<s>
In	O
information	O
theory	O
,	O
turbo	B-Error_Name
codes	I-Error_Name
(	O
originally	O
in	O
French	O
Turbocodes	B-Error_Name
)	O
are	O
a	O
class	O
of	O
high-performance	O
forward	B-Error_Name
error	I-Error_Name
correction	I-Error_Name
(	O
FEC	O
)	O
codes	O
developed	O
around	O
1990	O
–	O
91	O
,	O
but	O
first	O
published	O
in	O
1993	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
are	O
used	O
in	O
3G/4G	O
mobile	O
communications	O
(	O
e.g.	O
,	O
in	O
UMTS	B-Protocol
and	O
LTE	O
)	O
and	O
in	O
(	O
deep	O
space	O
)	O
satellite	B-Application
communications	O
as	O
well	O
as	O
other	O
applications	O
where	O
designers	O
seek	O
to	O
achieve	O
reliable	O
information	O
transfer	O
over	O
bandwidth	O
-	O
or	O
latency-constrained	O
communication	O
links	O
in	O
the	O
presence	O
of	O
data-corrupting	O
noise	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
compete	O
with	O
low-density	B-Error_Name
parity-check	I-Error_Name
(	O
LDPC	B-Error_Name
)	O
codes	O
,	O
which	O
provide	O
similar	O
performance	O
.	O
</s>
<s>
The	O
name	O
"	O
turbo	B-Error_Name
code	I-Error_Name
"	O
arose	O
from	O
the	O
feedback	O
loop	O
used	O
during	O
normal	O
turbo	B-Error_Name
code	I-Error_Name
decoding	O
,	O
which	O
was	O
analogized	O
to	O
the	O
exhaust	O
feedback	O
used	O
for	O
engine	O
turbocharging	O
.	O
</s>
<s>
Hagenauer	O
has	O
argued	O
the	O
term	O
turbo	B-Error_Name
code	I-Error_Name
is	O
a	O
misnomer	O
since	O
there	O
is	O
no	O
feedback	O
involved	O
in	O
the	O
encoding	O
process	O
.	O
</s>
<s>
The	O
fundamental	O
patent	O
application	O
for	O
turbo	B-Error_Name
codes	I-Error_Name
was	O
filed	O
on	O
23	O
April	O
1991	O
.	O
</s>
<s>
The	O
patent	O
application	O
lists	O
Claude	O
Berrou	O
as	O
the	O
sole	O
inventor	O
of	O
turbo	B-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
The	O
first	O
public	O
paper	O
on	O
turbo	B-Error_Name
codes	I-Error_Name
was	O
"	O
Near	O
Shannon	O
Limit	O
Error-correcting	O
Coding	O
and	O
Decoding	O
:	O
Turbo-codes	B-Error_Name
"	O
.	O
</s>
<s>
However	O
,	O
it	O
is	O
clear	O
from	O
the	O
original	O
patent	O
filing	O
that	O
Berrou	O
is	O
the	O
sole	O
inventor	O
of	O
turbo	B-Error_Name
codes	I-Error_Name
and	O
that	O
the	O
other	O
authors	O
of	O
the	O
paper	O
contributed	O
material	O
other	O
than	O
the	O
core	O
concepts	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
were	O
so	O
revolutionary	O
at	O
the	O
time	O
of	O
their	O
introduction	O
that	O
many	O
experts	O
in	O
the	O
field	O
of	O
coding	O
did	O
not	O
believe	O
the	O
reported	O
results	O
.	O
</s>
<s>
The	O
first	O
class	O
of	O
turbo	B-Error_Name
code	I-Error_Name
was	O
the	O
parallel	B-Error_Name
concatenated	I-Error_Name
convolutional	I-Error_Name
code	I-Error_Name
(	O
PCCC	O
)	O
.	O
</s>
<s>
Since	O
the	O
introduction	O
of	O
the	O
original	O
parallel	O
turbo	B-Error_Name
