Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
5
,
No
. 3,
J
une
2
0
1
5
,
pp
. 46
4~
47
6
I
S
SN
: 208
8-8
7
0
8
4
64
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Hybrid Concatenated Coding
Scheme for MIMO Systems
Ilesanmi B
a
njo Oluw
afemi
Departem
ent
of
Ele
c
tri
cal
and
E
l
ectron
i
c
Engin
e
e
r
ing,
Ekit
i S
t
ate
Univers
i
t
y
,
Ado- Ek
iti, Nigeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 20, 2014
Rev
i
sed
Feb
20
, 20
15
Accepted
Mar 16, 2015
In this paper
,
t
w
o h
y
brid
concaten
ated super-o
rthogonal space-tim
e trellis
codes (SOSTTC) apply
i
ng iterative d
ecod
i
ng ar
e proposed for flat fad
i
ng
channels. The
encoding oper
a
tion is based on the concatenation o
f
convolution
a
l
codes, int
e
rleavi
ng a
nd super-orthogonal space-tim
e trellis
codes
.
Th
e firs
t
conca
t
ena
t
ed s
c
hem
e
cons
is
ts
of a s
e
ria
l
con
cat
enat
ion of
a
parallel con
c
atenated convo
lutio
nal c
ode with a
SOSTTC while the second
consists of par
a
llel
concaten
atio
n of
two serially concaten
ated co
nvolution
a
l
and SOSTTC codes. The d
ecoding of th
ese two
schemes is described,
their
pairwise error
probabilities are deri
ved
and the frame error
rate (FER
)
perform
ances
ar
e evalu
a
t
e
d b
y
com
puter s
imulation in R
a
yl
eigh fadin
g
channels. The pr
oposed topol
ogies are shown to
perfo
rm better than existing
conca
t
ena
t
ed s
c
hem
e
s
with a
c
onstituent
code
of convolutional and space-
tim
e cod
e
s in
li
t
e
ratur
e
.
Keyword:
Space
-tim
e coding
iter
a
tiv
e d
ecodin
g
;
diversity
fadi
ng
cha
n
nel
co
nvo
lu
tion
a
l co
d
e
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ilesanm
i
Banjo Oluwa
f
em
i
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
c E
n
gi
nee
r
i
n
g,
Ek
iti State Un
iv
ersity,
Ado
-
Ek
iti, Ni
g
e
ria
Em
a
il: ib
to
7
5
@g
m
a
il.co
m
1.
INTRODUCTION
Th
e info
rm
atio
n
cap
acity g
a
in o
f
a wireless syste
m
can
b
e
in
creased
b
y
em
p
l
o
y
in
g
m
u
lt
ip
le tran
sm
i
t
and/
or receive
antennas
in a
comm
unication system
[1
-5]. Space-tim
e c
odi
ng lead
t
o
an inc
r
ease i
n
both
b
a
ndwid
th
effi
cien
cy an
d
reliab
ility o
f
wirel
e
ss co
mm
u
n
i
catio
n
ch
ann
e
ls
b
y
co
m
b
in
in
g
sp
atial an
d
tem
p
o
r
al
diversity [6]. S
uper-orthogonal space-tim
e
t
r
ellis code (SOSTTC)
is the recently introd
uced space-tim
e
code
th
at o
f
fers im
p
r
ov
ed
p
e
rfo
r
m
a
n
ce ov
er earlier sp
ace-tim
e
co
nstru
c
tion
s
. SOSTTC co
mb
in
e set p
a
rtitio
n
i
ng
base
d on the codi
ng
gain
distance and a super set of space-
tim
e
block c
o
des in a syste
m
a
tic way to offe
r full
di
ve
rsi
t
y
and
i
m
prove
d c
odi
n
g
gai
n
[
7
-
9
]
.
Th
e inv
e
n
tion o
f
tu
rbo
co
din
g
with
its asto
n
i
sh
ing
p
e
rform
a
n
ce h
a
s attracted
th
e in
terest
o
f
researc
h
ers to the subj
ect of concat
e
n
ated coding schem
e
s i
n
recent ti
m
e
s. Turbo c
odes
whic
h are built from
p
a
rallel con
caten
atio
n
of conv
o
l
u
tio
n
a
l codes with
itera
tive d
ecod
i
ng
p
e
rform
clo
s
e to
th
e Sh
anno
n
li
mit
in
ad
d
itiv
e
wh
ite Gau
s
sian
n
o
i
se (AWGN) ch
ann
e
ls [10
]
. Serially co
n
c
aten
ated
conv
o
l
u
tio
n
a
l co
d
e
s
were
in
v
e
stig
ated
in
[8
]
with
th
e t
u
rb
o prin
cip
l
es
wh
ile in
[9
]
hy
bri
d
co
ncat
e
n
a
t
ed co
n
vol
ut
i
o
nal
co
des
wi
t
h
a So
ft
-
i
n
p
u
t
S
o
ft
-
O
ut
put
(S
IS
O) m
a
xi
m
u
m
a po
st
eri
o
ri
dec
o
di
n
g
m
odul
e was
p
r
op
ose
d
.
The use
of cha
nnel coding wi
th space-tim
e
code
s
(STC)
has the adva
ntage
of provi
ding
additional
t
i
m
e
di
versi
t
y
especi
al
l
y
i
n
f
a
st
fadi
ng c
h
a
nnel
s
. Va
ri
o
u
s
co
ncat
enat
ed
t
o
p
o
l
o
gi
es ha
v
e
bee
n
p
r
op
os
ed i
n
literatu
re with
repo
rted
im
p
r
ov
ed p
e
rfo
r
m
a
n
ce ov
er con
v
e
ntio
n
a
l STC
[13-21
]. In
[18
]
serial co
ncaten
atio
n of
con
v
o
l
u
t
i
o
nal
code
s and s
p
ac
e-t
i
m
e
t
r
ell
i
s
code
s (STTC
) was p
r
o
p
o
sed
whi
l
e
i
n
[2
2]
a do
ubl
e co
nca
t
enat
ed
to
po
log
y
con
s
i
s
tin
g
of a
p
a
ral
l
el co
n
caten
ated
conv
o
l
u
tio
n
a
l co
d
e
(PCCC) with
an
i
n
n
e
r
STTC was
p
r
op
o
s
ed.
