CODEWITHSUNDEEP
matlabrandompseudocode
nkp
nkp

Reputation: 13

Non-binary pseudo random sequences

PRBS sequences are for binary bits 0 and 1. Using two PRBS 7 sequence I have generated the next level sequence having 4 symbols, A, B, C and D.
In one sequence, I have some combination of A,B,C and D repeating. The repetition occurs after 127 bits similar to PRBS 7. But here there are 127 bits of 4 symbols(A,B,C,D) and not 2 bits (0, 1).
I have 126 different sequences. I want to analyze them in Matlab and form some repetition pattern like PRBS 7. I want to use Galois field to do it.

Does anyone have any idea on Galois field and if it can be used for them? If not, is there any other way I can analyze the pattern?

Upvotes: 0

Views: 699

Answers (1)

user2271770
user2271770

Reputation:

First of all, is not at all surprising that the repetition occurs after 127 steps. What you do is use the same cyclic sequence s : N → {0, 1}, with s(k) = s(k + 127) starting from different positions, so you look for pairs [s(k), s(k + k0)], where k0 is the delay between first PRBS sequence and the second that you use. You associate a symbol for each bit combination, i.e. {A, B, C, D} = {[0,0], [0,1], [1,0], [1,1]}.

Now, watch what happens when you go 127 steps further:

[s(k + 127), s(k + k0 + 127)] = [s(k), s(k + k0)]

Nice, isn't it? :-)

You might fall for the illusion that you have 2 bits of information per bit pair (or associated symbol) in the sequence, but actually the only true information is contained in the second (i.e. the delayed) PBRS: once you define the delay, everything is the same. That's why generating multi-bit pseudo-random sequences is a little more complicated than that.

Now, about using Galois fields, I'm not sure what your interest is. The question sounds a bit like: "I have this piano; do you know what it is, and if I can play the <insert-here-a-song> song?" :-) It would be helpful to clearly outline your analysis: what are the notions and the definitions that you use, what you're trying to prove or disprove, how this relates to quantitative information that may be extracted from your data. But this might go better in the Math section of the StackExchange.

Upvotes: 1

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