TELKOM
NIKA
, Vol.14, No
.4, Dece
mbe
r
2016, pp. 13
83~138
9
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i4.4158
1383
Re
cei
v
ed
Jun
e
7, 2016; Re
vised O
c
tobe
r 27, 2016; A
c
cepted
No
ve
m
ber 11, 201
6
Binary LDPC Codes Decoding Algorithm Based on MRF
and FPGA Implementation
Zhongxu
n
Wang*, Wen
q
iang Wu
Institute of Science a
nd T
e
chnol
og
y for Opto-e
l
e
ctronics In
formation, Yant
ai Univ
ersit
y
,
Yantai Sh
an
do
ng, Chi
na, 05
3
5
-69
025
06
*Corres
p
o
n
n
d
i
ng auth
o
r, e-mail:
y
t
w
z
x3@
1
2
6
.com
A
b
st
r
a
ct
T
he improv
ed
LDPC cod
e
decod
ing a
l
gorith
m
mai
n
l
y
refereed to
impr
ovin
g d
e
cod
i
ng
perfor
m
a
n
ce o
r
reducin
g the deco
d
in
g co
mputatio
n co
mpl
e
xity. No matt
er hard dec
isio
n or soft decisi
o
n
LDPC
cod
e
de
codi
ng
al
gorith
m
, w
e
c
an
get
all r
i
n
g
n
u
m
b
e
r
by
on
e test, i
n
stead
of testin
g e
a
ch
lo
ng
rin
g
nu
mb
er, after opti
m
i
z
i
n
g ri
ng
detectio
n
al
go
rithm. W
e
p
u
tted forw
ard the
app
licati
on of
Gaussia
n
Mark
o
v
Ran
d
o
m
F
i
el
d
mo
del to re
ali
z
e
th
e sourc
e
para
m
eter
estimatio
n
, and
mak
e
lo
garit
h
m
ic l
i
kel
i
h
ood
ratio
correctio
n of
b
i
t seq
uenc
e r
e
ceive
d
by
the
chan
nel
d
e
cod
i
ng
en
d. Jo
ini
n
g so
urce r
e
sid
ual
red
u
n
danc
y
infor
m
ati
on
is
to incr
ease
th
e d
e
co
der
err
o
r corr
ection
a
b
ility. S
ource
estimatio
n
a
d
a
p
tive v
a
ria
b
l
e
can
correct coeffici
ent, and
it w
a
s regul
ated
by
error rate.
Un
d
e
r the co
nditi
o
n
that co
mp
utation
a
l co
mple
xity
incre
a
sed
littlel
y, the LDPC code d
e
co
din
g
alg
o
ri
th
m bas
e
d
on MRF
effectively i
m
prov
ed the d
e
cod
i
ng
perfor
m
a
n
ce a
nd i
m
ple
m
ente
d
the i
m
prove
m
e
n
t of LDP
C
code
dec
odi
ng
alg
o
rith
m .In th
e en
d, w
e
real
i
z
e
d
the deco
d
i
ng al
gorith
m
by us
in
g F
P
GA.
Ke
y
w
ords
:
LD
PC code, MRF
,
para
m
eters e
s
timati
on, dec
o
d
in
g alg
o
rith
m,
F
P
GA
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
LDPC
co
de, low de
nsity p
a
rity che
c
k code
[1-3], bel
ong
s to the li
near
blo
ck
code. Its
che
c
k matrix is spa
r
se mat
r
ix of 0 and 1. G
enerali
z
e
d
LDPC co
de
s have sho
w
n relatively goo
d
perfo
rman
ce.
Schola
r
s G
a
l
l
age broug
ht forwa
r
d the re
lated theo
ry basi
s
of LDP
C
co
de
s in 1
962
[4]. Becau
s
e
the LDP
C
co
de de
co
ding
compl
e
xity is
not high, a
n
d
its de
scri
ption is
relativel
y
simple, it can
be reali
z
ed
by hard
w
are, so it
immediately draw att
ention and b
e
cam
e
acade
mi
c
resea
r
ch hot
[5]: increa
si
ng the tran
smissi
on di
sta
n
ce, p
r
opo
si
ng ene
rgy-sa
ving scheme
and
improvin
g ant
i interferen
ce
ability, etc [6]. In fa
ct, the re
sea
r
ch
steps
of furthe
r enha
nci
ng t
he
perfo
rman
ce of
LDPC co
d
e
s
n
e
ver sto
p
.
