Information Technology Reference
In-Depth Information
Construction using a multiple steps FCSR.
A multiple steps FCSR is a net-
work of interconnected shift registers with a carry path: the computation of the
feedback at time
t
depends directly on the carry generated at time
t
1. The
transformation of an
m
-bit FCSR into a
d
sub-sequences generator uses first
Equation 1 to modify the mapping of the shift register. For the Fibonacci setup,
the transformation uses the following equations:
(
x
i
)
t
+
d
=
g
(
X
t
+
d−m
+
i
,c
t
+
d−m
+
i
)mod2 if
m
−
−
d
≤
i<m
(5)
(
x
i
+
d
)
t
if
i<m
−
d
c
t
+
d
=
g
(
X
t
+
d−
1
,c
t
+
d−
1
)
/
2
(6)
with
g
(
X
t
,c
t
)=
h
(
X
t
)+
c
t
the feedback function of an FCSR in Fibonacci setup
and
m
−
1
h
(
X
t
)=
a
i
(
x
i
)
t
.
(7)
i
=0
Due to the nature of the function
g
, we can split the automaton into two parts.
The first part handles the computation related to the shift register
X
t
and the
other part is the carry path as shown in Figure 5 for
q
= 347.
1-decimation
c
x
7
x
6
x
5
x
4
x
3
x
2
x
1
x
0
S
2-decimation
c
2
s
6
x
4
x
2
x
0
S
2
x
7
x
5
x
3
x
1
S
Fig. 5.
Multiple steps generator for a Fibonacci FCSR
