How/Why a digital signal is inherently more immune to noise?

On Wed, 20 May 2015 15:57:33 -0500, a.s. wrote:

> The primary advantage of digital transmission over analog transmission
> is Noise Immunity. A digital signal (in comparison to an analog signal)
> is inherently more immune to noise. Why the word "inherent"?
> 
> Please make it more clear to me.

Sorta-kinda because as they're generally used, a digital signal has an 
excess of signal to noise for the information that's actually carried.  
The excess information is thrown away at detection along with much of the 
effect of noise.

That's not a good description, but it's the best I can come up with at 
the moment.

-- 
www.wescottdesign.com

On Wednesday, May 20, 2015 at 4:57:36 PM UTC-4, a.s. wrote:
> The primary advantage of digital transmission over analog transmission is
> Noise Immunity. A digital signal (in comparison to an analog signal) is
> inherently more immune to noise. Why the word "inherent"? 
> 
> Please make it more clear to me.
> 
> 
> 
> ---------------------------------------
> Posted through http://www.DSPRelated.com

Under a rather broad set of conditions, using digital communication to convey information allows you to play around with signaling, bandwidth, ECC, processing, etc. such that **for sufficiently high SNR** you can reproduce the input to that system at very high fidelity. 

Things get murkier when you start to go deeper into what fidelity means, introduce constraints in complexity, and most importantly on end-to-end delay. 

It's been known for a long time, due to Toby Berger, that for a Gaussian source and Gaussian channel under MMSE fidelity constraint, the best you can do is uncoded transmission. Google this up. 

Further work by Michael Gastpar expanded the set of sources, channels, fidelity constraints, such that this holds true. His PhD thesis was, "To Code or Not to Code." 

Back to earth and practical stuff, a lot of PHY today operate at very high rate, so the channel coding part isn't a big deal. But the source coding part is still tricky, in particular when you do two-way interactive communication. What's really valuable in using digital transmission (channel coding) is that you can design the signal to best fit the channel you are allowed to use. Noise immunity is often compromised for the sake of having good signal conditioning. The problem of noise immunity is often solved elsewhere, using rate adaptive source coding, ARQ, iterative processing, etc. 

So that statement is vague, in rare cases misleading, and not so insightful.

Tim Wescott <tim@seemywebsite.com> wrote:
> On Wed, 20 May 2015 15:57:33 -0500, a.s. wrote:

>> The primary advantage of digital transmission over analog transmission
>> is Noise Immunity. A digital signal (in comparison to an analog signal)
>> is inherently more immune to noise. Why the word "inherent"?
 
> Sorta-kinda because as they're generally used, a digital signal has an 
> excess of signal to noise for the information that's actually carried.  
> The excess information is thrown away at detection along with much of the 
> effect of noise.

OK, but that is because we have some convenient channels with
appropriate excess bandwidth and noise characteristics.
 
> That's not a good description, but it's the best I can come up with at 
> the moment.

But the other reason is that the cost of digital electronics, per
transistor, is so much less than for analog. If built using discrete
transistors in little metal cans, none of what we do today would
make sense. 

I was explainging Software (sic) Defined Radio to my (non engineer)
brother, and he couldn't see why anyone would want to do that.
Why make something so simple (analog radio) so complicated. 

I think most people don't realize how complicated things like CD
players actually are, compared to analog audio. 

Even with integrated circuitry, analog electronics is nowhere near
where digital electronics is.

A 128GB USB drive, smaller than your thumb, has trillions of
transistors.  As far as I know, all the analog electronics ever made
so far hasn't used a trillion transistors. Well, maybe close.

-- glen
 

On Thu, 21 May 2015 15:08:03 +0000, glen herrmannsfeldt wrote:

> Tim Wescott <tim@seemywebsite.com> wrote:
>> On Wed, 20 May 2015 15:57:33 -0500, a.s. wrote:
> 
>>> The primary advantage of digital transmission over analog transmission
>>> is Noise Immunity. A digital signal (in comparison to an analog
>>> signal)
>>> is inherently more immune to noise. Why the word "inherent"?
>  
>> Sorta-kinda because as they're generally used, a digital signal has an
>> excess of signal to noise for the information that's actually carried.
>> The excess information is thrown away at detection along with much of
>> the effect of noise.
> 
> OK, but that is because we have some convenient channels with
> appropriate excess bandwidth and noise characteristics.

