<s>
In	O
coding	B-Error_Name
theory	I-Error_Name
and	O
related	O
engineering	O
problems	O
,	O
coding	B-Error_Name
gain	I-Error_Name
is	O
the	O
measure	O
in	O
the	O
difference	O
between	O
the	O
signal-to-noise	O
ratio	O
(	O
SNR	O
)	O
levels	O
between	O
the	O
uncoded	O
system	O
and	O
coded	O
system	O
required	O
to	O
reach	O
the	O
same	O
bit	O
error	O
rate	O
(	O
BER	O
)	O
levels	O
when	O
used	O
with	O
the	O
error	B-Error_Name
correcting	I-Error_Name
code	I-Error_Name
(	O
ECC	O
)	O
.	O
</s>
<s>
If	O
the	O
uncoded	O
BPSK	O
system	O
in	O
AWGN	O
environment	O
has	O
a	O
bit	O
error	O
rate	O
(	O
BER	O
)	O
of	O
10−2	O
at	O
the	O
SNR	O
level	O
4dB	O
,	O
and	O
the	O
corresponding	O
coded	O
(	O
e.g.	O
,	O
BCH	O
)	O
system	O
has	O
the	O
same	O
BER	O
at	O
an	O
SNR	O
of	O
2.5dB	O
,	O
then	O
we	O
say	O
the	O
coding	B-Error_Name
gain	I-Error_Name
=	O
,	O
due	O
to	O
the	O
code	O
used	O
(	O
in	O
this	O
case	O
BCH	O
)	O
.	O
</s>
<s>
In	O
the	O
power-limited	O
regime	O
(	O
where	O
the	O
nominal	O
spectral	B-Protocol
efficiency	I-Protocol
[	O
b/2D	O
or	O
b/s/Hz	O
]	O
,	O
i.e.	O
</s>
<s>
the	O
domain	O
of	O
binary	O
signaling	O
)	O
,	O
the	O
effective	O
coding	B-Error_Name
gain	I-Error_Name
of	O
a	O
signal	O
set	O
at	O
a	O
given	O
target	O
error	O
probability	O
per	O
bit	O
is	O
defined	O
as	O
the	O
difference	O
in	O
dB	O
between	O
the	O
required	O
to	O
achieve	O
the	O
target	O
with	O
and	O
the	O
required	O
to	O
achieve	O
the	O
target	O
with	O
2-PAM	O
or	O
(	O
22	O
)	O
-QAM	O
(	O
i.e.	O
</s>
<s>
This	O
definition	O
is	O
normalized	O
so	O
that	O
for	O
2-PAM	O
or	O
(	O
22	O
)	O
-QAM	O
.	O
</s>
<s>
If	O
the	O
average	O
number	O
of	O
nearest	O
neighbors	O
per	O
transmitted	O
bit	O
is	O
equal	O
to	O
one	O
,	O
the	O
effective	O
coding	B-Error_Name
gain	I-Error_Name
is	O
approximately	O
equal	O
to	O
the	O
nominal	O
coding	B-Error_Name
gain	I-Error_Name
.	O
</s>
<s>
However	O
,	O
if	O
,	O
the	O
effective	O
coding	B-Error_Name
gain	I-Error_Name
is	O
less	O
than	O
the	O
nominal	O
coding	B-Error_Name
gain	I-Error_Name
by	O
an	O
amount	O
which	O
depends	O
on	O
the	O
steepness	O
of	O
the	O
vs.	O
curve	O
at	O
the	O
target	O
.	O
</s>
<s>
For	O
the	O
special	O
case	O
of	O
a	O
binary	O
linear	O
block	O
code	O
with	O
parameters	O
,	O
the	O
nominal	O
spectral	B-Protocol
efficiency	I-Protocol
is	O
and	O
the	O
nominal	O
coding	B-Error_Name
gain	I-Error_Name
iskd/n	O
.	O
</s>
<s>
The	O
table	O
below	O
lists	O
the	O
nominal	O
spectral	B-Protocol
efficiency	I-Protocol
,	O
nominal	O
coding	B-Error_Name
gain	I-Error_Name
and	O
effective	O
coding	B-Error_Name
gain	I-Error_Name
at	O
for	O
Reed	O
–	O
Muller	O
codes	O
of	O
length	O
:	O
</s>
<s>
the	O
domain	O
of	O
non-binary	O
signaling	O
)	O
,	O
the	O
effective	O
coding	B-Error_Name
gain	I-Error_Name
of	O
a	O
signal	O
set	O
at	O
a	O
given	O
target	O
error	O
rate	O
is	O
defined	O
as	O
the	O
difference	O
in	O
dB	O
between	O
the	O
required	O
to	O
achieve	O
the	O
target	O
with	O
and	O
the	O
required	O
to	O
achieve	O
the	O
target	O
with	O
M-PAM	O
or	O
(	O
MM	O
)	O
-QAM	O
(	O
i.e.	O
</s>
<s>
This	O
definition	O
is	O
normalized	O
so	O
that	O
for	O
M-PAM	O
or	O
(	O
MM	O
)	O
-QAM	O
.	O
</s>
