Cryptography Reference
In-Depth Information
Assume, for example, that the couples are inverted (1 becomes 2 and vice-
versa), every other time, before being applied to the vertical encoder. Then the
error patterns presented in Figure 7.9(a) no longer exist; for example, although
30002 does represent an RTZ sequence for the encoder considered, 30001 no
longer does. Thus, many of the error patterns, in particular the smallest, disap-
pear thanks to the disorder introduced inside the symbols. Figure 7.9(b) gives
two examples of patterns that the periodic inversion does not modify. The cor-
responding distances are high enough (24 and 26 for a rate 1/2) not to pose
a problem for small or average block sizes. For long blocks (several thousand
bits), additional intersymbol disorder, of low intensity, can be added to the
intra-symbol non-uniformity, to obtain even higher minimum distances.
Figure 7.10 - Permutation of the DRP type. This is a circular regular permutation to
which local permutations before writing and after reading are added.
Irregular permutations
In this section, we will not describe all the irregular permutations that have
been imagined so far, and that have been the subject of numerous publications
and several topic chapters (see [7.40, 7.34] for example). We prefer to present
what seems, for the moment, to be both the simplest and the most ecient type
of permutation. These are almost regular circular permutations, called almost
regular permutation (ARP)[7.17] or dithered relatively prime ( DRP ) [7.21]
permutations, depending on their authors. In all cases, the idea is not to stray
too far away from the regular permutation, which is well adapted to simple RTZ
error patterns and to instil some small, controlled disorder to counter multiple
RTZ error patterns.
Figure 7.10 gives an example, taken from [7.21], of what this small disorder
can be. Before the circular regular permutation is performed, the bits undergo
local permutation. This permutation is performed in groups of C W bits. C W ,
which is the writing cycle disorder, is a divisor of length k of the message. Sim-
ilarly, a local C R reading cycle permutation is applied before the final reading.
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