Shannon's theorem - how does adsl compare?

/ Techie Ten Minutes/
Some time ago someone asked what maximum data rates one could expect
with adsl, and I posted back the famous result of the good Doctor
Shannon:-
maximum error-free bit rate = bandwidth*log2(1 + signal-to-noise-ratio)
I did this as a bit of joke - when I first came across this lovely
result, in the sixties, the rates it predicted were an unattainable
joke...

But (as an article at www.iec.org clearly sets out) modern dialup modems
working to highly optimised error-correcting standards like V.34, come
near the Shannon limit. (eg a 3kHz Bandwidth channel with 30db Signal-
to-Noise would give about 24kb/s, quite comparable to what V34 actually
gives)

But how does ADSL compare with its theoretical maximum?
(my intuition is it's not as highly optimised as its older brother???
We can check if we know what's the effective bandwidth and signal-to-
noise?)
//
Bob




--
robert w hall

> But how does ADSL compare with its theoretical maximum?
> (my intuition is it's not as highly optimised as its older brother???
> We can check if we know what's the effective bandwidth and signal-to-
> noise?)

Well, working backwards with a SNR of 27.9 (thats what mine is anyway) and
assuming around 500k capacity gives bandwidth of 100.3kHz - doesn't sound
like very much though, since I'm sure ADSL goes well up into the MHz ranges
doesn't it? Which either means I am wrong about ADSL, or the formula is
completely screwy, or I typed the numbers in wrong and missed a few decimal
points.... Not very useful I know, but there ya go! )

David

David Walker <(E-Mail Removed)> wrote:
>> But how does ADSL compare with its theoretical maximum?
>> (my intuition is it's not as highly optimised as its older brother???
>> We can check if we know what's the effective bandwidth and signal-to-
>> noise?)
>
> Well, working backwards with a SNR of 27.9 (thats what mine is anyway) and
> assuming around 500k capacity gives bandwidth of 100.3kHz - doesn't sound
> like very much though, since I'm sure ADSL goes well up into the MHz ranges
> doesn't it? Which either means I am wrong about ADSL, or the formula is
> completely screwy, or I typed the numbers in wrong and missed a few decimal
> points.... Not very useful I know, but there ya go! )

It's not, ADSL goes a lot higher than that in terms of frequency.
There is a tradeoff between complexity of the decoder, and bandwidth.
I suspect the noise may vary with frequency.

--
http://inquisitor.i.am/ | private.php?do=newpm&u= | Ian Stirling.
---------------------------+-------------------------+--------------------------
Q: What do you call a train that doesn't stop at stations?
A: Thomas the Bastard. -- Ben

In article <bmd2up$heh$1$(E-Mail Removed)>, Ian Stirling
<(E-Mail Removed)> writes
>David Walker <(E-Mail Removed)> wrote:
>>> But how does ADSL compare with its theoretical maximum?
>>> (my intuition is it's not as highly optimised as its older brother???
>>> We can check if we know what's the effective bandwidth and signal-to-
>>> noise?)
>>
>> Well, working backwards with a SNR of 27.9 (thats what mine is anyway) and
>> assuming around 500k capacity gives bandwidth of 100.3kHz - doesn't sound
>> like very much though, since I'm sure ADSL goes well up into the MHz ranges
>> doesn't it? Which either means I am wrong about ADSL, or the formula is
>> completely screwy,
**see below

> or I typed the numbers in wrong and missed a few decimal
>> points.... Not very useful I know, but there ya go! )
>
>It's not, ADSL goes a lot higher than that in terms of frequency.
>There is a tradeoff between complexity of the decoder, and bandwidth.
>I suspect the noise may vary with frequency.

(yes - I suspect that too- but let's start with what reads like a
plausible number, 27.5db).

>
....
OK, that gives one useful number (the SNR); (no point in using the band-
width back-calculation, since that's what we're trying to prove).
So, bandwidth -I thought I'd read 300kHz?-(suggesting present data rates
are about 3 less than Shannon)
Bob

(**There are several websites purporting to derive Shannon's result on
the web - my own preference was for Wozencraft & Jacobs, Principles of
Communications Engineering, Wiley 1965 -I used to have a treasured copy
but a fellow student borrowed it and our paths have never crossed since-
that was 30 years ago!)



--
robert w hall

In article <bmd2up$heh$1$(E-Mail Removed)>, Ian Stirling
<(E-Mail Removed)> writes
>David Walker <(E-Mail Removed)> wrote:
>>> But how does ADSL compare with its theoretical maximum?
>>> (my intuition is it's not as highly optimised as its older brother???
>>> We can check if we know what's the effective bandwidth and signal-to-
>>> noise?)
>>
>> Well, working backwards with a SNR of 27.9 (thats what mine is anyway) and
>> assuming around 500k capacity gives bandwidth of 100.3kHz - doesn't sound
>> like very much though, since I'm sure ADSL goes well up into the MHz ranges
>> doesn't it?
well, as a check, 30 db is log10 (1000) I think (Hmm, I suspect there's
a power/voltage confusion possible here), and log2(1000+1) is 10 near as
dammit. So Shannon's max rate predicts more or less 10 bps per Herz of
bandwidth. (This is the same sort as value as the audio-band V34 setups,
I read.)


>Which either means I am wrong about ADSL, or the formula is
>> completely screwy,
(**see below)
>or I typed the numbers in wrong and missed a few decimal
>> points.... Not very useful I know, but there ya go! )
>
(I think you're nearly right - my answer would be nearer to 50kHz I
think)

>It's not, ADSL goes a lot higher than that in terms of frequency.
>There is a tradeoff between complexity of the decoder, and bandwidth.
>I suspect the noise may vary with frequency.
Yes, (but isn't that effect strongest in the audio?)
>


Well, that's one good number (for S/N), and one good back-estimate,
thanks!
My own recollection is that the bandwidth of Broadband down-channel is
about 300kHz, suggesting that we're about a factor 5 off the Shannon
rate ... Anyone confirm?

Bob

(** you'll find discussions/derivations of Shannon's formula on several
sites on the web - my own preference was for the discussion in in
Wozencraft & Jacobs, Principles of Communications Engineering, Wiley,
1965 - I had my own copy, but lent it to a fellow student, some 30 years
ago - our paths have never crossed since...)

--
robert w hall

In article <Dm7tRCAUBmi$(E-Mail Removed)>, robert w hall
<(E-Mail Removed)> writes
>My own recollection is that the bandwidth of Broadband down-channel is
>about 300kHz,

(er,I think I mean up-channel!)

>suggesting that we're about a factor 5 off the Shannon
>rate
>

Anyone like to help on this - (it potentially has relevance to the
extended-reach question??)
--
robert w hall