signal transmission with cheats

Hello everyone!

There's a rather bizarre thought experiment, that's hopefully 
interesting to discuss.

Suppose I'm a transmitter which is about to transmit a frame of data. 
According to all textbooks, when the frame of data arrives to the 
receiver, the data will be superimposed by noise. In the simplest case, 
AWG noise.

Now, suppose I (the transmitter) have managed to acquire support of a 
supernatural being, which has provided me with the information about 
future noise samples to originate at the receiver side. (That is, 
there's an Universe which enables cheating.)

Now the question is, is it possible to use that information to transmit 
less power while keeping the same SNR (or improving it) at the receiver 
side?

In the case of uncoded transmissions it's only needed to cancel the 
noise at the receiver while transmitting arbitrarily low signal power. 
The benefits are clear.

However there's something like a fundamental limit which requires to 
transmit the power equal to the noise power. Which suggests that 
something like Shannon capacity limit is still in place.

That leads to some questions I don't have ready answers on.

Would coded transmissions improve the situation?

Also, what happens to the Shannon capacity limit when noise is known to 
the transmitter (but is unknown to the receiver)?

Gene

On 09.06.2016 12:48, Evgeny Filatov wrote:

(snip)

> In the case of uncoded transmissions it's only needed to cancel the
> noise at the receiver while transmitting arbitrarily low signal power.
> The benefits are clear.

Oops. That's wrong! I only need to cancel a HALF of the noise -- that 
half which goes in the opposite direction to the useful signal. I'm okey 
with the noise which goes in the same direction as my signal. That 
suggests the SNR limit to uncoded transmissions as low as -3 dB (which 
is already normally impossible).

The question is, would coded transmissions provide any further benefits?

Best regards,
Gene

On Thu, 09 Jun 2016 12:48:04 +0300, Evgeny Filatov
<filatov.ev@mipt.ru> wrote:

>Hello everyone!
>
>There's a rather bizarre thought experiment, that's hopefully 
>interesting to discuss.
>
>Suppose I'm a transmitter which is about to transmit a frame of data. 
>According to all textbooks, when the frame of data arrives to the 
>receiver, the data will be superimposed by noise. In the simplest case, 
>AWG noise.
>
>Now, suppose I (the transmitter) have managed to acquire support of a 
>supernatural being, which has provided me with the information about 
>future noise samples to originate at the receiver side. (That is, 
>there's an Universe which enables cheating.)
>
>Now the question is, is it possible to use that information to transmit 
>less power while keeping the same SNR (or improving it) at the receiver 
>side?
>
>In the case of uncoded transmissions it's only needed to cancel the 
>noise at the receiver while transmitting arbitrarily low signal power. 
>The benefits are clear.
>
>However there's something like a fundamental limit which requires to 
>transmit the power equal to the noise power. Which suggests that 
>something like Shannon capacity limit is still in place.
>
>That leads to some questions I don't have ready answers on.
>
>Would coded transmissions improve the situation?
>
>Also, what happens to the Shannon capacity limit when noise is known to 
>the transmitter (but is unknown to the receiver)?
>
>Gene

Hmm, sounds like one of those dither cancellation systems
where the known dither source can be subtracted at the other
end.

For that matter, it also sounds like an encryption system
where the transmitter and receiver are both using a known
(pseudo) random stream.  Without the known encryption
source, any other receiver gets 100% noise; with the source
they get 100% signal.

Best regards,


Bob Masta
 
              DAQARTA  v9.20
   Data AcQuisition And Real-Time Analysis
              www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
 Frequency Counter, Pitch Track, Pitch-to-MIDI 
FREE 8-channel Signal Generator, DaqMusiq generator    
          Science with your sound card!

> 
> The question is, would coded transmissions provide any further benefits?


well if you had PERFECT information about the noise at the Rx, the Tx could simply transmit a signal that exactly cancels that noise using whatever power that takes.   Then the noise at the Rx = 0 (ideally)  and you would need only  an incremental amount of additional power to send your message.

This rasies all sorts of unanserable questions, are we able to cancel the noise at the Rx antenna only or also the noise in the Rx front end itself as well?  and the second stage noise?   etc?