In [23],
the hybri
d
concatena
t
ed
STC
ap
pl
y
i
ng i
t
e
rat
i
v
e
de
codi
ng
was a
n
al
y
zed. It
was
sho
w
n t
h
at
ch
oosi
n
g
recursiv
e co
des as th
e constitu
en
t cod
e
s resu
lts in
h
i
g
h
e
r cod
i
ng
g
a
in
. C
o
n
caten
atio
n
i
n
vo
lv
i
n
g
t
h
e
con
v
o
l
u
t
i
o
nal
code
(C
C
)
an
d
SOST
TC
w
a
s i
nve
st
i
g
at
ed
o
v
e
r fl
at
fadi
ng
c
h
an
nel
s
i
n
[
2
4-
26]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 3
,
Jun
e
201
5
:
4
64–
4
76
46
5
In
o
r
de
r t
o
i
m
pr
o
v
e t
h
e
per
f
o
rm
ance o
f
S
O
STTC
, t
w
o c
oncat
e
n
at
ed
S
O
STTC
t
o
pol
o
g
i
e
s
ove
r
fl
at
fadi
ng
cha
n
nel
s
are
p
r
o
p
o
se
d
i
n
t
h
i
s
pa
pe
r.
The
fi
rst
c
o
nsi
s
t
s
o
f
a
pa
ral
l
e
l
conc
at
enat
ed
co
nv
ol
ut
i
onal
co
d
e
concate
n
ated s
e
rially with a
n
inner SOSTT
C
(PC-SO
STTC) wh
ile th
e seco
nd
, ca
lled hybrid
c
o
ncate
n
ated
SOSTTC
(HC
-
SOSTTC
),
inv
o
l
v
e
s h
ybrid
co
n
caten
at
ed
co
nvo
lu
tion
a
l co
d
e
s (HCCC)
an
d inn
e
r
SOSTTC
code
s. Sim
u
lations
res
u
lts are
pre
s
ente
d for
the case
of
t
w
o tra
n
sm
it and one
receive ant
e
nna
in
qua
ssi
static
and fa
st
fadi
n
g
R
a
y
l
ei
gh cha
n
nel
s
. B
o
t
h
rec
u
rsi
v
e an
d n
o
n-recursi
v
e convolutional codes were consi
d
ere
d
as
the outer codes
and the
res
u
lts
are
pre
s
ente
d i
n
term
s of
f
r
a
m
e erro
r
rate (
F
ER).
The pa
per i
s
o
r
ga
ni
zed as f
o
l
l
o
ws. Fi
rst
l
y
, the sy
st
em
m
o
del
of t
h
e p
r
o
p
o
se
d schem
e
consi
s
t
i
n
g o
f
th
e ch
ann
e
l m
o
d
e
l, t
h
e en
cod
e
r an
d th
e d
e
cod
e
r stru
ctures i
s
d
e
scrib
e
d
.
Then
t
h
e
p
a
irwise error
p
r
ob
ab
ility of
the concatenat
ed schem
e
s is prese
n
te
d. T
h
e
r
eafter, the
perform
a
nce of th
e concate
n
ated schem
e
is evaluated
by
com
put
er
si
m
u
l
a
t
i
ons a
n
d
fi
nal
l
y
t
h
e
pap
e
r i
s
c
oncl
ude
d
.
2.
R
E
SEARC
H M
ETHOD
2
.
1
Pa
ra
llel Co
nca
t
enated-Super Orth
og
ona
l
Spa
c
e-Time Trellis Code
2.
1a
E
n
c
o
der
The bl
ock
di
agram
of t
h
e PC
-SO
S
TTC
en
code
r i
s
sho
w
n i
n
Fi
g
u
re 1
where t
h
e i
n
put
bi
t
s
ar
e
enco
de
d by
co
nv
ol
ut
i
o
nal
co
de 1 (C
C
1
) as
wel
l
as by
con
v
o
l
u
t
i
o
nal
code
2 (C
C
2
)
aft
e
r i
n
t
e
rl
ea
vi
ng
by
in
terleav
er
p
. All th
e ou
tput b
its fro
m
CC1
an
d CC2
are co
nv
erte
d t
o
a
single seri
al stream
. The serial
stream
is th
en in
terleav
ed
by
s
and
fi
nal
l
y
SOSTTC
e
n
code
d t
o
p
r
o
d
u
ce t
h
e c
o
m
p
l
e
x sy
m
bol
s t
h
at
are
transm
itted acc
ording t
o
the
SOSTTC
trans
m
ission m
a
trix at each
of th
e
transm
it
antennas. The
interl
eavers
are al
l
pseu
d
o
-ra
nd
om
and
ope
rat
e
o
n
bi
t
s
an
d n
o
t
sy
m
bol
s
.
The c
o
n
vol
ut
i
onal
e
n
c
ode
rs a
r
e ei
t
h
er b
o
t
h
recu
rsi
v
e sy
st
e
m
at
i
c
conv
ol
ut
i
onal
(R
SC
)
or
no
n-
recu
rsi
v
e
con
vol
ut
i
onal
(NR
C
)
enc
o
d
e
rs. Al
l
t
h
e en
code
rs
are term
in
ated
with
tail b
its an
d to
en
su
re unco
r
rela
ted
fad
i
n
g
and
all t
h
e an
tenn
as are
well sep
a
rated
.
p
s
Fi
gu
re
1.
Enc
o
der
bl
ock
di
a
g
r
a
m
of t
h
e PC
-S
OSTTC
sy
st
em
2.
1b Dec
o
der
I
n
t
h
is section
,
th
e iter
a
tiv
e
deco
d
i
n
g
pr
ocess of
th
e
pr
oposed
co
n
caten
at
ed
sch
e
m
e
s is d
e
scr
i
b
e
d.
The receive
d signal after m
a
t
c
h filtering at antenna
j (
j
=1,…,n
R
)
at
tim
e
inst
ant
t
i
s
a noi
sy
super
p
o
s
i
t
i
on
o
f
th
e
n
T
t
r
an
sm
it
ted si
gnal
s
gi
v
e
n
by
j
t
n
i
i
t
j
i
t
j
t
T
s
r
1
,
(1
)
whe
r
e
j
i
t
,
is th
e
path
g
a
i
n
fro
m
t
r
an
sm
it an
ten
n
a
i
to
receive a
n
tenna
j
,
j
t
is the add
itiv
e no
ise,
n
T
is the
num
ber
of t
r
a
n
sm
i
t
ant
e
nna
s an
d
i
t
s
repres
ent the
Quadrature Phas
e Sh
ift
Keying
(QPSK)
sym
b
o
l
s
tran
sm
it
ted
th
ro
ugh
th
e
i
th
tran
sm
it
an
ten
n
a
,
i=1
,
2
at tim
e
t
. B
o
t
h
j
i
t
,
and
j
t
are
m
odel
e
d as i
nde
pe
nde
nt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Hybri
d
C
onc
at
enat
e
d
C
odi
ng
Sche
me f
o
r M
I
MO
Syst
em
s
(
I
l
e
sa
nmi
B
a
nj
o
Ol
uw
af
emi
)
46
6
sam
p
l
e
s of t
h
e
zero
m
ean com
p
l
e
x Gaussi
a
n
ra
n
dom
vari
abl
e
wi
t
h
va
ri
ance
0.
