Cellular Automata for Efficient Image and Video Compression - Cellular Automata in Image Processing and Geometry - page 10

Fig. 1.7 Structure of HCA (left) and LFSR or NLFSR (right) chaotic counters. Unlike HCA,
binary synchronization can be used with LFSR/NLFSR only for the cells in the shift-register
area, i.e. without cryptographic protection. In the case of HCA cryptographic protection is
ensured since synchronization is only possible if the the Rx-CA structure (ID, mask vector)
is identical for the Tx-CA. Consequently, the key is given by the specific CA structure.

“good chaotic counter” property. The problem of locating good chaotic counters in
the very large space of all possible 2 32 rules for the 5-cell neighborhood CA is a
computationally demanding problem, and so far we solved it only for the case of up
to 4 inputs cell within a 5-cell neighborhood.

1.2.3 Designing Good Chaotic Counters as Hybrid Cellular

Automata

Ordinary chaotic maps (i.e. logistic, tent, etc.) cannot be used as good chaotic coun-
ters because their finite computing precision implementations often produce cycles
with only a very small fraction of state vectors (each addressing a pixel in the image
sensor array) belonging to the counting cycle. Consequently, only a small fraction of
the sensing elements will be addressed, compromising the information acquisition
process [15]. As discussed above, a hybrid cellular automaton model proved to be
very effective in ensuring the properties of a good chaotic counter. To explain the
HCA structure let us consider the case m 3 (3 cells neighbourhood). It expands

naturally to a 5-cell or larger neighbourhood. Figure 1.7 presents the HCA automa-
ton structure compared to the widely known LFSR. Note that both of them may
be operated in either autonomous mode (as it is the case in the transmitter system
Tx) or with one input forced by the synchronization signal (as it is the case in the
receiving system Rx).

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