<s>
Recognised	O
by	O
John	O
Wozencraft	O
,	O
sequential	B-Error_Name
decoding	I-Error_Name
is	O
a	O
limited	O
memory	O
technique	O
for	O
decoding	O
tree	O
codes	O
.	O
</s>
<s>
Sequential	B-Error_Name
decoding	I-Error_Name
is	O
mainly	O
used	O
as	O
an	O
approximate	O
decoding	O
algorithm	O
for	O
long	O
constraint-length	O
convolutional	B-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
This	O
approach	O
may	O
not	O
be	O
as	O
accurate	O
as	O
the	O
Viterbi	B-Algorithm
algorithm	I-Algorithm
but	O
can	O
save	O
a	O
substantial	O
amount	O
of	O
computer	O
memory	O
.	O
</s>
<s>
It	O
was	O
used	O
to	O
decode	O
a	O
convolutional	B-Error_Name
code	I-Error_Name
in	O
1968	O
Pioneer	O
9	O
mission	O
.	O
</s>
<s>
Sequential	B-Error_Name
decoding	I-Error_Name
explores	O
the	O
tree	O
code	O
in	O
such	O
a	O
way	O
to	O
try	O
to	O
minimise	O
the	O
computational	O
cost	O
and	O
memory	O
requirements	O
to	O
store	O
the	O
tree	O
.	O
</s>
<s>
There	O
is	O
a	O
range	O
of	O
sequential	B-Error_Name
decoding	I-Error_Name
approaches	O
based	O
on	O
the	O
choice	O
of	O
metric	O
and	O
algorithm	O
.	O
</s>
<s>
For	O
sequential	B-Error_Name
decoding	I-Error_Name
to	O
a	O
good	O
choice	O
of	O
decoding	O
algorithm	O
,	O
the	O
number	O
of	O
states	O
explored	O
wants	O
to	O
remain	O
small	O
(	O
otherwise	O
an	O
algorithm	O
which	O
deliberately	O
explores	O
all	O
states	O
,	O
e.g.	O
</s>
<s>
the	O
Viterbi	B-Algorithm
algorithm	I-Algorithm
,	O
may	O
be	O
more	O
suitable	O
)	O
.	O
</s>
<s>
Sequential	B-Error_Name
decoding	I-Error_Name
may	O
introduce	O
an	O
additional	O
error	O
above	O
Viterbi	O
decoding	O
when	O
the	O
correct	O
path	O
has	O
or	O
more	O
highly	O
scoring	O
paths	O
above	O
it	O
;	O
at	O
this	O
point	O
the	O
best	O
path	O
will	O
drop	O
off	O
the	O
stack	O
and	O
be	O
no	O
longer	O
considered	O
.	O
</s>
<s>
The	O
famous	O
Fano	B-Error_Name
algorithm	I-Error_Name
(	O
named	O
after	O
Robert	O
Fano	O
)	O
has	O
a	O
very	O
low	O
memory	O
requirement	O
and	O
hence	O
is	O
suited	O
to	O
hardware	O
implementations	O
.	O
</s>
<s>
The	O
Fano	B-Error_Name
algorithm	I-Error_Name
is	O
a	O
sequential	B-Error_Name
decoding	I-Error_Name
algorithm	O
that	O
does	O
not	O
require	O
a	O
stack	O
.	O
</s>
<s>
The	O
Fano	B-Error_Name
algorithm	I-Error_Name
can	O
only	O
operate	O
over	O
a	O
code	O
tree	O
because	O
it	O
cannot	O
examine	O
path	O
merging	O
.	O
</s>
<s>
At	O
each	O
decoding	O
stage	O
,	O
the	O
Fano	B-Error_Name
algorithm	I-Error_Name
retains	O
the	O
information	O
regarding	O
three	O
paths	O
:	O
the	O
current	O
path	O
,	O
its	O
immediate	O
predecessor	O
path	O
,	O
and	O
one	O
of	O
its	O
successor	O
paths	O
.	O
</s>
<s>
Based	O
on	O
this	O
information	O
,	O
the	O
Fano	B-Error_Name
algorithm	I-Error_Name
can	O
move	O
from	O
the	O
current	O
path	O
to	O
either	O
its	O
immediate	O
predecessor	O
path	O
or	O
the	O
selected	O
successor	O
path	O
;	O
hence	O
,	O
no	O
stack	O
is	O
required	O
for	O
queuing	O
all	O
examined	O
paths	O
.	O
</s>
<s>
The	O
movement	O
of	O
the	O
Fano	B-Error_Name
algorithm	I-Error_Name
is	O
guided	O
by	O
a	O
dynamic	O
threshold	O
that	O
is	O
an	O
integer	O
multiple	O
of	O
a	O
fixed	O
step	O
size	O
¢	O
.	O
</s>
<s>
For	O
the	O
Fano	B-Error_Name
algorithm	I-Error_Name
,	O
if	O
a	O
path	O
is	O
revisited	O
,	O
the	O
presently	O
examined	O
dynamic	O
threshold	O
is	O
always	O
lower	O
than	O
the	O
momentary	O
dynamic	O
threshold	O
at	O
the	O
previous	O
visit	O
,	O
guaranteeing	O
that	O
looping	O
in	O
the	O
algorithm	O
does	O
not	O
occur	O
,	O
and	O
that	O
the	O
algorithm	O
can	O
ultimately	O
reach	O
a	O
terminal	O
node	O
of	O
the	O
code	O
tree	O
,	O
and	O
stop	O
.	O
</s>