5 an
d
N
0
/2
res
p
ectively per
dim
e
nsion. T
h
e signal to noise ratio
(SNR) is defi
ned
pe
r receive a
n
tenna as
E
b
/No
,
where
E
b
is the energy
per
bi
t
.
The
fl
at
R
a
y
l
ei
gh fadi
n
g
cha
n
nel
i
s
con
s
i
d
ere
d
a
nd t
h
e fa
di
n
g
i
s
st
at
i
s
t
i
call
y
inde
pe
nde
nt
f
r
o
m
on
e
transm
it-receive antenna
pair to a
n
y ot
her.
The PC
-S
OST
T
C
dec
ode
r (
F
i
g
u
r
e
2) em
pl
oy
s t
h
ree
SIS
O
m
odul
es
de
code
r t
h
at
e
x
c
h
an
ge s
o
f
t
in
fo
rm
atio
n
ite
rativ
ely b
e
tween
th
em
selv
es. Th
e sy
m
b
o
l
-by-sy
m
b
o
l
m
a
x
i
m
u
m
a post
e
ri
ori
(M
AP
) dec
ode
r is
use
d
fo
r t
h
e i
nne
r SO
STTC
deco
der an
d
a bi
t
-
by
-
b
i
t
MAP dec
o
der i
s
used f
o
r t
h
e
out
e
r
con
v
o
l
u
t
i
onal
deco
de
r. T
h
e
f
o
u
r
po
rt
s
of
t
h
e SIS
O
sy
st
em
of
t
h
e
C
C
s
ar
e use
d
i
n
t
h
e
i
t
e
rat
i
v
e dec
o
di
ng
o
f
t
h
e t
w
o
out
e
r
d
ecod
e
rs in ord
e
r to
fu
lly ex
plo
it th
e po
ten
tials o
f
th
e
a p
o
s
t
eri
o
ri
prob
ab
ility (APP) algorith
m
.
Fi
gu
re 2 s
h
ow
s
a sim
p
l
i
f
i
e
d di
agram
for t
h
e
PC
-S
OSTTC
d
ecode
r. F
o
r t
h
e
pu
rp
ose
of si
m
p
li
fi
cat
i
on
of desc
ri
pt
i
o
n,
t
h
e
s
ubsc
r
i
p
t
t
of
λ
an
d th
e
s
u
p
e
r
s
cr
ip
t
j
of
c
an
d
u a
r
e
dr
o
ppe
d.
T
h
e
dec
ode
r i
s
s
p
eci
fi
ed
by
the subscri
p
t of
c
or
u
where
the SOSTTC e
n
code
r is repre
s
ented
by
st,
C
C
1
i
s
rep
r
ese
n
t
e
d by
1 a
nd C
C
2 i
s
rep
r
ese
n
t
e
d
by
2.
Si
nce
a pr
i
o
ri
in
fo
rm
atio
n
is un
av
ailab
l
e on
th
e
first iteratio
n, th
e
SISO inpu
ts
)
,
(
I
st
u
,
)
,
1
(
I
u
and
)
,
2
(
I
u
are all set to
zero
.
Th
e
co
d
e
d
in
t
r
in
sic lo
g
lik
eliho
od ratio
(LLR
) fo
r th
e
SOSTTC
SIS
O
m
odul
e
i
s
com
put
ed
as
sho
w
n i
n
(
2
)
2
11
0
,
2
2
11
,
2
2
1
2
1
)
,
(
RT
RT
n
j
n
i
i
j
i
t
n
j
n
i
i
t
j
i
t
ST
s
r
s
r
I
c
(2
)
whe
r
e
i
s
0
is the
refe
rence sy
m
bol,
n
R
is the num
ber of receive antenna
s
and
2
is the varia
n
ce of the
AW
GN
.
T
h
e SO
S
T
T
C
SI
SO
tak
e
s th
e in
trinsic LLR
)
,
(
I
st
c
and t
h
e
a pri
o
ri
i
n
f
o
rm
at
i
on fr
om
bot
h t
h
e
CC1
SISO and
CC2
SISO
wh
ic
h
are i
n
itially set to
zero
and
co
m
p
u
t
e th
e ex
tri
n
sic LLR
).
,
(
ˆ
O
st
u
The
ex
trin
sic LLR is th
en
p
a
ssed
to
th
e inv
e
rse in
terv
al
1
s
from
whe
r
e the i
n
form
ation pe
rtaining to the code
d
bi
t
s
of C
C
1
a
nd C
C
2
,
)
,
1
(
I
c
and
)
,
2
(
I
c
respectively, are ex
tracted. The output LLRs
)
,
1
(
O
c
and
)
,
1
(
O
u
are calculated
by the CC1-SISO. T
h
e LLR
)
,
1
(
I
u
is subtracted from
)
,
1
(
O
u
to
ob
tain
th
e LLR
)
,
1
(
~
O
u
whi
c
h i
s
sent
t
h
r
o
ug
h t
h
e i
n
t
e
rl
eaver
p
to ob
t
a
in
th
e in
tri
n
si
c in
form
at
io
n
)
,
2
(
I
u
fo
r t
h
e CC2
-
SIS
O
. The
out
put LLRs
)
,
2
(
O
c
and
)
,
2
(
O
u
are also calcul
a
ted by t
h
e CC
2-SISO. The
L
L
R
)
,
2
(
I
u
is
subt
racted from
)
,
2
(
O
u
to
ob
tain
th
e LLR
)
,
2
(
~
O
u
whic
h is then se
nt
via the de-i
nt
erleaver
1
p
to
o
b
t
ain
t
h
e in
trin
sic in
fo
rm
atio
n
)
,
1
(
I
u
fo
r the
CC1-SI
S
O
.
A sin
g
le LLR stream
constructe
d fr
om
)
,
2
(
~
O
c
and
)
,
1
(
~
O
c
is in
terleav
ed
b
y
s
to
b
e
c
o
me
)
,
(
I
st
u
λ
o
n
th
e nex
t
iteration
.