LDPC
co
d
e
s h
a
ve bee
n extensively
studie
d
in the
literature usin
g cod
e
modif
y
ing techniq
u
e
s such
as in
formation n
u
lling or shorte
ning, extendi
ng
[7, 8], punctu
ring [9], a
nd
combi
n
ing
[1
0]. We fo
cu
sed on
stu
d
yin
g
the
stru
cture of L
D
PC
code
and LDP
C
co
de decodin
g
algorith
m
, improved L
D
PC
code de
co
di
ng algo
rithm became the most
c
r
uc
ial part [11].
Due to the
prog
re
ss of comp
uter
co
mputi
ng cap
a
city, the cal
c
ulatio
n of stocha
stic
model is
no longer the bottleneck
,
we give more
and more
attention to s
t
oc
has
tic
model, and
Markov [12]
Ra
ndo
m Fi
eld i
s
one
of the im
po
rtant bran
che
s
. M
R
F i
n
trodu
ced
st
ru
cture
informatio
n th
roug
h the
nei
ghbo
rho
od
sy
stem,
so th
at
it can
exp
r
ess inte
ra
ction
model
betwe
en
spatial
relativ
e
ran
dom va
riable
s
, and fi
nd the soluti
o
n
of the probl
em acco
rd
in
g
to the statisti
cal
deci
s
io
n a
nd
estimation
th
eory o
p
timal
crite
r
ion.
No
matter h
a
rd d
e
ci
sion
or soft deci
s
io
n L
D
PC
cod
e
de
co
di
ng alg
o
rithm
,
after opti
m
izing
rin
g
detectio
n
alg
o
rithm,
we
put forwa
r
d
the
appli
c
ation o
f
Gaussian
Markov Ran
dom Fiel
d
model to re
alize the so
urce parame
t
er
estimation, a
nd reali
z
e the
LDPC
code
decodin
g
alg
o
rithm ba
se
d on MRF.
The be
st wa
y of
testing wheth
e
r an a
l
gorithm
is ef
fective is to apply the alg
o
rithm to
pra
c
tice
it. So we
use FPG
A
[13] model
to real
i
z
e th
e
algorith
m
, an
d to verify the
effectivene
ss,
so that it can
provide g
u
ida
n
ce
whe
n
we
use thi
s
algo
rithm in bad communi
catio
n
environ
men
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1383 – 138
9
1384
2. LDPC Cod
e
Deco
ding Algorithm Based on M
R
F
C
u
rr
en
tly, in
th
e
pr
oc
es
s
o
f
r
e
s
e
ar
ch
on
LDPC code
s,
the imp
r
oved
decodin
g
alg
o
rithm
became a v
e
ry impo
rtan
t and a
key
part, and it
mainly incl
ude imp
r
ovin
g the de
codi
ng
perfo
rman
ce
or re
du
cing
computing
co
mplexity, or makin
g
a co
mpromi
se.
2.1. Rese
arc
h
Method
2.1.1. Ring Analy
s
is Detect
ion Algori
t
hm Optimiza
tion
Both hard de
cisi
on a
nd
so
ft decisi
on b
e
l
ong to
the ite
r
ative de
codi
ng alg
o
rithm,
the key
lies in the in
depe
nden
ce
of the messa
ge tran
sfer.
For any give
n LDPC
co
d
e
, rapid d
e
te
cting
ring
-num
be
r of Tanner graph
whi
c
h che
c
k ma
tr
ix correspo
nding to
in
very important.
Optimizatio
n
algorith
m
, poi
nted at the chara
c
te
risti
c
s of Tanner g
r
aph which L
D
PC code
ch
eck
matrix co
rrespondi
ng to,
was
con
s
tructe
d acco
rdi
ng t
o
Dij
kst
ra al
g
o
rithm. Th
e key gist i
s
that
we
can g
e
t all rin
g
numbe
r by one testin
g, instea
d of
testing ring
-n
um
ber in turn, which
ring len
g
t
h
is 4, 6, 8, 10
, etc, so as t
o
reali
z
e the
rapi
d d
e
tecti
on of ring
-nu
m
ber. So it can re
du
ce th
e
comp
utationa
l complexity and improve d
e
tection
spe
e
d
.
