[time-nuts] PPS pulse length (was: 1PPS for the beginner)

[Gregory Maxwell]

On Tue, Aug 14, 2018 at 10:34 PM Tom Van Baak <tvb at leapsecond.com> wrote:
> One version of this would be to make the pulse width 100 ns * (1+STOD), where STOD (Seconds-Time-Of-Day) varies from 00000 to 86399. So your pulse width would vary from 100 ns to 8640000 ns = 8.64 ms. If 100 ns is too short use a range of, say, 1 us to 86400 us (86.4 ms). Maybe there's a reason no one has implemented this but I always thought it would be a cool self-clocking, self-identifying, IRIG-like format. And trivial to implement both the sender and receiver with a microcontroller

I wonder if the self clocking wouldn't be a bit tricky in that you'd
have to distinguish very close ratios, e.g. 86398/86399 vs
86397/86398. One downside of this scheme is that it requires handling
a range of 86400x in pulse size, not so good if you care about keeping
them short.  But this is wasteful because the seconds in a day come in
a predictable order.

I once needed to solve a non-timing related problem of recovering a
48-bit sequence number used for synchronizing a stream cipher with
receivers that could tune in at any time but could only spend 8-bits
per packet, I solved it using a de Bruijn sequence.

Applied here, you'd have two unambiguous pulse lengths and a 2^17 de
bruijn sequence. You send pulses based on your position in the
sequence. The receiver can unambiguously recover its position after
seeing 17 pulses due to the debruijn property.  Even short vs long can
be clocked from the sequence because every 17 pulses will have a least
one of each (except for the time a run of 17 ones or the time 17 zeros
come up, but since 2^17 > 86400 you can position this out of the
sequence that you're using).  17 might be more than you'd like, but it
can be made smaller by having more pulses to distinguish from...  so
you can get a trade-off between recovery time vs pulses that need to
be distinguished.

With this added flexibility it might be plausible to add additional
data like a small day number field, so even more devices can enjoy the
GPS wraparound problems. :P