Pseudo random sequence

hi 

my question is related to maximal length sequence in m sequence
pseudorandom code. for example for 3 linear feedback shift registers the
maximal length sequence would be 2^3 -1 =7  ( with specific feed back
network ) . my question is that by changing feedback network can i increase
the length to say 14 in case of three LFSRs . 

On Oct 20, 9:05&#4294967295;am, "Avier" <shahanwark...@hotmail.com> wrote:
> hi
>
> my question is related to maximal length sequence in m sequence
> pseudorandom code. for example for 3 linear feedback shift registers the
> maximal length sequence would be 2^3 -1 =7 &#4294967295;( with specific feed back
> network ) . my question is that by changing feedback network can i increase
> the length to say 14 in case of three LFSRs .

No.

On Tue, 20 Oct 2009 09:05:34 -0500, Avier wrote:

> hi
> 
> my question is related to maximal length sequence in m sequence
> pseudorandom code. for example for 3 linear feedback shift registers the
> maximal length sequence would be 2^3 -1 =7  ( with specific feed back
> network ) . my question is that by changing feedback network can i
> increase the length to say 14 in case of three LFSRs .

Here's how you can answer this question yourself next time:

First ask yourself "does my shift register know anything about it's past 
values beyond what it has stored in three bits?"

Then ask yourself "how many past values can my shift register store with 
just three bits?".

Then ask yourself "so what's the absolute maximum number of time steps my 
shift register can remember?"

Then ask yourself your question, and see what the answer is.

-- 
www.wescottdesign.com

Avier wrote:
> hi 
> 
> my question is related to maximal length sequence in m sequence
> pseudorandom code. for example for 3 linear feedback shift registers the
> maximal length sequence would be 2^3 -1 =7  ( with specific feed back
> network ) . my question is that by changing feedback network can i increase
> the length to say 14 in case of three LFSRs . 

The three shift-register elements can gave between them at most seven 
states. Whatever the feedback arrangement, each of those states 
transitions to a specific other state. Do you see why your answer must 
be "no"?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins <jya@ieee.org> wrote in news:WAkDm.8855$MZ1.4216@newsfe11.iad:

> Avier wrote:
>> hi 
>> 
>> my question is related to maximal length sequence in m sequence
>> pseudorandom code. for example for 3 linear feedback shift registers
>> the maximal length sequence would be 2^3 -1 =7  ( with specific feed
>> back network ) . my question is that by changing feedback network can i
>> increase the length to say 14 in case of three LFSRs . 
> 
> The three shift-register elements can gave between them at most seven 
> states. Whatever the feedback arrangement, each of those states 
> transitions to a specific other state. Do you see why your answer must 
> be "no"?
> 
> Jerry

There is a reason they are called maximum length sequences. The longest is   
2^n-1, the other state is length 1, usually all 1s or all 0s. If you want 14 
(15) states, use one more stage. It's easy to make very long sequences. I 
think Xilinx has an ap note that shows up to 64 stages. 

Al Clark
www.danvillesignal.com

thanks for the reply to all

the thing is, that  is all i studied and learned. i know all the things ,
the  one can be solved with  mathematics  throudh polynomials. this is all
what i studied but. let me rephrase what i asked . i did not ask about the
different states which are no doubt limited to 7 by three registers . the
thing is can i achieve a  PN sequence  of greater than 7 (with repetitions
in 7 states  ).Is there a possibility ,there may be only 7 states but they
are repeating themselves after 14 samples . i think i made the point clear
, talking in general is there any way in PN sequence generation  including
all methods (orthognal ---non orthognal) to do this

Avier wrote:
> thanks for the reply to all
> 
> the thing is, that  is all i studied and learned. i know all the things ,
> the  one can be solved with  mathematics  throudh polynomials. this is all
> what i studied but. let me rephrase what i asked . i did not ask about the
> different states which are no doubt limited to 7 by three registers . the
> thing is can i achieve a  PN sequence  of greater than 7 (with repetitions
> in 7 states  ).Is there a possibility ,there may be only 7 states but they
> are repeating themselves after 14 samples . i think i made the point clear
> , talking in general is there any way in PN sequence generation  including
> all methods (orthognal ---non orthognal) to do this

It is not a possibility. After each state comes a next state. The 
sequence is invariable: if you know what a state is, you know what the 
next state will be. With three switches, you can have at most eight 
states. One of them, all ones or all zeros with an ordinary feedback 
shift register, is its own next state and therefore useless. That leaves 
zeven useful states; represent them by the integers 0, 1, ... 6. In 
general, those states can be ordered 7!, or 5040 ways. In the case of a 
maximum-length sequence, an integer's successor must be the same every 
time it appears. You should be easily able demonstrate to yourself that 
that constraint limits the sequence length to seven.