2.1.2. Param
e
ter Es
tim
a
ti
on Metho
d
For pa
ramete
r model, pa
ra
meter e
s
timation is very important. But param
eter e
s
timatio
n
need to
ide
n
tify accu
rate
result
s, so
we
need
to alte
rnately iterate pa
ramete
r
estimation
an
d
identificatio
n, that i
s
to
say we
will u
s
e
prev
iou
s
para
m
eter e
s
timation for t
he n
e
xt patt
e
rn
recognitio
n
, to update
pa
ramete
r e
s
timation after getting re
cognition
re
su
lts. In the end,
recy
cling
the
s
e
step
s u
n
til conve
r
g
e
n
c
e. This
arti
cl
e uses the
Dynami
c
Mo
nte Ca
rlo
me
thod
estimation.
Gibb
s sa
mpli
ng, whi
c
h wi
ll be use
d
in Dy
nami
c
Monte Ca
rlo
method, ha
s a fast
conve
r
ge
nce spe
ed, so the
param
eter e
s
timation u
s
u
a
lly use
s
Gib
b
s samplin
g.
We a
s
sum
e
that
12
(,
,
,
)
n
x
xx
x
and
12
(,
,
,
)
n
yy
x
x
are two
realitie
s which hav
e
differen
c
e
s
o
n
ly in the first compo
nent i
n
the Ma
rkov Field, then de
fine the transi
t
ion prob
abilit
y:
1
11
1
\
1
(|
)
e
x
p
(
(
)
)
s
Py
x
z
U
y
x
(1)
Among them
1\
1
1
2
(,
,
,
)
s
n
yx
y
y
x
x
Thus exten
d
ing, two
realitie
s i
n
any Ma
rkov Fi
eld,
12
(,
,
,
)
n
x
xx
x
and
12
(,
,
,
)
n
yy
y
y
, after
n
st
ep
s,
)
...
,
)...(
...
,
(
)
...
,
(
2
1
2
1
2
1
n
n
n
y
y
y
x
x
y
x
x
x
, then
trans
fer of x t
o
y is
rea
lized. Trans
fer matrix is
:
12
(|
)
(
,
)
n
P
yx
P
P
P
x
y
(2)
Limiting di
stri
bution of the
tr
ansition mat
r
ix probability is
Markov Fi
eld true di
stri
bution
P(x).
2.1.3. Marko
v
Random Field Model
The
choi
ce
of
dista
n
ce me
asu
r
e
ha
s a
n
impo
rtant
rel
a
tionship
with
pattern reco
gnition,
becau
se the
dire
ctly affect
t
he iterative
conve
r
ge
nce effect
in th
e end. F
r
ob
e
n
ius
norm ca
n
effectively measure
matri
x
and ve
ctor,
it also
can
be rega
rde
d
an exten
s
ion
of two
or th
ree
-
dimen
s
ion
a
l vector le
ngth.
For chan
ge
s of calculating
amount, this area u
s
ually
relatively co
nce
n
trated, if we ca
n
find the clo
s
e
d
cu
rve whi
c
h disting
u
ish
e
s bet
we
e
n
chang
e and n
on-cha
nge
re
gion
s, then it can
be se
parate
d
from the curve in
sid
e
and outsi
de
and even resid
ual won’t affect it.
()
PL
rep
r
e
s
ent
clo
s
ed
curve
bo
unda
ry p
r
ob
a
b
ility den
sity function
of
,then clo
s
e
d
curve
i
n
tern
al
prob
ability
d
ensity <bo
u
n
dary pro
babil
i
ty
densit
y,
clo
s
ed
curve
extern
al p
r
obability d
e
n
s
ity
<bo
und
ary p
r
obability d
e
n
s
ity, pro
babili
ty density
of
cro
s
sing
the
clo
s
ed
curve.
In oth
e
r words,
we only ne
ed
to find the largest on
e of the boun
dary p
r
oba
bility den
sity.
()
()
()
P
L
P
i
n
P
out
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Binary LDP
C
Cod
e
s
De
cod
i
ng Algorithm
Based o
n
MRF and FPGA
… (Zho
ng
xun
Wang
)
1385
Among the
m
,
()
Pi
n
represent
s probability within the
area,
()
Pout
r
e
pr
es
e
n
t
s
prob
ability ou
tside the are
a
. For Marko
v
chain,
the boun
dary curve of the next moment is only
related to th
e
bound
ary
cu
rve of pre
s
e
n
t
moment,
an
d it must satisfy aperi
odi
city and ergodi
city.
The be
st way to con
s
tru
c
t
Markov chain
is to u
s
e the
dynamic
Mo
nte Ca
rlo m
e
thod to e
s
tima
te
para
m
eters.
More th
an 5
0
times, we
should
stop
o
peratio
n, and
the 50
th
stat
e will be opti
m
al
boun
dary cl
o
s
ed
curve.