Th
e LLR
)
,
2
(
O
u
is
in
terleav
ed
)
(
p
π
t
o
obt
ai
n
)
,
2
(
~
O
u
whi
c
h
i
s
adde
d t
o
)
,
1
(
O
u
o
n
t
h
e fi
n
a
l iteratio
n
up
on
wh
ich
th
e
d
ecision
d
e
v
i
ce acts to
d
e
termin
e th
e inpu
t
b
its.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 3
,
Jun
e
201
5
:
4
64–
4
76
46
7
1
s
s
p
1
p
1
p
)
,
(
I
c
st
λ
)
,
(
I
u
st
λ
)
,
(
O
u
st
λ
)
,
(
~
O
u
st
λ
)
,
(
2
I
c
λ
)
,
(
2
O
c
λ
)
,
(
~
1
O
c
λ
)
,
(
~
2
O
c
λ
)
,
(
~
~
2
O
u
λ
)
,
(
~
1
O
u
λ
)
,
(
~
2
O
u
λ
)
,
(
2
O
u
λ
)
,
(
1
O
u
λ
)
,
(
1
O
c
λ
)
,
(
2
I
u
λ
)
,
(
1
I
u
λ
)
,
(
1
I
c
λ
Fi
gu
re
2.
Dec
o
di
n
g
bl
oc
k
di
a
g
ram
of t
h
e PC
-SO
S
TTC
sy
st
em
2.
2
Hybrid Co
nca
t
enated Super-Orth
og
ona
l
Spa
c
e-Time Trellis Code
2.
2a
E
n
c
o
der
In Fi
gu
re
3, t
h
e t
r
ansm
i
t
t
i
ng bl
oc
k di
a
g
ram
of t
h
e
HC
-
S
O
S
TTC
sy
st
em
is sh
ow
n. T
h
e
HC
-S
OST
T
C
to
po
log
y
con
s
ists o
f
a p
a
rallel co
n
caten
ati
o
n of two
se
rially concatenated schem
e
s.
Each
of the
serial
concat
e
n
at
ed
s
c
hem
e
s consi
s
t
s
o
f
a
n
out
er
c
o
n
v
o
l
u
t
i
o
nal
c
ode
concatenat
ed
via an
in
terleav
er with
an
in
n
e
r
SOST
TC e
n
coder. In the sy
ste
m
, a bloc
k of
N
i
nde
pe
n
d
ent
bi
t
s
i
s
e
n
co
de
d
by
t
h
e
co
nv
ol
ut
i
onal
o
u
t
e
r
enco
de
r, C
C
1
,
of t
h
e
up
pe
r se
ri
al
part
of
t
h
e
schem
e
. The
out
put
of
t
h
e
u
ppe
r c
o
n
v
o
l
u
t
i
onal
e
n
c
ode
r i
s
t
h
en
p
a
ssed
thr
oug
h a r
a
ndo
m
b
it i
n
ter
l
eav
er
(
Th
e
p
e
rm
u
t
ed
b
its fro
m
th
e in
terl
eave
r
are
then
fe
d to t
h
e
uppe
r
SOST
TC
enc
o
der t
o
gene
rat
e
a st
ream
of com
p
l
e
x da
ta th
at are tran
smit
ted
fro
m
e
ach
of th
e tran
sm
i
t
an
tenn
as
u
s
ing th
e SOSTTC t
r
an
sm
issio
n
matrix
.
1
2
Fi
gu
re
3.
Enc
o
der
bl
ock
di
a
g
r
a
m
of t
h
e
HC
-
S
OST
T
C
sy
st
e
m
In the l
o
we
r
serial part of
the enc
odi
ng, th
e lowe
r convolutional en
code
r, CC2, receives the
perm
ut
ed versi
o
n
o
f
t
h
e bl
oc
k of
N
i
n
de
pe
nde
nt
bi
t
s
an
d
ge
nerat
e
s
bl
o
c
ks
of
co
de
d
bi
t
s
w
h
i
c
h
are
passe
d
th
ro
ugh
an
o
t
h
e
r in
terleav
er
)
(
2
to t
h
e l
o
we
r S
O
STTC
enc
o
d
e
r. The c
o
m
p
lex dat
a
fr
om
the o
u
t
p
ut
of t
h
e
lo
wer SOSTTC en
cod
e
r are tran
sm
itted
fro
m
th
e tran
sm
it an
ten
n
a
s.
It sho
u
l
d
b
e
n
o
t
ed
th
at th
e sam
e
con
v
o
l
u
t
i
o
nal
and SO
STTC
code
s
are
us
ed in the
upper and lower
syst
e
m
s. Each of t
h
e enc
oders is
termin
ated
usin
g approp
riate
tail b
its.
All the fo
ur tran
sm
it
an
tenn
as are
well sep
a
rated
to
ensure
u
n
c
orrelated
fadi
ng
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Hybri
d
C
onc
at
enat
e
d
C
odi
ng
Sche
me f
o
r M
I
MO
Syst
em
s
(
I
l
e
sa
nmi
B
a
nj
o
Ol
uw
af
emi
)
46
8
2.
2b Dec
o
der
The HC
-S
OST
T
C
deco
de
r co
nsi
s
t
s
o
f
t
w
o s
e
ri
al
arm
s
and one
pa
ral
l
e
l
sect
or as s
h
o
w
n
i
n
Fi
g
u
re
4.
The dec
o
der is specified by the subscri
p
t of
c
or
u,
where
for the uppe
r SOSTTC enc
oder
st1
i
s
used,
and
st2
is u
s
ed
f
o
r t
h
e
l
o
we
r SOS
T
T
C
encode
r, 1 i
s
used f
o
r t
h
e
up
pe
r con
v
o
l
u
t
i
onal
enc
ode
r,
C
C
1
, w
h
i
l
e
2 is used
for th
e lower
co
nvo
lu
tion
a
l en
cod
e
r, CC2. The coded i
n
trinsic LLR
for the SOST
TC SIS
O
m
o
dule is
com
puted as
in (2).
Th
e
SOSTTC
1 SISO tak
e
s the in
trinsic LLR
)
,
1
(
I
st
c
an
d th
e
a p
r
io
ri
inform
atio
n
fro
m
th
e CC
1
SISO wh
ich
is in
itiall
y set
to
zero
and
co
m
p
u
t
e th
e ex
trinsic LLR
)
,
1
(
~
O
st
u
. Th
is ex
trin
sic LLR
fro
m
th
e
SOST
TC
1 SIS
O
i
s
passe
d
t
h
ro
u
gh
t
h
e de-i
nt
erl
eave
r
(
1
1
) t
o
obt
ai
n
)
,
1
(
I
c
.
