<s>
In	O
the	O
field	O
of	O
data	B-General_Concept
compression	I-General_Concept
,	O
Shannon	B-Algorithm
coding	I-Algorithm
,	O
named	O
after	O
its	O
creator	O
,	O
Claude	O
Shannon	O
,	O
is	O
a	O
lossless	B-Algorithm
data	I-Algorithm
compression	I-Algorithm
technique	O
for	O
constructing	O
a	O
prefix	B-Algorithm
code	I-Algorithm
based	O
on	O
a	O
set	O
of	O
symbols	O
and	O
their	O
probabilities	O
(	O
estimated	O
or	O
measured	O
)	O
.	O
</s>
<s>
It	O
is	O
suboptimal	O
in	O
the	O
sense	O
that	O
it	O
does	O
not	O
achieve	O
the	O
lowest	O
possible	O
expected	O
code	O
word	O
length	O
like	O
Huffman	B-General_Concept
coding	I-General_Concept
does	O
,	O
and	O
never	O
better	O
than	O
but	O
sometimes	O
equal	O
to	O
the	O
Shannon	B-Algorithm
–	I-Algorithm
Fano	I-Algorithm
coding	I-Algorithm
.	O
</s>
<s>
The	O
method	O
was	O
the	O
first	O
of	O
its	O
type	O
,	O
the	O
technique	O
was	O
used	O
to	O
prove	O
Shannon	B-Protocol
's	I-Protocol
noiseless	I-Protocol
coding	I-Protocol
theorem	I-Protocol
in	O
his	O
1948	O
article	O
"	O
A	O
Mathematical	O
Theory	O
of	O
Communication	O
"	O
,	O
and	O
is	O
therefore	O
a	O
centerpiece	O
of	O
the	O
information	O
age	O
.	O
</s>
<s>
This	O
coding	O
method	O
gave	O
rise	O
to	O
the	O
field	O
of	O
information	O
theory	O
and	O
without	O
its	O
contribution	O
,	O
the	O
world	O
would	O
not	O
have	O
any	O
of	O
the	O
many	O
successors	O
;	O
for	O
example	O
Shannon-Fano	B-Algorithm
coding	I-Algorithm
,	O
Huffman	B-General_Concept
coding	I-General_Concept
,	O
or	O
arithmetic	B-Algorithm
coding	I-Algorithm
.	O
</s>
<s>
Much	O
of	O
our	O
day-to-day	O
lives	O
are	O
significantly	O
influenced	O
by	O
digital	B-General_Concept
data	I-General_Concept
and	O
this	O
would	O
not	O
be	O
possible	O
without	O
Shannon	B-Algorithm
coding	I-Algorithm
and	O
the	O
ongoing	O
evolution	O
of	O
its	O
methods	O
.	O
</s>
<s>
In	O
Shannon	B-Algorithm
coding	I-Algorithm
,	O
the	O
symbols	O
are	O
arranged	O
in	O
order	O
from	O
most	O
probable	O
to	O
least	O
probable	O
,	O
and	O
assigned	O
codewords	O
by	O
taking	O
the	O
first	O
bits	O
from	O
the	O
binary	O
expansions	O
of	O
the	O
cumulative	O
probabilities	O
Here	O
denotes	O
the	O
ceiling	O
function	O
(	O
which	O
rounds	O
up	O
to	O
the	O
next	O
integer	O
value	O
)	O
.	O
</s>