Gau
s
s-Ma
rko
v
rand
om fiel
d bel
ong
s to t
he
stat
iona
ry autore
g
ressiv
e
pr
ocess, a
n
d
it is a
linear mo
del.
So its
cova
rian
ce
matrix
is po
sitive definite
a
nd its
nei
ghb
orh
ood syste
m
is
s
y
mmetric
.
()
c
Vx
is a potential
function of po
tential gr
ou
p C, the obje
c
t’s prio
r mod
e
l is:
1
()
e
x
p
[
(
)
]
c
cC
P
Xx
V
x
Z
(4)
Z is a reg
u
lar
con
s
tant, a priori ene
rgy wil
l
be defined a
s
the followi
n
g
:
()
()
(
(
)
,
(
)
)
rR
r
N
r
Ux
Vx
r
x
r
(5)
Usi
ng the maximum posterior
i probability estimation:
*
ar
g
m
a
x
(
)
X
X
PX
Y
(6)
Acco
rdi
ng to the Bayesia
n
formul
a:
()
()
(
)
PX
Y
P
Y
X
PX
(7)
So there are:
*
ar
g
m
ax
(
)
(
)
X
XP
Y
X
P
X
(8)
Taggin
g
the voxel with the way of minim
u
m ene
rgy, so that we ca
n
deal with po
sterior
energy pro
b
le
m.
*
ar
g
m
i
n
(
;
)
(
)
X
X
UD
x
U
x
(9)
Among them,
the poste
rior
for ene
rgy is:
2
2
2
()
1
(
;
)
(
(
)
(
)
)
l
og(
)
22
k
F
k
rR
rR
k
Dr
UD
x
U
D
r
x
r
(
1
0
)
The Ga
ussia
n
para
m
eters
,
kk
kK
In the class K
,
defining t
he cente
r
of the cla
ss:
()
1
()
k
Xr
k
k
Dr
L
(11)
Definin
g
the varian
ce of the
class:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1383 – 138
9
1386
2
()
1
()
kk
F
Xr
k
k
Dr
L
(12)
And
k
L
is the v
o
xel num
ber of, whi
c
h
b
e
long
s to th
e cl
ass K,
()
k
F
Dr
is the
Frob
eniu
s
no
rm. It also meets the cha
r
acte
rs of
po
sitive definite
n
ess, homo
g
eneity, triang
le
inequ
ality and comp
atibility.
2.1.4. LDPC
Code
Dec
oding Algorith
m Based on
MRF
The main
ste
p
s of LDP
C
code de
co
ding
algorithm b
a
s
ed o
n
MRF
are a
s
follows:
First, we
will initialization
and set the al
l
o
wed maxim
u
m iteration
number, use Gauss-
Markov rand
om
field
mod
e
l
to reali
z
e
the sou
r
ce pa
ramete
r esti
mation,
a
nd
make logarithmi
c
likeliho
od
rati
o co
rrectio
n
of bit se
que
nce
re
ceive
d
by the cha
nnel d
e
codin
g
end. So
urce
estimation a
d
aptive variabl
e can
corre
c
t coeffi
ci
ent, and it will be re
gulated by error rate.
The second step,
it will calcul
at
e respectively from
the hori
zontal
direction and verti
c
al
dire
ction. In decodin
g
iterati
on for the first time, ch
eck nod
es wi
ll not get any information
on
input co
de
word from vari
able no
de. S
o
the exte
rn
al informatio
n of informat
ion nod
es f
r
om
che
c
k nod
es i
s
ze
ro.
The third
ste
p
, it will make judgme
n
t informatio
n for all variabl
e
node
s
, and
decid
e
wheth
e
r it
sh
ould e
nd th
e i
t
erative de
co
ding p
r
o
c
e
s
s
according
to t
hat judg
ment
informatio
n. If it
gets a ze
ro vector, then
showi
ng t
hat it is a legal co
de wo
rd,
and
it has decod
ed su
ccessful
ly.
Otherwise, it will begi
n the
iterativ
e process of che
ck
node
s a
nd va
riable
nod
e
s.
It will repe
at the
above step
s
until all erro
rs pattern is ze
ro or
the max
i
mum iteratio
n numbe
r
ha
s been rea
c
h
ed,
and outp
u
t the decodin
g
re
sults.