Thinking about this...the interenting observation is that even with this magic knowledge of the Rx noise, the amount of Tx power needed to send the message is not reduced all that much.  It still takes almost the same about of power (within 2 to 6 dB) to send the noise cancelling signal as it does to send a message today without using magic.

 M

Evgeny Filatov  <filatov.ev@mipt.ru> wrote:

>Hello everyone!
>
>There's a rather bizarre thought experiment, that's hopefully 
>interesting to discuss.
>
>Suppose I'm a transmitter which is about to transmit a frame of data. 
>According to all textbooks, when the frame of data arrives to the 
>receiver, the data will be superimposed by noise. In the simplest case, 
>AWG noise.
>
>Now, suppose I (the transmitter) have managed to acquire support of a 
>supernatural being, which has provided me with the information about 
>future noise samples to originate at the receiver side. (That is, 
>there's an Universe which enables cheating.)
>
>Now the question is, is it possible to use that information to transmit 
>less power while keeping the same SNR (or improving it) at the receiver 
>side?
>
>In the case of uncoded transmissions it's only needed to cancel the 
>noise at the receiver while transmitting arbitrarily low signal power. 
>The benefits are clear.

Yes, a fundamental result is that AWGN is the worst possible type of
noise.  Any additional information that exists about the noise
improves capacity, for a given noise power and signal power.

>However there's something like a fundamental limit which requires to 
>transmit the power equal to the noise power. 

Why do you say this?

Steve

On Thu, 09 Jun 2016 12:48:04 +0300, Evgeny Filatov
<filatov.ev@mipt.ru> wrote:

>Hello everyone!
>
>There's a rather bizarre thought experiment, that's hopefully 
>interesting to discuss.
>
>Suppose I'm a transmitter which is about to transmit a frame of data. 
>According to all textbooks, when the frame of data arrives to the 
>receiver, the data will be superimposed by noise. In the simplest case, 
>AWG noise.
>
>Now, suppose I (the transmitter) have managed to acquire support of a 
>supernatural being, which has provided me with the information about 
>future noise samples to originate at the receiver side. (That is, 
>there's an Universe which enables cheating.)
>
>Now the question is, is it possible to use that information to transmit 
>less power while keeping the same SNR (or improving it) at the receiver 
>side?

Of course.   Anything that improves SNR at the receiver (either
increasing S or decreasing N) improves signal reliability.

>In the case of uncoded transmissions it's only needed to cancel the 
>noise at the receiver while transmitting arbitrarily low signal power. 
>The benefits are clear.
>
>However there's something like a fundamental limit which requires to 
>transmit the power equal to the noise power. Which suggests that 
>something like Shannon capacity limit is still in place.

Not sure what you mean here.

>That leads to some questions I don't have ready answers on.
>
>Would coded transmissions improve the situation?
>
>Also, what happens to the Shannon capacity limit when noise is known to 
>the transmitter (but is unknown to the receiver)?

What matters is the SNR at the detector/slicer.   All kinds of things
may have happened before that, e.g., diversity combining,
equalization, interference cancellation, etc., etc.   The final SNR
when the symbol decision is made (assuming decent statistical
distribution of N), determines the basic capacity.

I think I see where you're going with this, and in the limit if you
keep ratcheting the noise and then the signal powers down, you
ultimately wind up at some minimum quantum level that will then
determine the limit.   Electron volts and valence shells and all that.

On Thu, 09 Jun 2016 13:10:58 +0300, Evgeny Filatov
<filatov.ev@mipt.ru> wrote:

>On 09.06.2016 12:48, Evgeny Filatov wrote:
>
>(snip)
>
>> In the case of uncoded transmissions it's only needed to cancel the
>> noise at the receiver while transmitting arbitrarily low signal power.
>> The benefits are clear.
>
>Oops. That's wrong! I only need to cancel a HALF of the noise -- that 
>half which goes in the opposite direction to the useful signal. I'm okey 
>with the noise which goes in the same direction as my signal.

Assuming there's no information in the amplitude.

>That 
>suggests the SNR limit to uncoded transmissions as low as -3 dB (which 
>is already normally impossible).

-3dB?   Checked the Shannon limit lately?   ;)


>The question is, would coded transmissions provide any further benefits?

