FreeLists / si-list / [SI-LIST] Re: 回复： Re: Stimulus Patterns

[agathon <hreidmarkailen@xxxxxxxxx>]

Hello,
Y'all got me thinkin' ... darn....  That's what I get for reading these
things.

* First, a source for more info on "channel memory" is:
Design Con 2005 paper  "New Techniques for Designing and Analyzing
Multi-GigaHertz Serial Links".  Try google.  The authors call it the "ISP"
or interconnect storage potential in sec. 2.  oooh.

* "unit impulse"   Scott meant to say "1-UI pulse",  a single 0 or 1 pulse
equal to one bit time in width.

* Data sheet won't tell you; you have to read and understand The Book.
Others may tell you, for a fee.

* Even if length of prbs = or > channel memory, to be best it must invoke
the important frequencies for long enough time to be effective.  A vna on a
sample interconn. could tell you some S11 and S21 frequencies of interest,
perhaps.  S11 more for the benefit of things attaching to it.

* "worst case pattern".  What is it?  It's a mysterious creature that is
only easy to find when you're not looking.  It hides and is vindictive.  It
has no mercy.  It can be found by a process of superposition of 1-UI pulse
responses, using first a 1 and then a 0 pulse excitation.  It's called peak
distortion analysis (PDA) and is a bitch to implement.  Once you've tamed
it, its usefulness comes into doubt.  Hair of the worstcasepattern dog that
bit you.  Well, it's useful if you commit fully, like finding many wc
patterns for each eye segment, and for 2 neighbor crosstalk.  And then only
as a holy grail enabling you to simulate against only it and thereby
guarateeing the link integrity as modeled.  Of course, for each physical
channel there is a different wc pattern.  So,  a long-enough prbs may be
sufficient from a BER viewpoint if the wc pattern probability < desired_BER
, for a serial channel, which is probable :-).

* It seems safe to say:  The actual wc pattern may be a little shorter or
longer than a prbs of duration equal to the channel memory.

* Whether a prbs is long enough depends on the probability of it containing
1 copy of the wc pattern.  Assume the prbs is very random (per the
chi-squared test).  The wc pattern is typically NOT, but it's short compared
to a long prbs so that may not matter; I'm not sure.

* First, ignoring the non-randomness of the wc pattern, what is the
probability of flipping bits one at a time and coming up with the wc
pattern, which assumes you know the wc pattenr already?  Use the binomial
distribution:  it's the p^m * p^(n-m) part, where m=# of 1s and n=length of
wc pattern.

* Now, the probability of finding that wc pattern _in_ a much longer prbs is
determined by formulating a Markov process.  This isn't the issue  in the
original post.  This assumes you know the wc pattern and want to know how
long a prbs has to be in order to be some % confident that the wc pattern is
contained within it, like 99%.
http://answers.google.com/answers/threadview?id=508010

The above link goes into it, but it's fairly opaque, with commentary by
"mathtalk", who hasn't communicated all the issues, nor altogether clearly.
A Markov process is a random process with time dependence (stochastic) but
no memory beyond the current state.  The discrete Markov process (like we
have) is called a Markov chain.  The rest can be found within the tender
mercies of Markov.  The problem is to formulate the transition matrix,
realizing that the wc pattern may contain two identical concatenated strings
(pathological case for prefix memory).  So, a 2 to n/2 bit valid prefix of
the search pattern may exist within itself.  It seems the transition matrix
will be  of size (n+1) x (n+1).   The markov walk starts, say, at the
leftmost bit of the prbs and compares bitwise to the pattern, remembering
(as it were, by recurrent states) a max. (n-1)/2 bit prefix that recurs
within the wc pattern as the prbs is being walked.  The final positive
detection state is a 1 in the matrix, the "absorbing state", and never
changes position through any # of transitions.   The formulation is to find
the 1st occurence of the pattern in the prbs, not more than one.  I aim t'
figure this thing out prit' near quick.

I leave you to your Markovian delights.  Most people punt and just say
"Awww, use a 256 (or 128 or whatever) prbs an' be done wid it.".

Regards,
Agathon


On 1/6/07, ¾¸ Àî <lijingdea@xxxxxxxxxxxx> wrote:
>
> Dear Scott and all,
>
>   How to find channel memory time? I mean I don't know what is "a unit
> impulse excitation, or a unit step excitation", and how to find the "channel
> memory time" in data sheet?
>
>   Another question: What's the worstcase pattern? As I know pulse and PRBS
> are not worstcase pattern. If I want to see the worstcase what pattern
> should I use?
>
>   A friend of mine give me a worstcase pattern, but I don't understand.
>
>   
> 1011110000111110101100000101001111101011000001010011111000011111000011110011110000110000111110101100000101100111000011110010110010000100001011111011011000011001101011011101001110010100111111111101001100001001001001001100001110101101101110000111010001010010
>   This is the worstcase bit pattern he given to me. In the same boat the
> waveforms are really worse. Look at the pattern, can you tell me why?
>
>   Thank you very much!
>
>
> Scott McMorrow <scott@xxxxxxxxxxxxx> дµÀ£º
>   Nikhil,
> The length of the PRBS used depends on what you're trying to do. If
> you're simulating a serial channel, you would use a PRBS that has a
> maximum run length that is as large or 1 bit larger than the worst case
> pattern run length in the channel. For 8B10B encoding, the maximum run
> length is 5 bits, so a PRBS7 would be adequate for simulation purposes.
>
> If you are concerned with pattern dependent ISI, then you'll need a
> pattern that is long enough to just encompass the channel memory time.
> Channel memory time is the time that it takes for a channel to return to
> it's quiescent state after a unit impulse excitation, or a unit step
> excitation. It is the amount of time in bits, that it takes for all
> ringing to dampen and die off. I would usually use a PRBS pattern that
> is 1 bit longer than the expected channel memory time, just to be sure.
>
> regards,
>
> Scott
>
> Scott McMorrow
> Teraspeed Consulting Group LLC
> 121 North River Drive
> Narragansett, RI 02882
> (401) 284-1827 Business
> (401) 284-1840 Fax
>
> http://www.teraspeed.com
>
> Teraspeed?is the registered service mark of
> Teraspeed Consulting Group LLC
>
>
>
> npatel@xxxxxxxxxx wrote:
> > Hello all,
> >
> > I wanted to know if there is a way to determine what stimulus pattern
> > and length would be adequate to use in SI simulations. For example 32
> > bit PRBS, 24 bit PRBS etc.
> >
> > How does one find out which stimulus will cover all scenarios.
> >
> > Thanks,
> > Nikhil =20
> > ------------------------------------------------------------------

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