Jerry
-- 
                      "Hack mir kein tchainik nit."
�����������������������������������������������������������������������

On Sun, 25 Oct 2009 00:42:18 -0400, Jerry Avins wrote:

> Avier wrote:
>> thanks for the reply to all
>> 
>> the thing is, that  is all i studied and learned. i know all the things
>> , the  one can be solved with  mathematics  throudh polynomials. this
>> is all what i studied but. let me rephrase what i asked . i did not ask
>> about the different states which are no doubt limited to 7 by three
>> registers . the thing is can i achieve a  PN sequence  of greater than
>> 7 (with repetitions in 7 states  ).Is there a possibility ,there may be
>> only 7 states but they are repeating themselves after 14 samples . i
>> think i made the point clear , talking in general is there any way in
>> PN sequence generation  including all methods (orthognal ---non
>> orthognal) to do this
> 
> It is not a possibility. After each state comes a next state. The
> sequence is invariable: if you know what a state is, you know what the
> next state will be. With three switches, you can have at most eight
> states. One of them, all ones or all zeros with an ordinary feedback
> shift register, is its own next state and therefore useless. That leaves
> zeven useful states; represent them by the integers 0, 1, ... 6. In
> general, those states can be ordered 7!, or 5040 ways. In the case of a
> maximum-length sequence, an integer's successor must be the same every
> time it appears. You should be easily able demonstrate to yourself that
> that constraint limits the sequence length to seven.

To put this another way: the sequence generator does not know its whole 
past; it only knows the three bits of its state.  After seven iterations 
of the sequence generator the state returns to the _same_ value that it 
was before.

So how, with no knowledge of the past other than three binary states, how 
can the sequence generator know to generate an eighth, much less a ninth, 
tenth or eleventh unique output?

-- 
www.wescottdesign.com

Tim Wescott wrote:
> On Sun, 25 Oct 2009 00:42:18 -0400, Jerry Avins wrote:
> 
>> Avier wrote:
>>> thanks for the reply to all
>>>
>>> the thing is, that  is all i studied and learned. i know all the things
>>> , the  one can be solved with  mathematics  throudh polynomials. this
>>> is all what i studied but. let me rephrase what i asked . i did not ask
>>> about the different states which are no doubt limited to 7 by three
>>> registers . the thing is can i achieve a  PN sequence  of greater than
>>> 7 (with repetitions in 7 states  ).Is there a possibility ,there may be
>>> only 7 states but they are repeating themselves after 14 samples . i
>>> think i made the point clear , talking in general is there any way in
>>> PN sequence generation  including all methods (orthognal ---non
>>> orthognal) to do this
>> It is not a possibility. After each state comes a next state. The
>> sequence is invariable: if you know what a state is, you know what the
>> next state will be. With three switches, you can have at most eight
>> states. One of them, all ones or all zeros with an ordinary feedback
>> shift register, is its own next state and therefore useless. That leaves
>> zeven useful states; represent them by the integers 0, 1, ... 6. In
>> general, those states can be ordered 7!, or 5040 ways. In the case of a
>> maximum-length sequence, an integer's successor must be the same every
>> time it appears. You should be easily able demonstrate to yourself that
>> that constraint limits the sequence length to seven.
> 
> To put this another way: the sequence generator does not know its whole 
> past; it only knows the three bits of its state.  After seven iterations 
> of the sequence generator the state returns to the _same_ value that it 
> was before.
> 
> So how, with no knowledge of the past other than three binary states, how 
> can the sequence generator know to generate an eighth, much less a ninth, 
> tenth or eleventh unique output?

(tongue in cheek) Easy! Let's add a memory element to tell the sequence 
generator that this is an even or an odd pass. Then we could generate 15 
sates with only three state memories and an even/odd memory. That's more 
than double!

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

thanks for the reply

now the thing is that i actually simulated this pseudo random generator in
system generator matlab (provided by xilinx for implemeattion on FPGA)  

with normal circuitry i was able to get 7 states with three shift
registers and then i changeed the circuit (feed back path ) and achieved
the PN sequence of 14 samples . i did with all 8 combinations and achieved
this thing .(normal PN generator can not generate for all zero states of
LSFRs but this one can!!!!)  i am also working on 28 and 56 samples and
hope they will also work (just making right adjustments). i just needed to
verify that this has not been done before and now i think this is not done
before

but then this has to be seen in terms of autocorrelation and other
properties for its worth and i am also working on it. even if it is of no
use atleast i made a point to friend of mine who insisted that we cant go
beyond maximal length,, but i did it !!!!