As long as there is noise, coding helps, all the way down to the
capacity limit.

On 09/06/2016 15:37, Bob Masta wrote:

(snip)

> Hmm, sounds like one of those dither cancellation systems
> where the known dither source can be subtracted at the other
> end.
>
> For that matter, it also sounds like an encryption system
> where the transmitter and receiver are both using a known
> (pseudo) random stream.  Without the known encryption
> source, any other receiver gets 100% noise; with the source
> they get 100% signal.
>
> Best regards,
>
>
> Bob Masta
>
>                DAQARTA  v9.20
>     Data AcQuisition And Real-Time Analysis
>                www.daqarta.com
> Scope, Spectrum, Spectrogram, Sound Level Meter
>   Frequency Counter, Pitch Track, Pitch-to-MIDI
> FREE 8-channel Signal Generator, DaqMusiq generator
>            Science with your sound card!
>

I was thinking about a system where the sole source of noise is the 
transmitter (e.g. you cool the detector of the receiver with liquid 
nitrogen, so it's not noisy). And some kind of a feedback loop so that 
the transmitter makes use of the noise to transmit less power. It's 
still far-fetched or impossible, but I thought it might make for a fun 
mind exercise. :)

Of course, you are correct about the situation when both the receiver 
and the transmitter know the dither (or pseudo-random stream), which is 
a standard and well-researched case.

Gene

On 09/06/2016 15:59, makolber@yahoo.com wrote:
>
>>
>> The question is, would coded transmissions provide any further benefits?
>
>
> well if you had PERFECT information about the noise at the Rx, the Tx could simply transmit a signal that exactly cancels that noise using whatever power that takes.   Then the noise at the Rx = 0 (ideally)  and you would need only  an incremental amount of additional power to send your message.
>
> This rasies all sorts of unanserable questions, are we able to cancel the noise at the Rx antenna only or also the noise in the Rx front end itself as well?  and the second stage noise?   etc?
>
> Thinking about this...the interenting observation is that even with this magic knowledge of the Rx noise, the amount of Tx power needed to send the message is not reduced all that much.  It still takes almost the same about of power (within 2 to 6 dB) to send the noise cancelling signal as it does to send a message today without using magic.
>
>   M
>
>

Yeah, that's the funny part! That even knowing the noise at the Rx you 
would still need to transmit power. Usually when some quantity cannot 
equal (or asymptotically approach) zero, that implies some sort of a 
mathematical limit... I'm sure that some mathematician has solved that 
problem. But I'm a mathematical noob, and (as the answer is not obvious) 
I'm unaware of it. :)

Gene.

On 09/06/2016 18:12, Eric Jacobsen wrote:

(snip)

>>
>> Now the question is, is it possible to use that information to transmit
>> less power while keeping the same SNR (or improving it) at the receiver
>> side?
>
> Of course.   Anything that improves SNR at the receiver (either
> increasing S or decreasing N) improves signal reliability.
>
>> In the case of uncoded transmissions it's only needed to cancel the
>> noise at the receiver while transmitting arbitrarily low signal power.
>> The benefits are clear.
>>
>> However there's something like a fundamental limit which requires to
>> transmit the power equal to the noise power. Which suggests that
>> something like Shannon capacity limit is still in place.
>
> Not sure what you mean here.
>
>> That leads to some questions I don't have ready answers on.
>>
>> Would coded transmissions improve the situation?
>>
>> Also, what happens to the Shannon capacity limit when noise is known to
>> the transmitter (but is unknown to the receiver)?
>
> What matters is the SNR at the detector/slicer.   All kinds of things
> may have happened before that, e.g., diversity combining,
> equalization, interference cancellation, etc., etc.   The final SNR
> when the symbol decision is made (assuming decent statistical
> distribution of N), determines the basic capacity.
>
> I think I see where you're going with this, and in the limit if you
> keep ratcheting the noise and then the signal powers down, you
> ultimately wind up at some minimum quantum level that will then
> determine the limit.   Electron volts and valence shells and all that.
>

Thanks for all the responses! It's a mathematical, not a physical 
question. I think it's just a puzzle without any applications (because 
you'd run into serious problems with casuality in the real world).

Gene