Re: [Discuss-gnuradio] *much* faster filtering --- plus vhf mountaintopping

[Frank Brickle]

James Cooley wrote:

> ...I'm sure 
> there's a way to come up with a compression scheme that's tailored to 
> the sort of sample data we see...

A topic for a dissertation if ever there was one :-)

In the general case, you're going to have to work hard to 
beat Ziv-Lempel. You might improve the performance somewhat 
by tweaking the parameters, but probably not a lot.

The problem is that, as we know, in the general case, 
compressibility is basically the reciprocal of entropy. 
Ziv-Lempel depends on conditional entropy being lower, and 
thus compressibility being higher, through markovity.

For most human-generated signals, the influence of the past 
(the markovity) decays exponentially towards the past. For 
general signals, the decay is very rapid, so there's going 
to be a lot of slop at the boundaries of the underlying 
markov model. There's also a theorem in there somewhere (due 
to Rissanen, I think) that says there's a limit on how much 
slop you can trim by tuning the adaptation.

Where you might win is by picking different compression 
algorithms depending on the signals. For example, for 
voice-bandwidth channels, you might gain a lot from first 
converting to mu-law and then gzipping. And so on. For wide, 
densely-packed signals, you can probably forget it. The fact 
that they're densely packed means they're already high-entropy.

Regards
Frank