Outline of a Cue Editor - Brain Theory from a Circuits and Systems Perspective - page 92

Incidentally, the presence of a maximal length can be predicted. If the following
characteristic polynomial cannot be factored, a sequence is maximal length:

X

n

c j x j p ð x Þ¼ 1 : (5.2)

j ¼ 1

x 2 x 3 cannot be factored. So the circuit in Fig. 5.9

For example, p(x) ¼ 1

should have maximal length.
Note that XOR1 acts like a simple buffer when the inputs are all zero. The shift
register needs to be initialized to something other than all zeros. If initialized to 0, 1,
0 the resulting sequence will be as in Table 5.1 :
It then repeats. This has a length of 7, which is maximal since 2 3

7.
Cue selection may be based on a shift register sequence. Figure 5.10 shows a plan.
Shown in part (b) of the figure is an alternative to using a long pseudorandom
code; several shorter codes may be used instead. The code is organized as M
clusters of code, each with N pseudorandom bits in an attempt to randomize
cleverly the selection of attributes. In this way it may be possible to research only
those attributes that are unknown.
The shift register is initialized to all ones to begin. Initially none of the cues are
masked (blocked by AND gates), so all are permitted to be applied to long-term

1 ¼

Fig. 5.9 Maximal length pseudorandom number generator example

Table 5.1 Pseudorandom
count

010
101
110
111
011
001
100