<s>
Elias	B-Algorithm
ω	I-Algorithm
coding	I-Algorithm
or	O
Elias	B-Algorithm
omega	I-Algorithm
coding	I-Algorithm
is	O
a	O
universal	B-Algorithm
code	I-Algorithm
encoding	O
the	O
positive	O
integers	O
developed	O
by	O
Peter	O
Elias	O
.	O
</s>
<s>
Like	O
Elias	B-Algorithm
gamma	I-Algorithm
coding	I-Algorithm
and	O
Elias	B-Algorithm
delta	I-Algorithm
coding	I-Algorithm
,	O
it	O
works	O
by	O
prefixing	O
the	O
positive	O
integer	O
with	O
a	O
representation	O
of	O
its	O
order	O
of	O
magnitude	O
in	O
a	O
universal	B-Algorithm
code	I-Algorithm
.	O
</s>
<s>
Unlike	O
those	O
other	O
two	O
codes	O
,	O
however	O
,	O
Elias	O
omega	O
recursively	O
encodes	O
that	O
prefix	O
;	O
thus	O
,	O
they	O
are	O
sometimes	O
known	O
as	O
recursive	B-Algorithm
Elias	I-Algorithm
codes	I-Algorithm
.	O
</s>
<s>
Omega	O
coding	O
is	O
used	O
in	O
applications	O
where	O
the	O
largest	O
encoded	O
value	O
is	O
not	O
known	O
ahead	O
of	O
time	O
,	O
or	O
to	O
compress	B-General_Concept
data	O
in	O
which	O
small	O
values	O
are	O
much	O
more	O
frequent	O
than	O
large	O
values	O
.	O
</s>
<s>
Included	O
is	O
the	O
so-called	O
implied	O
distribution	O
,	O
describing	O
the	O
distribution	O
of	O
values	O
for	O
which	O
this	O
coding	O
yields	O
a	O
minimum-size	O
code	O
;	O
see	O
Relationship	O
of	O
universal	B-Algorithm
codes	I-Algorithm
to	O
practical	O
compression	O
for	O
details	O
.	O
</s>
<s>
Under	O
Elias	B-Algorithm
delta	I-Algorithm
coding	I-Algorithm
,	O
the	O
same	O
number	O
is	O
33,250	O
bits	O
long	O
:	O
000000000000000	O
1000000111000100	O
(	O
31	O
bits	O
)	O
followed	O
by	O
33,219	O
bits	O
of	O
the	O
value	O
.	O
</s>
<s>
Elias	B-Algorithm
omega	I-Algorithm
coding	I-Algorithm
does	O
not	O
encode	O
zero	O
or	O
negative	O
integers	O
.	O
</s>
<s>
One	O
way	O
to	O
encode	O
all	O
non-negative	O
integers	O
is	O
to	O
add	O
1	O
before	O
encoding	O
and	O
then	O
subtract	O
1	O
after	O
decoding	O
,	O
or	O
use	O
the	O
very	O
similar	O
Levenshtein	B-Algorithm
coding	I-Algorithm
.	O
</s>
<s>
One	O
way	O
to	O
encode	O
all	O
integers	O
is	O
to	O
set	O
up	O
a	O
bijection	B-Algorithm
,	O
mapping	O
all	O
integers	O
(	O
0	O
,	O
1	O
,	O
-1	O
,	O
2	O
,	O
-2	O
,	O
3	O
,	O
-3	O
,	O
...	O
)	O
to	O
strictly	O
positive	O
integers	O
(	O
1	O
,	O
2	O
,	O
3	O
,	O
4	O
,	O
5	O
,	O
6	O
,	O
7	O
,	O
...	O
)	O
before	O
encoding	O
.	O
</s>
