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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?

Schorsch
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nkp
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1 Answers1

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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.

  • Hello CST-Link, Many thanks for your reply. Everything what you have explained in the beginning is what I know. As you have explained, the association I am using it is A = [0 0], B = [0 1], C = [1 0] and D = [1 1]. I have written the code with the delay in Matlab. – nkp Aug 02 '14 at 15:32
  • In PRBS 7, we have continuous 6 0's and 7 1's. The number of 0's and 1's are almost same in PRBS 7. Now, I want to analyze whether there is any pattern which repeats when you get maximum number of A's, B's etc with different delays. I want to use this pattern for testing. So, it is better if it is equal number of inputs of each symbol. I was reading in an IEEE paper that they were using Galois field to analyze nonbinary pseudo-random sequences.I dont know how to use Galois field.I wanted to confirm if it is possible to use it. – nkp Aug 02 '14 at 15:53
  • @nkp Well, Galois fields (as you may see from Wikipedia, for example), is a field that has a finite number of elements (as opposed to Z, that's field too, but with an infinite number of elements). My guess is that are special theoretical results valid in this algebraic structure, for recursive sequences defined using the internal operations (like the PRBS that you used), and those results may be used to foresee periodicity, and period length. Check the bibliography of the article that you read; usually is the best starting point. –  Aug 04 '14 at 14:42
  • @nkp Also, you could study them empirically :-) as I think you already started doing: 1) generate all the possible sequences over all the significant delays, 2) use MATLAB (or other number-crunching software that's handy) to get the patterns that you're interested in, 3) try to correlate the delay (or other PRBS properties) with the quantities that you just extracted from the pattern. This may give you hints on what to focus on; you may try afterwards to give a theoretical explanation to what you just revealed empirically. –  Aug 04 '14 at 14:49
  • Many thanks for your help :). I will try to do the things you have suggested. – nkp Aug 06 '14 at 06:56