Cryptography Reference
In-Depth Information
enough minimum distance. A good permutation cannot be found independently
of the properties of elementary codes, of their RTZ patterns, their periodicities,
etc.
Intra-symbol disorder
When the elementary codes are
m
-binary codes, we can introduce a certain
disorder into the permutation of a turbo code without however removing its
regular nature! To do this, in addition to intersymbol classical permutation, we
implement intra-symbol permutation, that is, a non-regular modification of the
content of the symbols of
m
bits, before coding by the second code [7.11]. We
briefly develop this idea with the example of double-binary turbo codes (
m
=2
).
Figure 7.7 - Possible error patterns with binary (a) and double-binary (b) turbo codes
and regular permutation.
Figure 7.7(a) presents the minimum pattern of errors with weight
w
=4
,
again using the code of Figure 7.6. It is a square pattern whose side is equal
to the period of the pseudo-random generator with polynomial
15
,thatis,
7
.
It has already been mentioned that some disorder had to be introduced into
the permutation to "break" this kind of error pattern but without altering the
properties of the regular permutation in relation to patterns with weight
2
and
3
, which is not easy. If, as an elementary encoder, we replace the binary encoder
by a double-binary encoder, the error patterns to consider are no longer made up
of bits but of couples of bits. Figure 7.7(b) gives an example of a double-binary
encoder and of possible error patterns, when the permutation is regular. The
couples are numbered from 0 to 3, according to the following correspondence:
(0
,
0) :
0
;
,
1) :
1
;
,
0) :
2
;
,
1) :
3