codes	I-Error_Name
in	O
1993	O
,	O
many	O
other	O
classes	O
of	O
turbo	B-Error_Name
code	I-Error_Name
have	O
been	O
discovered	O
,	O
including	O
serial	O
versions	O
serial	B-Error_Name
concatenated	I-Error_Name
convolutional	I-Error_Name
codes	I-Error_Name
and	O
repeat-accumulate	B-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
Iterative	O
turbo	O
decoding	O
methods	O
have	O
also	O
been	O
applied	O
to	O
more	O
conventional	O
FEC	O
systems	O
,	O
including	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
corrected	O
convolutional	B-Error_Name
codes	I-Error_Name
,	O
although	O
these	O
systems	O
are	O
too	O
complex	O
for	O
practical	O
implementations	O
of	O
iterative	O
decoders	O
.	O
</s>
<s>
Turbo	B-Algorithm
equalization	I-Algorithm
also	O
flowed	O
from	O
the	O
concept	O
of	O
turbo	B-Error_Name
coding	I-Error_Name
.	O
</s>
<s>
In	O
addition	O
to	O
turbo	B-Error_Name
codes	I-Error_Name
,	O
Berrou	O
also	O
invented	O
recursive	O
systematic	O
convolutional	O
(	O
RSC	O
)	O
codes	O
,	O
which	O
are	O
used	O
in	O
the	O
example	O
implementation	O
of	O
turbo	B-Error_Name
codes	I-Error_Name
described	O
in	O
the	O
patent	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
that	O
use	O
RSC	O
codes	O
seem	O
to	O
perform	O
better	O
than	O
turbo	B-Error_Name
codes	I-Error_Name
that	O
do	O
not	O
use	O
RSC	O
codes	O
.	O
</s>
<s>
Prior	O
to	O
turbo	B-Error_Name
codes	I-Error_Name
,	O
the	O
best	O
constructions	O
were	O
serial	O
concatenated	O
codes	O
based	O
on	O
an	O
outer	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
error	I-Error_Name
correction	I-Error_Name
code	O
combined	O
with	O
an	O
inner	O
Viterbi-decoded	B-Algorithm
short	O
constraint	B-Error_Name
length	I-Error_Name
convolutional	B-Error_Name
code	I-Error_Name
,	O
also	O
known	O
as	O
RSV	O
codes	O
.	O
</s>
<s>
There	O
are	O
many	O
different	O
instances	O
of	O
turbo	B-Error_Name
codes	I-Error_Name
,	O
using	O
different	O
component	O
encoders	O
,	O
input/output	O
ratios	O
,	O
interleavers	O
,	O
and	O
puncturing	O
patterns	O
.	O
</s>
<s>
This	O
example	O
encoder	O
implementation	O
describes	O
a	O
classic	O
turbo	O
encoder	O
,	O
and	O
demonstrates	O
the	O
general	O
design	O
of	O
parallel	O
turbo	B-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
The	O
second	O
sub-block	O
is	O
n/2	O
parity	O
bits	O
for	O
the	O
payload	O
data	O
,	O
computed	O
using	O
a	O
recursive	B-Error_Name
systematic	I-Error_Name
convolutional	I-Error_Name
code	I-Error_Name
(	O
RSC	O
code	O
)	O
.	O
</s>
<s>
The	O
third	O
sub-block	O
is	O
n/2	O
parity	O
bits	O
for	O
a	O
known	O
permutation	B-Algorithm
of	O
the	O
payload	O
data	O
,	O
again	O
computed	O
using	O
an	O
RSC	O
code	O
.	O
</s>
<s>
The	O
permutation	B-Algorithm
of	O
the	O
payload	O
data	O
is	O
carried	O
out	O
by	O
a	O
device	O
called	O
an	O
interleaver	O
.	O
