<s>
A	O
multidimensional	B-Error_Name
parity-check	I-Error_Name
code	I-Error_Name
(	O
MDPC	O
)	O
is	O
a	O
simple	O
type	O
of	O
error	B-Error_Name
correcting	I-Error_Name
code	I-Error_Name
that	O
operates	O
by	O
arranging	O
the	O
message	O
into	O
a	O
multidimensional	O
grid	O
,	O
and	O
calculating	O
a	O
parity	B-Error_Name
digit	I-Error_Name
for	O
each	O
row	O
and	O
column	O
.	O
</s>
<s>
In	O
general	O
,	O
an	O
n-dimensional	O
parity	B-Error_Name
scheme	O
can	O
correct	O
n/2	O
errors	O
.	O
</s>
<s>
The	O
two-dimensional	O
parity-check	O
code	O
,	O
usually	O
called	O
the	O
optimal	O
rectangular	O
code	O
,	O
is	O
the	O
most	O
popular	O
form	O
of	O
multidimensional	B-Error_Name
parity-check	I-Error_Name
code	I-Error_Name
.	O
</s>
<s>
Assume	O
that	O
the	O
goal	O
is	O
to	O
transmit	O
the	O
four-digit	O
message	O
"	O
1234	O
"	O
,	O
using	O
a	O
two-dimensional	O
parity	B-Error_Name
scheme	O
.	O
</s>
<s>
Parity	B-Error_Name
digits	I-Error_Name
are	O
then	O
calculated	O
by	O
summing	O
each	O
column	O
and	O
row	O
separately	O
:	O
</s>
<s>
In	O
order	O
to	O
handle	O
two	O
errors	O
,	O
a	O
4-dimensional	O
scheme	O
would	O
be	O
required	O
,	O
at	O
the	O
cost	O
of	O
more	O
parity	B-Error_Name
digits	I-Error_Name
.	O
</s>
<s>
An	O
n-dimensional	O
parity	B-Error_Name
scheme	O
is	O
only	O
guaranteed	O
to	O
correct	O
up	O
to	O
n/2	O
errors	O
,	O
as	O
the	O
minimum	O
distance	O
is	O
(	O
n	O
+	O
1	O
)	O
.	O
</s>
<s>
As	O
with	O
all	O
block	O
codes	O
,	O
a	O
soft-decision	B-Error_Name
decoder	I-Error_Name
may	O
be	O
able	O
to	O
correct	O
more	O
than	O
this	O
.	O
</s>
