Information Technology Reference
In-Depth Information
Table 1.
Comparison of the two methods for the synthesis of a sub-sequences generator
Method
Memory cells Logic Gates
d
×
m
d
×
wt
(
Q
)
LFSR synthesis
Multiple steps LFSRs [11]
m
d
×
wt
(
Q
)
next
1
(
x
i
)=
x
i
−
1
if
i
=0
1-decimation
next
1
(
x
0
)=
x
7
(
x
2
)
t
+1
=(
x
3
)
t
⊕
(
x
0
)
t
x
7
x
6
x
5
x
4
x
3
x
2
x
1
x
0
S
(
x
3
)
t
+1
=(
x
4
)
t
⊕
(
x
0
)
t
(
x
4
)
t
+1
=(
x
5
)
t
⊕
(
x
0
)
t
(
x
i
)
t
+1
=(
x
i
+1 (mod
m
)
)
t
, ∀i ∈{
0
,
1
,
5
,
6
,
7
}
3-decimation
next
3
(
x
i
)=
x
i
−
3
if 2
<i≤
7
x
6
x
3
x
0
S
3
3
(
x
i
)=
x
m
+
i
−
d
if 0
≤ i ≤
2
next
(
x
0
)
t
+3
=(
x
3
)
t
⊕
(
x
0
)
t
(
x
3
)
t
+3
=(
x
6
)
t
⊕
(
x
1
)
t
⊕
(
x
2
)
t
(
x
6
)
t
+3
=(
x
1
)
t
(
x
1
)
t
+3
=(
x
4
)
t
⊕
(
x
0
)
t
⊕
(
x
1
)
t
x
7
x
4
x
1
S
3
(
x
4
)
t
+3
=(
x
2
)
t
⊕
(
x
7
)
t
(
x
7
)
t
+3
=(
x
2
)
t
(
x
2
)
t
+3
=(
x
5
)
t
⊕
(
x
0
)
t
⊕
(
x
1
)
t
⊕
(
x
2
)
t
(
x
5
)
t
+3
=(
x
0
)
t
x
5
x
2
S
3
Feedback
t
=0
Feedback
t
=1
Feedback
t
=2
Fig. 4.
Multiple steps generator for a Galois LFSR
Comparison.
We have summarized in the Table 1 the two methods used to synthe-
size the sub-sequences generator. By
wt
(
Q
(
x
)), we mean the Hamming weight of
Q
,
i.e.
the number of non-zero monomials. The method based on LFSR synthesis
proves that there exists a solution for the synthesis of the sub-sequences generator.
With this solution, both memory cost and gate number depends on the decima-
tion factor
d
. The method proposed by Lempel and Eastman [11] uses a constant
number of memory cells for the synthesis of the sub-sequences generator.
The sub-sequences generators defined with the Berlekamp-Massey algorithm
are not suitable to reduce the power consumption of an LFSR. Indeed,
d
LFSRs
will be clocked to produce the sub-sequences, however the power consumption
of such a sub-sequence generator is given by:
C
d
×
γf
d
V
dd
×
P
=
d
×
V
dd
×
=
λC
×
γf
with
C
d
=
λC
and
C
the capacity of the original LFSR. We can achieve a better
result with a multiple steps LFSR:
γf
d
P
=
λ
C
V
dd
×
×
with
C
d
=
λ
C
.