2.2. Results and An
aly
s
is
Simulation test in this paper m
a
inly incl
u
d
e
s
Perf
orma
nce sim
u
lation results an
d
averag
e itera
t
ion(we set a
ll maximum i
t
eration
nu
mb
e
r
to
10
0)
n
u
mb
er
o
f
LD
PC
c
o
de
so
ft
deci
s
io
n de
coding
algo
rith
m and
L
D
PC co
de
s de
c
o
d
i
ng
alg
o
rithm
based on
M
R
F.
The re
sult is
s
h
ow
n
in
F
i
gu
r
e
1
.
Figure 1. De
coding p
e
rfo
r
mance co
mp
arison
s
We can kno
w
from Figu
re 1: The de
c
odi
ng pe
rformance diffe
rence of LDP
C
co
de
decoding al
gorithm
s
difference
will begi
n to
emer
ge
when the SNR increa
ses. Especially when
the SNR i
s
m
o
re tha
n
0.5,
the de
codin
g
perfo
rman
ce of
LDPC co
d
e
s
d
e
coding algorith
m
ba
sed
on M
R
F i
s
o
b
viously b
e
tter tha
n
the
standard BP d
e
co
ding
algo
rithm, improve
d
BP de
codi
ng
algorith
m
an
d Min-Sum
decodin
g
alg
o
rithm. Spe
c
ifically whe
n
the bit error rate i
s
1
0
-3
,
comp
ared
with sta
nda
rd B
P
decodin
g
al
gorithm
, im
proved BP de
coding
algo
rith
m and
Min
-
Su
m
decodin
g
alg
o
rithm, the decodin
g
pe
rforma
nce of LDPC cod
e
deco
d
ing
based on M
R
F
increa
sed 0.3
d
B, 0.38dB, 0.5dB.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Binary LDP
C
Cod
e
s
De
cod
i
ng Algorithm
Based o
n
MRF and FPGA
… (Zho
ng
xun
Wang
)
1387
3. The FPGA Implementa
tion of L
D
PC Decoding
Algorithm Ba
s
e
d on MRF
No
w we will i
m
pleme
n
t the
above al
gorit
hm thro
ugh
F
P
GA and ve
ri
fy the effectivene
ss
of this algorit
h
m. So that it will provide
guida
nce in bad communication env
ironment. In order to
verify the efficient p
e
rfo
r
m
anc
e of the al
gorithm,
cod
e
length an
d code rate of bi
nary L
D
PC
code
will be set to 512 an
d 0.5 resp
ectively.
3.1. Rese
arc
h
Method
The tool
s a
d
opted by thi
s
part: the Ve
ril
og
lan
gua
ge;
Altera Q
uart
u
sll1
4.0 deve
l
opment
tools; DE1
-
SOC platform develop
ed b
y
Taiwan frie
nd Cry
s
tal Company, and
its main chi
p
;
partial pa
ralle
l deco
der.
3.1.1. The Ov
erall Architectur
e Diagr
a
m of Dec
o
d
e
r
The overall archite
c
ture di
a
g
ram i
s
sh
own in Figure 2.
Figure 2. Overall archite
c
tu
re diag
ram
s
The ab
ove figure i
s
the
overall a
r
chit
ecture dia
g
ra
m of FPGA
decode
r. Simply, the
whol
e pro
c
e
s
s is that: After re
ceiving inf
o
rmatio
n, it will be conve
r
t
ed thro
ugh b
u
ffer, and it will
get initial information
whi
c
h inclu
d
e
s
re
dund
ant information. The
will start de
co
ding.
The next step
is to update informatio
n of
che
ck no
de
and varia
b
le node, then to
make a
rea
s
sessm
e
n
t
of source
redu
nda
nt in
formati
on, a
nd to iterate
again. After rea
c
hi
ng t
he
maximum iteration num
ber, it will start decodin
g
ca
che and
outpu
tting the re
su
lts throu
gh th
e
String and
co
nversi
on mo
d
u
le.
3.1.2. Check
Node Mo
dul
e
This alg
o
rith
m adopts th
e binary LDPC cod
e
s lo
garithmi
c
do
main algo
rith
m. In this
pro
c
e
ss, it
wi
ll use
tanh
(x) function. It can be
divide
d into two pa
rts. On
e pa
rt
rep
r
e
s
ent
s t
he
sign bit, an
d
anothe
r pa
rt repre
s
e
n
ts n
u
m
eri
c
al bit. We ca
n implem
ent the num
e
r
ical
bit throu
gh
look-up tabl
e. The stru
ctu
r
e diagram
is
s
h
ow
n
in
F
i
gu
r
e
3
.
