<s>
In	O
information	O
theory	O
,	O
the	O
error	B-General_Concept
exponent	I-General_Concept
of	O
a	O
channel	O
code	O
or	O
source	B-General_Concept
code	I-General_Concept
over	O
the	O
block	O
length	O
of	O
the	O
code	O
is	O
the	O
rate	O
at	O
which	O
the	O
error	O
probability	O
decays	O
exponentially	O
with	O
the	O
block	O
length	O
of	O
the	O
code	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
the	O
probability	O
of	O
error	O
of	O
a	O
decoder	B-General_Concept
drops	O
as	O
,	O
where	O
is	O
the	O
block	O
length	O
,	O
the	O
error	B-General_Concept
exponent	I-General_Concept
is	O
.	O
</s>
<s>
The	O
source	B-General_Concept
coding	I-General_Concept
theorem	O
states	O
that	O
for	O
any	O
and	O
any	O
discrete-time	O
i.i.d.	O
</s>
<s>
source	O
such	O
as	O
and	O
for	O
any	O
rate	O
less	O
than	O
the	O
entropy	B-Algorithm
of	O
the	O
source	O
,	O
there	O
is	O
large	O
enough	O
and	O
an	O
encoder	O
that	O
takes	O
i.i.d.	O
</s>
<s>
In	O
order	O
to	O
minimize	O
the	O
probability	O
of	O
error	O
the	O
decoder	B-General_Concept
will	O
decode	O
to	O
the	O
source	O
sequence	O
that	O
maximizes	O
,	O
where	O
denotes	O
the	O
event	O
that	O
message	O
was	O
transmitted	O
.	O
</s>
<s>
Letting	O
see	O
that	O
the	O
error	B-General_Concept
exponent	I-General_Concept
for	O
the	O
source	B-General_Concept
coding	I-General_Concept
case	O
is	O
:	O
</s>
