<s>
In	O
coding	B-Error_Name
theory	I-Error_Name
,	O
Tornado	B-Error_Name
codes	I-Error_Name
are	O
a	O
class	O
of	O
erasure	O
codes	O
that	O
support	O
error	B-Error_Name
correction	I-Error_Name
.	O
</s>
<s>
Tornado	B-Error_Name
codes	I-Error_Name
require	O
a	O
constant	O
C	O
more	O
redundant	O
blocks	O
than	O
the	O
more	O
data-efficient	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
erasure	I-Error_Name
codes	I-Error_Name
,	O
but	O
are	O
much	O
faster	O
to	O
generate	O
and	O
can	O
fix	O
erasures	O
faster	O
.	O
</s>
<s>
Software-based	O
implementations	O
of	O
tornado	B-Error_Name
codes	I-Error_Name
are	O
about	O
100	O
times	O
faster	O
on	O
small	O
lengths	O
and	O
about	O
10,000	O
times	O
faster	O
on	O
larger	O
lengths	O
than	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
erasure	I-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
Since	O
the	O
introduction	O
of	O
Tornado	B-Error_Name
codes	I-Error_Name
,	O
many	O
other	O
similar	O
erasure	O
codes	O
have	O
emerged	O
,	O
most	O
notably	O
Online	O
codes	O
,	O
LT	O
codes	O
and	O
Raptor	O
codes	O
.	O
</s>
<s>
Tornado	B-Error_Name
codes	I-Error_Name
use	O
a	O
layered	O
approach	O
.	O
</s>
<s>
All	O
layers	O
except	O
the	O
last	O
use	O
an	O
LDPC	B-Error_Name
error	B-Error_Name
correction	I-Error_Name
code	O
,	O
which	O
is	O
fast	O
but	O
has	O
a	O
chance	O
of	O
failure	O
.	O
</s>
<s>
The	O
final	O
layer	O
uses	O
a	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
correction	O
code	O
,	O
which	O
is	O
slower	O
but	O
is	O
optimal	O
in	O
terms	O
of	O
failure	O
recovery	O
.	O
</s>
<s>
Tornado	B-Error_Name
codes	I-Error_Name
dictates	O
how	O
many	O
levels	O
,	O
how	O
many	O
recovery	O
blocks	O
in	O
each	O
level	O
,	O
and	O
the	O
distribution	O
used	O
to	O
generate	O
blocks	O
for	O
the	O
non-final	O
layers	O
.	O
</s>
<s>
All	O
levels	O
of	O
recovery	O
except	O
the	O
final	O
one	O
use	O
an	O
LDPC	B-Error_Name
,	O
which	O
works	O
by	O
xor	O
(	O
exclusive-or	O
)	O
.	O
</s>
<s>
The	O
final	O
level	O
is	O
a	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
code	I-Error_Name
.	O
</s>
<s>
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
codes	I-Error_Name
are	O
optimal	O
in	O
terms	O
of	O
recovering	O
from	O
failures	O
,	O
but	O
slow	O
to	O
generate	O
and	O
recover	O
.	O
</s>
<s>
Since	O
each	O
level	O
has	O
fewer	O
blocks	O
than	O
the	O
one	O
before	O
,	O
the	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
code	I-Error_Name
has	O
a	O
small	O
number	O
of	O
recovery	O
blocks	O
to	O
generate	O
and	O
to	O
use	O
in	O
recovery	O
.	O
</s>
<s>
So	O
,	O
even	O
though	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
is	O
slow	O
,	O
it	O
only	O
has	O
a	O
small	O
amount	O
of	O
data	O
to	O
handle	O
.	O
</s>
<s>
During	O
recovery	O
,	O
the	O
Reed	B-Error_Name
–	I-Error_Name
Solomon	I-Error_Name
code	I-Error_Name
is	O
recovered	O
first	O
.	O
</s>
<s>
Going	O
lower	O
,	O
the	O
LDPC	B-Error_Name
(	O
xor	O
)	O
recovery	O
level	O
can	O
be	O
used	O
to	O
recover	O
the	O
level	O
beneath	O
it	O
with	O
high	O
probability	O
if	O
all	O
the	O
recovery	O
blocks	O
are	O
present	O
and	O
the	O
level	O
beneath	O
is	O
missing	O
at	O
most	O
C	O
 '	O
fewer	O
blocks	O
than	O
the	O
recovery	O
level	O
.	O
</s>
<s>
Tornado	B-Error_Name
codes	I-Error_Name
were	O
formerly	O
patented	O
inside	O
the	O
United	O
States	O
of	O
America	O
.	O
</s>
<s>
Patents	O
US6163870	O
A	O
(	O
filed	O
Nov	O
6	O
,	O
1997	O
)	O
and	O
US	O
6081909	O
A	O
(	O
filed	O
Nov	O
6	O
,	O
1997	O
)	O
describe	O
Tornado	B-Error_Name
codes	I-Error_Name
,	O
and	O
have	O
expired	O
as	O
of	O
November	O
6	O
,	O
2017	O
.	O
</s>
<s>
Patents	O
US6307487	O
B1	O
(	O
filed	O
Feb	O
5	O
,	O
1999	O
)	O
and	O
US6320520	O
B1	O
(	O
filed	O
Sep	O
17	O
,	O
1999	O
)	O
also	O
mention	O
Tornado	B-Error_Name
codes	I-Error_Name
,	O
and	O
have	O
expired	O
as	O
of	O
February	O
5	O
,	O
2019	O
,	O
and	O
September	O
17	O
,	O
2019	O
,	O
respectively	O
.	O
</s>
