[sdiy] Non maximal-length LFSR

[Magnus Danielson]

As I have read this thread, I have been waiting for this to show up.
We use this technique a lot and it is fairly simple anyway.

It is also an important technique for bit-error testing, and not only 
for scrambling.

However, what technique makes the most efficient code for a processor is 
a different matter than if you do it in hardware as we usually do.

Originally I thought the matter was to get the sequence length to 
shorten to a particular number of symbols, say a power of 2 length. A 
technique being used is to shorten a maximum length sequence.

If you have X bits state, you can produce Y output bits from that X bits 
and then produce the next X bits. By taking the polynomial for producing 
1 bit, then shift 1 bit and produce the next bit etc. after doing this 
for Y bits you have the output of Y bits and the X bits output state. It 
is relatively simple, it's just as we jumped Y rather than 1 bits in the 
sequence and directly predict that. It's a bit of work to build the new 
update polynomial, but paper and pen is a good way to get started on a 
small polynomial, and once the exercise have been done you realize how 
you can do it for any size and even automate the polynomial length.

Cheers,
Magnus

On 03/04/2016 08:07 PM, Dave Manley wrote:
> It hasn't been mentioned, but the LFSR implementation can be done so that it generates multiple bits per update, not just a single bit.  This is commonly done in telecom/ networking descramblers which operate on a multi-bit serdes output.
>
> -Dave
>
> On March 4, 2016 5:24:02 AM PST, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
>> Yeah, but throwing away every 49th result would be throwing away 7
>> years
>> worth! ;-))  Could I live with that!?!?
>>
>> Thanks for everyone's help and suggestions about this.  I'm confident I
>> know
>> the way forward now, and also have some good pointers towards working
>> through the maths to back up my decisions, which always makes me feel
>> better.
>>
>> -Richie,
>>
>>
>>
>> -----Original Message-----
>> From: Tom Wiltshire
>> Sent: Friday, March 04, 2016 12:17 PM
>> To: Richie Burnett
>> Cc: mskala at ansuz.sooke.bc.ca ; synth-diy DIY
>> Subject: Re: [sdiy] Non maximal-length LFSR
>>
>> 371 years!!
>>
>> On 4 Mar 2016, at 11:34, Richie Burnett <rburnett at richieburnett.co.uk>
>> wrote:
>>
>>> Sure the resulting sequence will be a smidgen shorter, but 2^49-1 is
>> quite
>>> long anyway.
>>
>>
>>
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