T
h
e LLR
’s out
put
of
t
h
e
CC1 SISO m
o
dule which are
)
,
1
(
O
c
and
)
,
1
(
O
u
are calculated. The
LLR
)
,
1
(
I
c
λ
is subtracted
fr
om
)
,
1
(
O
c
λ
t
o
obt
ai
n t
h
e LLR
)
,
1
(
~
O
c
λ
wh
ich
is th
en
sen
t
v
i
a in
terleav
er
1
to
o
b
t
ai
n
th
e in
trin
sic
in
fo
rm
atio
n
)
,
1
(
I
st
c
fo
r the
S
O
STTC
1-S
I
S
O
fo
r t
h
e
next iteratio
n.
Fo
r th
e l
o
wer
p
a
rallel arm
,
th
e SOSTTC2 SISO tak
e
s th
e intrin
sic LLR
)
,
2
(
I
st
c
and the
a pri
o
ri
in
fo
rm
atio
n
fro
m
th
e CC2
SISO
wh
ich
i
s
also in
itia
lly set to
zero and
co
m
p
u
t
e th
e ex
tri
n
sic LLR
)
,
2
(
~
O
st
u
. Thi
s
e
x
t
r
i
n
si
c LLR
fr
om
the S
O
STTC
2
SIS
O
i
s
pas
s
e
d
t
h
ro
u
gh t
h
e
de-i
nt
erl
eave
r
(
1
_
2
π
) to
obt
ai
n
)
,
2
(
I
c
. The L
L
Rs
)
,
(
2
O
c
and
)
,
(
2
O
u
fr
o
m
t
h
e out
p
u
t
o
f
t
h
e C
C
2
S
I
S
O
m
odul
e i
s
t
h
en
calculated. T
h
e LLR
)
,
2
(
I
c
λ
is subtracted
from
)
,
2
(
O
c
λ
to
o
b
t
ain th
e LLR
)
,
2
(
~
O
c
λ
wh
ich
is th
en
p
a
ssed
thro
ugh th
e in
ter
l
eav
er
2
π
to
ob
tain
t
h
e i
n
trin
sic i
n
fo
rm
atio
n
)
,
2
(
I
st
c
fo
r
th
e SO
S
T
T
C
2
-
S
I
SO
.
Fo
r th
e p
a
rallel in
terconn
ectio
n co
m
p
on
en
t of th
e iterative d
e
co
d
i
ng
p
r
o
cess, th
e LLR
)
,
2
(
~
O
u
obt
ai
ne
d
by
s
u
bt
ract
i
n
g t
h
e
L
L
R
)
,
2
(
I
u
fr
om
the L
L
R
)
,
2
(
O
u
is se
nt
via the
de-i
nterl
eaver
1
_
π
to
obt
ai
n
t
h
e
LL
R
)
,
1
(
I
u
w
h
i
c
h i
s
t
h
e
u
n
co
de
d
a pri
o
ri
in
form
at
io
n p
a
ssed from
th
e CC2
SISO i
n
to th
e
CC1
SISO. Al
so
th
e LLR
)
,
1
(
~
O
u
o
b
t
ai
ned by
su
bt
r
act
i
ng LLR
)
,
1
(
I
u
from
the
LLR
)
,
1
(
O
u
is sen
t
v
i
a th
e in
terleav
e
r
π
t
o
obt
ai
n t
h
e LLR
)
,
2
(
I
u
wh
ich
is th
e un
co
ded
a pri
o
ri
i
n
f
o
rm
at
i
on passe
d f
r
om
th
e CC1
SISO
in
to
th
e CC2
SISO.
Th
e pro
cess is iterated
sev
e
ral ti
mes an
d
the b
it with
th
e
max
i
m
u
m
APP is ch
osen
b
y
th
e d
ecision
devi
ce i
n
t
h
e l
a
st
i
t
e
rat
i
on us
i
ng t
h
e s
u
m
m
ed val
u
es o
f
t
h
e
out
put
unc
o
d
e
d
LLR
s
of
bot
h t
h
e C
C
1
a
n
d
C
C
2
SISO decode
rs
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 3
,
Jun
e
201
5
:
4
64–
4
76
46
9
1
1
1
2
1
2
1
1
)
,
1
(
O
s
t
u
λ
)
,
1
(
~
O
st
u
λ
I
c
,
1
I
u
,
2
I
u
,
1
I
c
,
2
O
c
,
2
~
O
c
,
~
1
O
c
,
1
O
c
,
2
,O
u
λ
1
O
u
,
2
,O
u
λ
1
~
O
u
,
2
~
O
u
,
2
~
)
,
(
2
O
u
st
λ
)
,
(
~
2
O
u
st
λ
)
,
(
2
I
c
st
)
,
(
1
I
c
st
)
,
(
1
I
u
st
)
,
(
2
I
u
st
Fi
gu
re 4.
Dec
o
di
n
g
bl
oc
k di
a
g
ram
of
t
h
e H
C
-SO
S
TTC
sy
st
em
3.
PAI
R
WISE
ERR
O
R
PR
OB
ABILITY
(PE
P
)
AN
ALY
S
I
S
In
t
h
is sectio
n, th
e p
e
rfo
r
m
a
n
ce b
ound for t
h
e concatenated schem
e
s is
der
i
ved
fo
r t
h
e ca
se of
q
u
asi
-
st
at
i
c
and
fast
fadi
ng c
h
a
n
nel
s
. F
o
r
sl
o
w
fa
d
i
ng,
t
h
e e
n
t
i
r
e
fram
e
is sub
j
e
c
ted to t
h
e sa
m
e
fade
while
fo
r fa
st
fadi
ng
, t
h
e
sy
m
bol
s wi
t
h
i
n
t
h
e
fram
e
s are a
ssum
e
d t
o
be s
u
b
j
ect
ed
t
o
i
n
d
e
pen
d
e
n
t
fa
des
.
3
.
