Seeking hardware implementation for the pseudo-random sequence
Xu Yanbai
Pseudo-random sequences (or pseudo-noise sequences) showed a wide range of applications in important technical fields such as communication, radar, navigation, and cryptography. In the development of in recent years, its application ranges far exceeds the above-mentioned fields, such as automatic control, computer, acoustic and optical measurement, numerical tracking and ranging system and digital network system failure testing, etc. usage of. It has been such a colorful app that it has attracted a lot of engineering technicians and theoretists.
We don't come to promote the theory, where we only consider one aspect in this technical field. I still tell the preliminary knowledge about pseudo-random sequence before introducing.
First we will give an example of a 4-level linear shift register:
example 1
Figure one
It has four registers and a feedback switch circuit. The four small boxes in Fig. 1 represent four registers, referring to the first level, the second level, the third and fourth registers from left to right, each register can take 0, 1 state one. The switch circuit below has four inputs and one output, and when the input of the four inputs is A1, A2, A3, and A4 output is output.
A1 A2 A3 A4 (MOD 2)
Its working principle is that at a given group of non-zero initial states A0, A1, A2, A3, when a shift pulse is added, the content of each level is transferred to the next level, the last level The content is output, and the data mold 2 plus four registers is added to the first stage, so that the status of this 4-stage shift register becomes A1, A2, A3, A4 where A4 = A0 A1 A2 A3 (MOD 2) And A0 is output. Add a shift pulse, the state of this shift register becomes A2, A3, A4, A5 where A5 = A4 A3 A2 A1 (MOD 2), and the output is A1. So continuous addition of bit pulses, this level 4 shift register The output is called a shift register sequence.
A0, A1, A2, A3, A4, A5, ...,
And this sequence is suitable for recursive relationship
AK = AK-1 AK-2 AK-3 AK-4, K ≥ 4
We also call this recursive relationship with the feedback logic of this shift register. For example, the initial state of this shift register is 0001, then the output of this shift register is the following sequence.
0 0 0 1 1 0 0 0 1 1, ...,
This is a sequence equal to 5, that is, 6 to 10 items of this sequence repeat 1 to 5 items, and 11 to 15 items are still repeated by 1 to 5 values, and so on.
Ok, I believe that by the above example, the reader should have a basic understanding of the random sequence of shift registers. Below we enter the comprehensive problem of so-called linear shift registers, it is: given a binary sequence having N, and finds a linear shift register that generates its linear shift register. Of course, if the number of the linear shift registers does not limit, this comprehensive problem is difficult to solve, and there is an endless formation, so our comprehensive problem is to find the shortest shift register. With regard to the uniqueness of the shortest shift register, we will not discuss this, and interested readers can check the relevant information.