True.  Just as an observation, that applies to wideband FM radio, too, 
which is the only analog signal transmission scheme that I know of that 
has an input SNR to output SNR characteristic that resembles digital 
communications.

Which makes one wonder if it's the only way, or if major Armstrong was 
just an absolutely unique freakin' genius.

>> That's not a good description, but it's the best I can come up with at
>> the moment.
> 
> But the other reason is that the cost of digital electronics, per
> transistor, is so much less than for analog. If built using discrete
> transistors in little metal cans, none of what we do today would make
> sense.

Very little, at least.  People were starting to use digital 
communications, because of the possibility for error correction and 
whatnot, even when computers were built using discrete transistors in 
little metal cans.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim Wescott <seemywebsite@myfooter.really> wrote:
 

(snip on digital vs. analog, and S/N)

>> OK, but that is because we have some convenient channels with
>> appropriate excess bandwidth and noise characteristics.
 
> True.  Just as an observation, that applies to wideband FM radio, too, 
> which is the only analog signal transmission scheme that I know of that 
> has an input SNR to output SNR characteristic that resembles digital 
> communications.

Yes.  I didn't mean to leave that out. 
 
> Which makes one wonder if it's the only way, or if major Armstrong was 
> just an absolutely unique freakin' genius.

As well as I know the story, he must have been pretty close.

I don't remember well by now, but I think he used one tube for
both the oscillator and mixer. Seems detector, too:

https://en.wikipedia.org/wiki/Regenerative_circuit
 
>>> That's not a good description, but it's the best I can come up with at
>>> the moment.
 
>> But the other reason is that the cost of digital electronics, per
>> transistor, is so much less than for analog. If built using discrete
>> transistors in little metal cans, none of what we do today would make
>> sense.
 
> Very little, at least.  People were starting to use digital 
> communications, because of the possibility for error correction and 
> whatnot, even when computers were built using discrete transistors in 
> little metal cans.

Yes, but only for things like military, where they could afford it.

It always seems to me that if you look back, things were always
done earlier than they should have been.  The Wright brothers
got a working airplane knowing very little about aerodynamics.

Philips developed the CD before semiconductor lasers had developed
to the point that ordinary people could afford them. (I believe
the early ones used HeNe lasers.) 

CDs store the track number in BCD (1 to 99) to save on the
logic for the binary to BCD converter. 

-- glen

On 5/21/2015 11:08 AM, glen herrmannsfeldt wrote:
> Tim Wescott <tim@seemywebsite.com> wrote:
>> On Wed, 20 May 2015 15:57:33 -0500, a.s. wrote:
>
>>> The primary advantage of digital transmission over analog transmission
>>> is Noise Immunity. A digital signal (in comparison to an analog signal)
>>> is inherently more immune to noise. Why the word "inherent"?
>
>> Sorta-kinda because as they're generally used, a digital signal has an
>> excess of signal to noise for the information that's actually carried.
>> The excess information is thrown away at detection along with much of the
>> effect of noise.
>
> OK, but that is because we have some convenient channels with
> appropriate excess bandwidth and noise characteristics.

The "excess" capacity often comes from the reduced requirements of 
digital signal transmission compared to analog.  A TV signal, for 
example, uses less bandwidth once the image is compressed digitally or a 
much higher resolution digital image can be conveyed over the same 
channel.


>> That's not a good description, but it's the best I can come up with at
>> the moment.
>
> But the other reason is that the cost of digital electronics, per
> transistor, is so much less than for analog. If built using discrete
> transistors in little metal cans, none of what we do today would
> make sense.
>
> I was explainging Software (sic) Defined Radio to my (non engineer)
> brother, and he couldn't see why anyone would want to do that.
> Why make something so simple (analog radio) so complicated.
>
> I think most people don't realize how complicated things like CD
> players actually are, compared to analog audio.

But that complexity is relatively easy to manage compared to the 
problems analog circuits present.


> Even with integrated circuitry, analog electronics is nowhere near
> where digital electronics is.
>
> A 128GB USB drive, smaller than your thumb, has trillions of
> transistors.  As far as I know, all the analog electronics ever made
> so far hasn't used a trillion transistors. Well, maybe close.

And that difference is exactly why the huge complexity of digital 
devices can be practical and even preferable.

