Cryptography Reference
In-Depth Information
The periodicities of the double-binary encoder are resumed in the diagram
of Figure 7.8. There we can find all the combinations of pairs of couples of
the RTZ type. For example, if the encoder, initialized in state 0, is fed by the
successive couples 1 and 3, it immediately returns to state 0. It is the same for
the sequences 201 or 2003 or 3000001, for example.
Figure 7.8 - Periodicities of the double-binary encoder of Figure 7.7(b). The four
input couples
(0
,
0)
,
(0
,
1)
,
(1
,
0)
and
(1
,
1)
are denoted
0
,
1
,
2
and
3
, respectively. This
diagram gives all the combinations of pairs of couples of the RTZ type.
Figure 7.7(b) gives two examples of rectangular, minimum size error patterns.
First note that the perimeter of these patterns is larger than half the perimeter
of the square of Figure 7.7(a). Now, for a same coding rate, the redundancy of
a double-binary code is twice as dense as that of a binary code. We thus deduce
that the distances of the double-binary error patterns will naturally be larger,
everything else being equal, than those of binary error patterns. Moreover, there
is a simple way to eliminate these elementary patterns.
Figure 7.9 - The couples of the grey boxes are inverted before the second (vertical)
encoding.
remain unchanged. The patterns of
Figure 7.7(b), redrawn in (a), are no longer possible error patterns. But those of (b)
are, with distances
24
and
26
for coding rate
1
/
2
.
1
becomes
2
,
2
becomes
1
;
0
and
3
