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RE: [Discuss-gnuradio] information theory -- follow up (off topic )


From: Ettus, Matt
Subject: RE: [Discuss-gnuradio] information theory -- follow up (off topic )
Date: Thu, 13 Mar 2003 13:48:36 -0800

>   If I understand correctly, the basis of Dave's thoughts 
> referred to in the
> Salon article is that we need modern-day systems to use more 
> sophisticated
> tricks to encode channels than just "you get this 30kHz, and 
> you get this
> other 30kHz" -- the classic FDMA approach of 100 years ago. 

Exactly.

> /* Not a fair representation of what we're talking about -- it is not
> straight forward to describe the information transferred when 
> talking over a
> crowd in a football game. 

I disagree.  I would say conversations involve on the order of a couple of
words per second, and probably 8 bits per word of information.  They use
several kHz of bandwidth, so there is significant redundancy in the signal.
This is precisely why communication is successful in the presence of strong
interference (everyone else at the game) and noise (natural gaussian, wind,
etc.).

>   Example:  You hear your wife singing a familiar song -- at 
> one point, you
> can't hear a damn thing, but see her lips mouth the word
> "supercalifragilisticexpealladocious" so you know that's what 
> she said...

Basically you are saying we need efficient, robust encodings.  I agree
strongly.  You don't necessarily need the side-channel of lip reading,
though.  As long as you know the words of the song, you only need to hear a
few of them in order to fill in the rest.  But since you already know the
song, very few bits of information are being transmitted.  

> alternatively, you listen to two Japanese fellows with heavy 
> accents (seated
> in front of you) discuss their company's business -- at an 
> SNR of 3.0dB you
> still might not be able to make out what is being said.

VERY true.  But they also don't interfere with you becuase your brain can
filter their conversation out.  And since THEY know their coding system,
they are able to communicate well.  

>   It all comes down to how 'information' and SNR is defined 
> -- Shannon had a
> very particular definition where we have to reduce the symbol 
> set to remove
> redundancy and such -- difficult to do in discussions and 
> analogies like
> this

Reducing the symbol set and redundancy is bad, and I don't think Shannon
said anything which encourages that.


> 
> /* (bw) you mean non-zero SNR as a ratio, not in dB, right?  

Sorry, I switched between talking about SNR as a ratio and as dB.  Basically
I meant when the "noise" is much stronger than the signal.

> this is the
> part where my head explodes. Shannon tells us that there is 
> indeed minimum
> SNR required to support a given bandwidth efficiency (measured in
> bits-per-second-per-Hz -- units look like the timed 
> acceleration of a bit,
> funny, huh?)... with a theoretical asymptote at -1.6dB -- 

Basically, it says that you need an Eb/N0 of at least -1.6dB.  But you can
always send your bits slower, thus raising the Eb/N0 given a constant power.
But that is with respect to noise (N0).  It is different for interference
(not as bad), because it is not random.

> that is, with less
> than this, you can't transmit anything reliably.
>   Of course CDMA (and spreading in general) offers you a 
> 'spreading gain' --
> for CDMA, its just the ratio of the chip rate to the data 
> rate -- something
> like 10dB-20dB. This means that the RAKE receiver can still decode one
> channel when it look like its buried 10dB in the noise floor.

RAKE is a special case of a despreading receiver.  RAKE allows you to
constructively use multipath.

>   This appears to preclude the idea of not having a 
> fundamental limit on SNR
> required until you remember how Shannon talks about 
> 'information' -- these
> extra bits we're using to spread the signal, they're NOT 
> information...

Nobody said they were information bits.  Spreading is a form of encoding

> they're a known, predictable sequence -- just a mechanism we 
> use to share a
> given frequency band to reduce 'deadbands' required by 
> freqency-division
> multiple access methods -- in an effort to increase the 
> spectral effiency.

Although reduction of dead bands occurs, that is not the primary or even
secondary purpose.

Do you live/work in the valley?  I saw you mentioned hardware for GNURadio
before, and I'd love to talk to you about that more.  Would you like to get
together for lunch some time?  I work in Santa Clara.

Matt




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