-- 

Rick

Tim Wescott wrote:
> On Thu, 21 May 2015 15:08:03 +0000, glen herrmannsfeldt wrote:
>
>> Tim Wescott <tim@seemywebsite.com> wrote:
>>> On Wed, 20 May 2015 15:57:33 -0500, a.s. wrote:
>>
>>>> The primary advantage of digital transmission over analog transmission
>>>> is Noise Immunity. A digital signal (in comparison to an analog
>>>> signal)
>>>> is inherently more immune to noise. Why the word "inherent"?
>>
>>> Sorta-kinda because as they're generally used, a digital signal has an
>>> excess of signal to noise for the information that's actually carried.
>>> The excess information is thrown away at detection along with much of
>>> the effect of noise.
>>
>> OK, but that is because we have some convenient channels with
>> appropriate excess bandwidth and noise characteristics.
>
> True.  Just as an observation, that applies to wideband FM radio, too,
> which is the only analog signal transmission scheme that I know of that
> has an input SNR to output SNR characteristic that resembles digital
> communications.
>
> Which makes one wonder if it's the only way, or if major Armstrong was
> just an absolutely unique freakin' genius.
>
>>> That's not a good description, but it's the best I can come up with at
>>> the moment.
>>
>> But the other reason is that the cost of digital electronics, per
>> transistor, is so much less than for analog. If built using discrete
>> transistors in little metal cans, none of what we do today would make
>> sense.
>
> Very little, at least.  People were starting to use digital
> communications, because of the possibility for error correction and
> whatnot, even when computers were built using discrete transistors in
> little metal cans.
>


Telegraphy seems a lot digital.

-- 
Les Cargill

a.s. wrote:
> The primary advantage of digital transmission over analog transmission is
> Noise Immunity. A digital signal (in comparison to an analog signal) is
> inherently more immune to noise. Why the word "inherent"?
>
> Please make it more clear to me.
>

I see an unwarranted assumption that "Noise 
Immunity"/"SNR"/whatever has perfect correlation with "channel 
quality". CAVEAT LECTOR - note liberal use of quotation marks.

In my living room I have a daily demonstration that digital does 
not always outperform analog. It's my TV reception.

In the bad old analog days I could always get a useful signal on 
all the local channels.
Now I get acceptable reception for _all_ channels only under 
certain atmospheric conditions.

Yepp, there's some peculiar degenerate local conditions including 
rabbit ears at or near average terrain on path to transmitters 
(I'm on down slope of general terrain and there is a 20+ foot 
high ridge 2 blocks away). In analog days I could see very 
prominent ghosts.

All the discussion in this thread assumes the noise is random. 
The "noise" I deal with is inherently coherent.

On 5/21/2015 11:14 PM, Richard Owlett wrote:
> a.s. wrote:
>> The primary advantage of digital transmission over analog transmission is
>> Noise Immunity. A digital signal (in comparison to an analog signal) is
>> inherently more immune to noise. Why the word "inherent"?
>>
>> Please make it more clear to me.
>>
>
> I see an unwarranted assumption that "Noise Immunity"/"SNR"/whatever has
> perfect correlation with "channel quality". CAVEAT LECTOR - note liberal
> use of quotation marks.
>
> In my living room I have a daily demonstration that digital does not
> always outperform analog. It's my TV reception.
>
> In the bad old analog days I could always get a useful signal on all the
> local channels.
> Now I get acceptable reception for _all_ channels only under certain
> atmospheric conditions.
>
> Yepp, there's some peculiar degenerate local conditions including rabbit
> ears at or near average terrain on path to transmitters (I'm on down
> slope of general terrain and there is a 20+ foot high ridge 2 blocks
> away). In analog days I could see very prominent ghosts.
>
> All the discussion in this thread assumes the noise is random. The
> "noise" I deal with is inherently coherent.

You aren't comparing apples and oranges.  The digital transmission is 
capable of providing either a much higher resolution image than the 
analog signal did or providing multiple channels.  If the extra channel 
capacity were used for increased error recovery I expect the digital 
signal would be adequate under a much wider range of conditions.

-- 

Rick

I would not say a digital signal is inherently more immune to noise
than an analog signal.  Instead I would say that once a signal
is in the digital domain, there are a wealth of techniques that
can improve the noise immunity; in the analog domain, not so much.


S.