3.1.3. Variable Node Mo
d
u
le
Variabl
e nod
e upd
ating m
odule m
a
inly
absorb
s
the i
n
formatio
n from othe
r che
ck
nod
e
pro
c
e
ssi
ng, t
hen it
will me
rge
r
the
s
e i
n
formatio
n an
d
pa
ss th
em to
ch
eck n
ode
s. Variable
no
de
s
decodin
g
pa
rt
mainly a
b
sorbs th
e info
rm
ation fro
m
all
che
c
k n
ode
s
and th
e corre
s
po
ndin
g
initi
a
l
informatio
n, and the
n
it will start d
e
cod
i
ng. If the co
de word is n
o
t app
rop
r
iat
e
, it will e
s
timate
sou
r
ce re
dun
dant inform
ation wh
en the
numbe
r of
ite
r
ation di
dn’t reach it maximum point. T
hen
it will merg
e
this inform
a
t
ion into the
initia
l information, and
begin the
ne
xt proce
s
s. The
stru
cture diag
rami
s
sh
own in Figure 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1383 – 138
9
1388
Figure 3. che
ck n
ode
stru
cture diag
ram
Figure 4. Vari
able no
de structure diag
ra
ms
3.2. Results and An
aly
s
is
The pa
ram
e
ter of bina
ry
LDPC
co
de,
adopte
d
in th
is pa
rt, is(5
1
2
,3,6) , and
K=5. The
end result is
sho
w
n in Fi
g
u
re 5. From the pi
ctu
r
e
we
can
see that
it began to d
e
co
de when t
he
reset i
s
inval
i
d an
d
start
decode
=1. Af
ter
che
c
k n
o
des an
d va
ri
able
nod
es u
pdate ite
r
atio
n,
decode ove
r
=1, and it outputted the cod
e
wo
rd
s wh
e
n
the nu
mber of itera
t
ion rea
c
he
d
the
maximum po
int. It can be verified that the code
word is con
s
istent with that outputted by
MATLAB.
Figure 5. Output result of deco
der
This part use
s
Cyclon
e
V seri
es
5
C
ESMA5F31
C
6 d
e
velope
d
by Altera comp
a
n
y.
We
make
cod
e
compilation
an
d testin
g th
ro
ugh th
e
Qua
r
tusII 14.0
software.
After
comp
re
hen
si
ve
repo
rt, we ca
n see that co
nsum
ed reso
urce
s LE wa
s 50%, the RAM was 60%
, the maximum
clo
ck frequ
en
cy wa
s 2
00
MHZ. From
t
he
re
sult we can se
e
that the
logi
cal
re
sou
r
ces ca
n meet
the requi
rem
ent, and it ca
n achi
eve the
comp
romi
se
betwe
en re
so
urces a
nd efficien
cy.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Binary LDP
C
Cod
e
s
De
cod
i
ng Algorithm
Based o
n
MRF and FPGA
… (Zho
ng
xun
Wang
)
1389
4. Conclusio
n
For
Ring
anal
ysis d
e
tectio
n
,
algorithm
we ca
n get
all ring nu
mbe
r
throu
gh o
ne t
e
st, an
d
it no longe
r requires te
stin
g ring n
u
mb
er of ea
ch
ri
ng length. F
r
om uniqu
e p
e
rspe
ctive, this
pape
r first p
u
t
forward
that
we
can
co
m
b
ine
with
Markov
rand
om fi
eld to i
m
plem
ent the
so
urce
para
m
eter e
s
timation. At the sam
e
time, we can
im
prove the abi
lity of error correctio
n
thro
ugh
the u
s
ing
of
resi
dual
redu
ndan
cy info
rmation
wh
e
n
de
codi
ng. In
the e
nd,
we
use FPG
A
to
impleme
n
t the above alg
o
rithm.
Simulation
re
sult
sho
w
e
d
t
hat the
pe
rformanc
e
of L
D
PC
cod
e
d
e
coding
alg
o
rith
m ba
se
d
on M
R
F i
n
cre
a
se
d 0.4
d
B. So it is
better than th
e mai
n
stre
am
de
co
ding
algo
rith
m, and it A
c
hi
eve
a high p
e
rfo
r
man
c
e ta
rg
et. But the compl
e
xity
of the algorit
hm is in th
e
same
order of
magnitud
e
, so we
ne
ed to
simplify the
computation
a
l
compl
e
xity of the algo
rithm
in the follo
w-u
p
study.
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