1
Pa
irwise Erro
r Pro
b
a
b
ility fo
r
Quasi-Static Fa
ding
Cha
n
nels
Let th
e tran
smitted
co
d
e
word
an
d th
e erro
n
e
ou
sly d
ecoded
co
d
e
word
b
e
d
e
n
o
t
ed
by
c
and
c
ˆ
respectively. If the
sym
bol-wise Hamm
ing distance bet
w
ee
n
c
and
c
ˆ
,
i
s
de
not
e
d
by
)
ˆ
(
c
c,
d
an
d
assum
i
ng
maxi
m
u
m
like
lihood (ML) decodi
ng,
the c
o
nditional
pair-wise e
r
ror
proba
bility PEP that the receiver wil
l
select
c
ˆ
ov
er
c
con
d
i
t
i
one
d
on
t
h
e chan
nel
g
a
i
n
s an
d ass
u
m
i
ng pe
rfect c
h
annel state inform
ation CSI
at the
receiver,
is given by
(3)
TR
n
i
n
j
j
i
s
h
N
d
E
Q
c
c
P
11
2
,
0
2
2
)
ˆ
(
(3
)
w
h
er
e
)
ˆ
,
(
1
2
2
)
(
ˆ
)
(
c
c
d
l
l
c
l
c
d
(4
)
i
s
t
h
e
s
qua
re
d Eucl
i
d
ea
n di
st
ance of
t
h
e o
u
t
e
r
c
ode
.
B
y
usi
n
g
)
2
exp(
)
(
2
x
x
Q
,
we
have
TR
n
i
n
j
j
i
s
h
N
d
E
P
11
2
,
0
2
4
exp
)
|
ˆ
(
H
c
c
(5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Hybri
d
C
onc
at
enat
e
d
C
odi
ng
Sche
me f
o
r M
I
MO
Syst
em
s
(
I
l
e
sa
nmi
B
a
nj
o
Ol
uw
af
emi
)
47
0
Y i
s
defi
ned
as
TR
n
i
n
j
j
i
h
11
2
,
(6
)
whi
c
h i
s
a c
h
i
-
sq
uare
d
di
st
r
i
but
ed
ra
n
dom
va
ri
abl
e
,
eac
h
ha
vi
n
g
R
T
n
n
2
de
grees
of free
dom
with the
p
r
ob
ab
ility d
i
stribu
tio
n fu
n
c
ti
o
n
(pd
f
)
g
i
v
e
n
as
0
,
)!
1
(
1
)
(
)
1
(
y
e
y
n
n
y
P
y
n
n
R
T
R
T
(7
)
In orde
r t
o
c
o
m
pute the ave
r
age PEP, we
a
v
era
g
e
(5)
with res
p
ect to t
h
e
distribution of
,
dy
e
y
n
n
y
N
d
E
P
y
n
n
R
T
s
R
T
0
)
1
(
0
2
)!
1
(
1
4
exp
)
ˆ
(
c
c
(8
)
Using
t
h
e in
tegral fu
n
c
tion
[23
]
0
1
!
n
x
n
n
dx
e
x
(9
)
we have
R
T
n
n
s
N
d
E
P
0
2
4
1
)
ˆ
(
c
c
(1
0)
At
hi
gh
S
N
R
,
(
1
0
)
ca
n
be a
p
p
r
o
x
i
m
at
ed as
R
T
R
T
n
n
s
n
n
s
N
E
c
c
d
N
d
E
P
0
2
0
2
4
)
ˆ
,
(
4
)
ˆ
(
c
c
(1
1)
Eq
uat
i
on (
1
1)
i
ndi
cat
es t
h
at
t
h
e di
versi
t
y
orde
r o
f
R
T
n
n
is ach
iev
e
d
in
a q
u
a
si-static fad
i
n
g
channel. For t
h
e PC-SOST
T
C
syste
m
,
th
erefore, th
e d
i
v
e
rsity o
r
d
e
r of 2
is ach
iev
a
b
l
e wh
ile for the HC-
SOTTC
, t
h
e
di
versi
t
y
o
r
der
o
f
4 i
s
ac
hi
eva
b
l
e
.
3
.
2
Pa
irwise Erro
r Pro
b
a
b
ility fo
r Fa
st Fading
Cha
n
nels
In the case of
a fast fading c
h
annel, the conditional PEP
that th
e receiver will select c
ode
word
c
ˆ
ove
r
c
ass
u
m
i
n
g
t
h
at
C
S
I i
s
k
n
o
w
n at
t
h
e
rec
e
i
v
er a
n
d c
o
n
d
i
t
i
oned
o
n
t
h
e
chan
nel
gai
n
, i
s
gi
ven
by
[6]
)
ˆ
,
(
11
1
2
2
0
)
(
ˆ
)
(
,
2
)
ˆ
(
c
c
d
k
n
i
n
j
s
TR
k
c
k
c
j
hi
N
E
Q
P
H
|
c
c
(1
2)
whe
r
e
2
)
(
ˆ
)
(
k
c
k
c
is
the norm
a
lized squared E
u
clidea
n distan
ce between the correct
path signal and the
err
o
r
pat
h
si
g
n
a
l
at
t
i
m
e
i
nde
x
k
. By u
s
in
g
)
2
exp(
)
(
2
x
x
Q
,
we have
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 3
,
Jun
e
201
5
:
4
64–
4
76
47
1
)
ˆ
,
(
1
1
2
1
,
2
)
(
exp
)
ˆ
(
c
c
d
k
n
j
n
i
j
i
k
RT
k
h
d
P
H
|
c
c
(1
3)
whe
r
e
2
0
2
)
(
)
(
4
k
c
k
c
N
E
d
s
k
(1
4)
k
i
s
de
fi
ne
d as
)
ˆ
,
(
...,
,
2
,
1
,
)
(
2
11
,
c
c
d
k
for
k
h
RT
n
j
n
i
j
i
k
(1
5)
whi
c
h ar
e i
n
de
pen
d
e
n
t
an
d c
h
i
-
sq
uare
d
di
st
ri
but
e
d
, eac
h
wi
t
h
R
T
n
n
2
deg
r
ees of
f
r
eedom
wi
t
h
a pd
f gi
ve
n by
(7). In order
to com
pute
the
a
v
er
a
g
e P
E
P,
(
13)
is
av
e
r
ag
ed
with
resp
ect to th
e
d
i
stribu
tion
o
f
k
k
c
c
d
k
y
n
n
k
R
T
k
k
dy
e
y
n
n
y
d
P
R
T
)
ˆ
,
(
1
0
)
1
(
2
)!
