d
o
m
in
an
t
co
m
p
o
n
en
t
o
f
t
h
e
s
ig
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al
is
m
is
s
in
g
an
d
t
h
er
ef
o
r
e
t
h
er
e
ar
e
m
an
y
d
ip
s
with
f
ad
es.
T
h
is
ass
u
m
p
tio
n
is
u
s
ef
u
l
f
o
r
th
e
d
esig
n
o
f
r
eliab
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s
y
s
tem
s
.
T
h
e
R
ay
leig
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PDF
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f
th
e
en
v
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o
p
e
o
f
th
e
r
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eiv
ed
s
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n
al
(
0
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is
wr
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as
(
1
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)
:
(
0
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=
0
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xp
(
−
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2
)
;
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2
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p
o
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f
th
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m
u
ltip
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n
al.
T
h
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r
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f
ad
in
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c
h
an
n
el
m
o
d
el
is
u
s
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wh
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th
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r
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s
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co
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in
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f
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L
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p
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s
ev
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p
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f
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o
f
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f
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n
th
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tr
an
s
m
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will
b
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less
th
an
in
th
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ca
s
e
o
f
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ay
lei
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h
f
ad
in
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h
e
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