</s>
<s>
Hardware-wise	O
,	O
this	O
turbo	B-Error_Name
code	I-Error_Name
encoder	O
consists	O
of	O
two	O
identical	O
RSC	O
coders	O
,	O
C1	O
and	O
C2	O
,	O
as	O
depicted	O
in	O
the	O
figure	O
,	O
which	O
are	O
connected	O
to	O
each	O
other	O
using	O
a	O
concatenation	O
scheme	O
,	O
called	O
parallel	O
concatenation	O
:	O
</s>
<s>
It	O
is	O
known	O
that	O
the	O
Viterbi	B-Algorithm
algorithm	I-Algorithm
is	O
unable	O
to	O
calculate	O
APP	O
,	O
thus	O
it	O
cannot	O
be	O
used	O
in	O
.	O
</s>
<s>
Instead	O
of	O
that	O
,	O
a	O
modified	O
BCJR	B-Error_Name
algorithm	I-Error_Name
is	O
used	O
.	O
</s>
<s>
For	O
,	O
the	O
Viterbi	B-Algorithm
algorithm	I-Algorithm
is	O
an	O
appropriate	O
one	O
.	O
</s>
<s>
For	O
a	O
turbo	B-Error_Name
code	I-Error_Name
decoder	O
,	O
the	O
front	O
end	O
would	O
provide	O
an	O
integer	O
measure	O
of	O
how	O
far	O
the	O
internal	O
voltage	O
is	O
from	O
the	O
given	O
threshold	O
.	O
</s>
<s>
The	O
decoder	O
working	O
on	O
the	O
second	O
parity	O
sub-block	O
knows	O
the	O
permutation	B-Algorithm
that	O
the	O
coder	O
used	O
for	O
this	O
sub-block	O
.	O
</s>
<s>
The	O
key	O
innovation	O
of	O
turbo	B-Error_Name
codes	I-Error_Name
is	O
how	O
they	O
use	O
the	O
likelihood	O
data	O
to	O
reconcile	O
differences	O
between	O
the	O
two	O
decoders	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
perform	O
well	O
due	O
to	O
the	O
attractive	O
combination	O
of	O
the	O
code	O
's	O
random	O
appearance	O
on	O
the	O
channel	O
together	O
with	O
the	O
physically	O
realisable	O
decoding	O
structure	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
are	O
affected	O
by	O
an	O
error	B-Error_Name
floor	I-Error_Name
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
are	O
used	O
extensively	O
in	O
3G	B-Architecture
and	O
4G	B-Architecture
mobile	I-Architecture
telephony	O
standards	O
;	O
e.g.	O
,	O
in	O
HSPA	O
,	O
EV-DO	O
and	O
LTE	O
.	O
</s>
<s>
MediaFLO	B-Device
,	O
terrestrial	O
mobile	O
television	O
system	O
from	O
Qualcomm	O
.	O
</s>
<s>
The	O
interaction	O
channel	O
of	O
satellite	B-Application
communication	O
systems	O
,	O
such	O
as	O
DVB-RCS	B-Device
and	O
.	O
</s>
<s>
Recent	O
NASA	O
missions	O
such	O
as	O
Mars	O
Reconnaissance	O
Orbiter	O
use	O
turbo	B-Error_Name
codes	I-Error_Name
as	O
an	O
alternative	O
to	O
Reed	O
–	O
Solomon	O
error	O
correction-Viterbi	O
decoder	O
codes	O
.	O
</s>
<s>
IEEE	O
802.16	O
(	O
WiMAX	O
)	O
,	O
a	O
wireless	O
metropolitan	O
network	O
standard	O
,	O
uses	O
block	O
turbo	B-Error_Name
coding	I-Error_Name
and	O
convolutional	O
turbo	B-Error_Name
coding	I-Error_Name
.	O
</s>
<s>
From	O
an	O
artificial	B-Application
intelligence	I-Application
viewpoint	O
,	O
turbo	B-Error_Name
codes	I-Error_Name
can	O
be	O
considered	O
as	O
an	O
instance	O
of	O
loopy	O
belief	O
propagation	O
in	O
Bayesian	O
networks	O
.	O
</s>
