It looks to me that the Signal-to-Noise ratio (SNR or S/N) is completely arbitrary and it's set by the user according to his preferences.
Sorry I am amateur on the subject but I don't see any limitation on this value, it can be set according to what the person transmitting wants to do.
The bit / second rate can be adjusted for speed,quality or quantity, I think those are the only variables.
The Shannon–Hartley formula can be tweaked according to a user's needs:
$$ C = B * log_2(1 + S/N) $$
So for example if I have 1 hour to transmit a 64 bit message, I can choose the optimal S/N ratio.
1 hour is 3600 seconds, so I need a bit/sec rate of minimum 0.017778 bit/sec.
And do achieve that I either tweak S/N ratio or the bandwidth.
- So on 1 Hz a S/N of 0.0125 would give me 0.017921 b/s which would be enough to broadcast the 64 bit message in 1 hour.
- Or I could choose 1 KHz and a S/N rate of 0.0000125 which would give 0.01803 b/s.
- Or 1 Mhz with a S/N rate of 0.0000125 which would give 18.03 b/s that would deliver the message in 3.55 seconds.
So are there any other physical limitations here or is this completely arbitrary and it up to the user to choose.
I have heard that if the S/N rate is below 1, you need a special encoding with checksums to make sure the bits you receiver are genuine. So I guess you would need to send more than 64 bits of information in that case. So that could be an additional burden.
Is there anything else to keep in mind?