1
(
1
exp
)
ˆ
(
c
c
(1
6)
Usi
n
g (9
), we
have
)
ˆ
,
(
1
2
)
1
(
)
ˆ
(
c
c
d
k
n
n
k
R
T
d
P
c
c
(1
7)
At
hi
gh
S
N
R
,
(
1
7
)
ca
n
be a
p
p
r
o
x
i
m
at
ed as
R
T
n
n
c
c
d
k
k
d
P
)
(
)
ˆ
(
)
ˆ
,
(
1
2
c
c
(1
8)
R
T
R
T
n
n
s
n
n
c
c
d
k
N
E
k
c
k
c
P
)
4
(
)
)
(
ˆ
)
(
(
)
ˆ
(
0
2
)
ˆ
,
(
1
c
c
(1
9)
Fro
m
(19
)
, it is clear th
at th
e d
i
v
e
rsity o
r
d
e
r of
min
d
n
n
R
T
i
s
achi
e
ve
d i
n
a fast
fa
di
ng c
h
a
nnel
,
w
h
ere
d
min
is
th
e m
i
n
i
m
u
m
Hammin
g
d
i
stan
ce
o
f
th
e
ou
ter co
nvo
lu
tion
a
l cod
e
.
4.
R
E
SU
LTS AN
D ANA
LY
SIS
In th
is section
,
sim
u
lat
i
o
n
resu
lts are
p
r
esen
te
d
t
o
e
v
al
uat
e
t
h
e
pe
r
f
o
r
m
a
nce of
t
h
e
pr
o
pos
e
d
concat
e
n
at
ed
s
c
hem
e
over R
a
y
l
ei
gh fa
di
n
g
cha
nnel
s
.
The
per
f
o
rm
ance of t
h
e t
w
o
pr
o
pos
ed t
o
p
o
l
o
gi
es i
s
eval
uat
e
d o
v
er
bot
h sl
ow a
n
d fast
fa
di
n
g
chan
nel
s
.
Nar
r
o
w
ban
d
t
r
a
n
s
m
i
ssi
on i
s
assum
e
d. There
f
o
r
e, t
h
e
results illustrate the perform
a
nce in ti
m
e
division
m
u
lti
ple access (TDMA) type syste
m
s, like the
globa
l
sy
st
em
for m
obi
l
e
com
m
uni
cat
i
on (
G
SM
), I
S
1
3
6
,
o
r
e
nha
nced
dat
a
rat
e
s
fo
r G
S
M
Ev
ol
ut
i
on
(E
DG
E).
Th
e
resu
lts are presen
ted
in
terms o
f
FER v
e
rsu
s
E
b
/
N
o
.
I
n
al
l
t
h
e sim
u
l
a
ti
ons
, 13
0 sy
m
bol
s p
e
r f
r
am
e are
transm
itted from each of
the
transm
it ante
nna
s. Unless
othe
rwise st
at
ed the
num
ber of iterations
of the
sim
u
lation is set to six because the
performance of the sy
ste
m
s is observe
d t
o
reac
h s
a
turation at the sixth
iteratio
n
.
Th
e fou
r
-state, QPSK SOSTTC in
[7
] is
c
o
n
s
id
er
e
d
as
th
e in
n
e
r
c
o
d
e
.
Fo
r
th
e
ou
te
r
cod
e
,
RS
C an
d
NRC rate
1
/
2,
fou
r
-state co
nvo
lu
tion
a
l co
d
e
are em
ploy
ed fo
r
the
HC-S
O
S
TTC while f
o
r
the PC-S
OS
TTC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Hybri
d
C
onc
at
enat
e
d
C
odi
ng
Sche
me f
o
r M
I
MO
Syst
em
s
(
I
l
e
sa
nmi
B
a
nj
o
Ol
uw
af
emi
)
47
2
t
h
e rat
e
2/
3, f
o
u
r-st
a
t
e
R
S
C
and
NR
C
co
nv
ol
ut
i
o
nal
c
o
des are
use
d
.
In t
h
e t
w
o arc
h
i
t
ect
ures, t
h
e
out
e
r
co
nvo
lu
tion
a
l
co
d
e
s are bo
th
eith
er
RSC o
r
NRC.
Fi
gu
res 5 a
n
d
6 sh
ow t
h
e F
E
R
per
f
o
r
m
a
nce of t
h
e
HC
-
S
OST
T
C
an
d t
h
e PC
-S
OST
T
C
sy
st
em
s
respect
i
v
el
y
,
f
o
r va
ri
o
u
s n
u
m
bers of deco
di
n
g
i
t
e
rat
i
ons
i
n
quasi
-st
a
t
i
c
fadi
ng c
h
an
nel
s
. The pe
rf
orm
a
nce o
f
bot
h sc
hem
e
s is o
b
ser
v
e
d
t
o
i
m
prove
wi
t
h
a
n
i
n
c
r
ease i
n
the nu
m
b
er of iteratio
n
s
and
start satu
rating
at
ab
ou
t
th
e 4
th
i
t
e
rat
i
on. As ca
n be
obs
er
ved f
r
o
m
t
h
e FER
perf
orm
a
nce cur
v
e
,
t
h
e HC
-S
OS
TTC
achi
e
ves
ful
l
di
ve
rsi
t
y
or
der
of f
o
ur
w
h
i
c
h
i
s
consi
s
t
e
nt
wi
t
h
t
h
e
obse
r
vat
i
on
fr
om
t
h
e PEP anal
y
s
i
s
. The c
oncat
e
n
at
i
on
ad
ds no
add
itio
n
a
l
d
i
v
e
rsity to
th
e sch
e
m
e
bu
t ach
iev
e
s si
gn
ifican
t cod
i
ng g
a
in as seen
by th
e ho
rizon
t
al sh
ift
of the
FER perform
a
nce curve
.
Als
o
from the
FER perform
a
nce curve
of the
PC-SOSTTC,
no adde
d
di
ve
rsi
t
y
i
s
ach
i
e
ved
by
t
h
e
sy
st
em
but
t
h
e
r
e
i
s
si
gni
fi
cant
c
odi
ng
gai
n
i
m
pro
v
em
ent
by
t
h
e co
ncat
enat
i
o
n.
Fi
gu
re 5.
Fram
e
err
o
r
rat
e
(FE
R
)
pe
rf
o
r
m
a
nce
o
f
HC
-S
OST
T
C
f
o
r va
ri
o
u
s num
bers o
f
de
codi
ng
i
t
e
rat
i
o
ns
Figu
re
6.
