Scramblers are statically DC balanced?
I happended to come across a statement made by 'Paul' (on behalf of
Bartoff?) that 'Scramblers are statiscally DC balanced.'
This statement is *wrong*.
In line coding, DC-balance (or DC-free property) technically means:
P1) There be no line spectrum at f=0;
P2) There be a clear wide notch in the continous power spectrum.
To understand this, one has to recall that there are two components in
the power spectrum, aka power spectral density(psd); discrete part and
continuous part. A discrete component (or line spectrum) indicates an
existance of a determisnistic (ever lasting) signal wave of the
frequency; in this case, a DC bias.
The other continous part denotes a statistical average of the signal
power at the frequency.
Now, P1) is clear. No line spectrum. Good thing.
Why then P2)? Why is P1) enough?
The most popular reason is that many transmission links are either
ac-coupled on the way through long distances or the physical link has a
very poor transmission quality at low frequencies. Hence any of your
power, though of continous compenent, at low frequecies will not
properly pass through your link only to deteriate your receive signal
quality, especially, in ISI(intersymbol interference) and drooping.
What's the effect of scrambling? It clearly has a good effect in terms
of the line spectrum. Scrambling destroys any possible repeated symbol
patterns (or periodic patterns) which is the cause for the line spectral
What about the continous part of the spectrum? The thing is that, by
scrabling, your data get enough randomness in the pattern that it
resembles the pseudo-random patterns, of which the autocorrelation
function approaches the impluse, resuling in a flat and constant
continous power spectrum.
Therefore, properly scrambed symbol sequences does not generate a power
notch at zero frequency; on the contrary, you get a finite power density
at the frequecy.
Therefore, Scrambled NRZ is NOT DC-balanced as interpredted according to
the two criteria cited above.
Whe talking about DC-balance in line coding, the real point is not P1)
above, for that is out of the question. The point is whether you have a
power null (wide open nutch like well) around zero frequency.
One more reason why you would like to have small power near f=0 in
optical transmission. I might be wrong, but what I heard off is, that
the power near DC tends to heat your optical devices more than higher
frequencies do, and such heat is harmful for many reasons, and thus
DC-free property is seeked also in optical channels which, inherenly, is
capable of transferring the DC component.
Conclusion: Scrambling does not render DC-balance/DC-freedom.