[time-nuts] Timing over low bandwidth channels

[jimlux]

Hal Murray wrote:
>> If you can indeed track a 1W signal from ~ Colorado, there might indeed be
>> some timing use for the system. 
> 
> I have a start at understanding how much data you can get through a channel.  
> There is a tradeoff between data rate and error rate and it depends on the 
> signal/noise ratio.

That's the Shannon bound.. (or Shannon-Hartley)..
C = B*log2(1+S/N)

You can get pretty darn close (hundredths of a dB) to this limit with 
coding.

> 
> Is there a similar sort of high level picture about sending timing info?  I'm 
> not even sure what the units are.
> 

That's a bit trickier to conceptualize... In the data bit case, you can 
work at the "one bit" scale.. and say something about the probability 
that the bit is wrong.  ANd, you can combine multiple bits and drive the 
probability of an error over all those bits combined down.

But for "time" or "frequency" it's a bit trickier.  You have to specify 
the time scale over which you're interested  (I suppose that relates to 
the bandwidth in the Shannon formula).  But more to the point, in 
digital communications there's a clear "two-state" thing..either the bit 
is correct or it's not.   Time/Frequency has "degrees of wrongness"
> 
>