Fram
e err
o
r rate
(FE
R
) pe
rf
o
r
m
a
nce PC-S
OST
T
C
f
o
r
va
ri
o
u
s
nu
m
b
ers of
dec
o
di
n
g
i
t
e
rat
i
o
ns
4
6
8
10
12
10
-4
10
-3
10
-2
10
-1
10
0
S
NR[
d
B
]
FE
R
1s
t
i
t
e
r
2n
d i
t
er
3r
d i
t
e
r
4t
h i
t
e
r
5t
h i
t
e
r
6t
h i
t
e
r
0
2
4
6
8
10
12
10
-3
10
-2
10
-1
10
0
SN
R
[
d
B
]
FE
R
1s
t
i
t
e
r
2
nd i
t
er
3
r
d i
t
er
4
t
h i
t
er
5
t
h i
t
er
6
t
h i
t
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 3
,
Jun
e
201
5
:
4
64–
4
76
47
3
In Fig
u
r
e 7 the
FER perf
orm
a
nce fo
r the HC
-SO
S
TTC com
p
ari
ng the case
of RSC outer
code
, NRC
out
e
r
co
de, R
S
C
wi
t
h
STTC
i
nne
r c
ode a
n
d
NR
C
wi
t
h
ST
TC
i
nne
r co
de
i
s
sho
w
n.
On
t
h
e sam
e
pl
ot
t
h
e FER
p
e
rform
a
n
ce of su
p
e
r-ortho
g
o
n
a
l
sp
ace
-time-conv
o
l
u
tio
n
a
l co
d
e
(SOST-CC)
sch
e
m
e
fro
m
Pillai an
d
Mn
en
ey
[21] is plotted
for com
p
arison. The SOST-C
C concate
n
ates co
nvo
lu
tion
a
l co
d
e
serially with
SOSTTC wh
ich
i
s
equi
val
e
nt
t
o
o
n
e seri
al
ar
m
of t
h
e HC
-
S
OSTTC
sy
st
e
m
.
For the ST
TC inner c
o
de, the four states
STTC
fr
om
[6]
i
s
em
pl
oy
ed
. As ca
n be see
n
f
r
om
t
h
e FER
perform
ance curve
,
the HC-SOST
T
C syste
m
with RSC
out
e
r
c
ode
o
u
t
p
er
fo
rm
ed t
h
e
schem
e
wi
t
h
NR
S
o
u
t
e
r c
o
de a
n
d
t
h
e
H
C
-STTC
c
o
des
.
T
h
e c
ode
wi
t
h
R
S
C
oute
r
code
pre
s
ented better
c
odi
ng gain when
com
p
ar
e
d
with the sc
he
me with
NRC outer c
o
de because
recursive c
o
de
s, unlike their
non-rec
u
rsi
v
e
co
un
terp
arts, ach
i
ev
e in
terleav
ing
g
a
i
n
in
iterativ
e d
e
cod
i
n
g
. In
co
m
p
ariso
n
wi
th
th
e SOST-C
C, th
e HC
-SOSTTC ou
tp
erform
ed
it in
ter
m
s o
f
bo
th
d
i
v
e
rsity o
r
d
e
r and
co
d
i
n
g
g
a
in
. Th
e
HC-SOSTTC sch
e
me ach
iev
e
s a h
i
gh
er
d
i
v
e
rs
ity o
r
d
e
r b
ecause o
f
th
e
nu
mb
er
o
f
tran
sm
i
ttin
g
ant
e
n
n
as i
n
vol
ved
.
The
di
ve
r
s
i
t
y
order
of S
O
ST
-C
C
i
s
t
w
o w
h
i
l
e
t
h
at
of
HC
-S
OSTTC
i
s
fou
r
. I
n
t
e
r
m
s of
codi
ng
gai
n
, t
h
e HC
-
S
O
S
TTC
o
u
t
p
e
r
f
o
rm
ed
t
h
e S
O
ST
-C
C
by
3
.
5
dB
at
t
h
e FER
of
1
0
-2
.
Figu
re
7.
Fram
e err
o
r rate
(FE
R
) pe
rf
o
r
m
a
nce o
f
H
C
-
S
O
S
TTC ov
er qu
asi-static f
a
d
i
ng
chan
n
e
l
Fi
gu
re
8 s
h
ow
s a FER
pe
rf
or
m
a
nce com
p
ar
i
s
on
f
o
r t
h
e P
C
-SO
S
TTC
sy
st
em
wi
t
h
R
S
C
out
e
r
c
ode
,
NRC oute
r
code and the PC-STTC code. As can be obse
r
v
ed
fr
om
t
h
e perf
orm
a
nce
figu
re, th
e sch
e
m
e
with
out
e
r
R
S
C
co
d
e
achi
e
ves i
m
pro
v
e
d
c
odi
ng
gai
n
o
v
er
t
h
e
schem
e
wi
t
h
o
u
t
e
r
NR
C
c
o
d
e
. It
i
s
al
so
ob
serve
d
t
h
at
PC
-S
OS
T
T
C
achi
e
v
e
d
hi
ghe
r c
o
di
n
g
ga
i
n
s t
h
a
n
t
h
e PC
-STTC
c
o
de.
The
FER
perform
ance of the HC-SOSTT
C over
fast
f
a
di
n
g
c
h
an
nel
i
s
sh
o
w
n
i
n
Fi
gu
re
9.
The
p
e
rform
a
n
ce of th
e cod
e
is ev
alu
a
te
d ov
er t
h
is chann
e
l con
d
ition
u
s
ing
bo
th
NRC an
d
RSC ou
ter co
des. Th
e
schem
e
’s per
f
o
rm
ance i
s
al
so com
p
are
d
w
i
t
h
t
h
e C
C
-
S
O
STTC
sch
e
m
e
fr
om
Al
t
unba
s [2
4]
o
v
e
r
t
h
e sam
e
ch
ann
e
l cond
itio
n. Th
e sch
e
me with
ou
ter RSC co
d
e
is ob
serv
ed
fro
m
th
e FER p
l
o
t
s to
ach
i
ev
e
h
i
gh
er co
d
i
n
g
g
a
in
wh
en
com
p
ared
to
th
e
sch
e
m
e
with
NRC ou
ter
c
o
de.
In com
p
ari
s
on with the
CC-SOSTTC
code
, the
HC
-S
OST
T
C
wi
t
h
o
u
t
e
r R
S
C
code has a codi
ng
gai
n
ad
v
a
nt
age o
f
ab
ou
t
4 dB
over t
h
e C
C
-
SOSTT
C
at
t
h
e
FER of
10
-3
.
4
6
8
10
12
10
-4
10
-3
10
-2
10
-1
10
0
SN
R
[
d
B
]
FER
SO
ST
-
C
C
NRC-HC-S
T
T
C
RS
C-HC-S
T
T
C
NRC-HC-S
O
S
T
T
C
RS
C-HC-S
O
S
T
T
C
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