What I got is that SNR is relative to a time period. If you average the received signal over a longer period of time, the noise tends to cancel out but the signal tends to stack up (if the transmitter is still transmitting the same bit). Traditionally you'd use a narrower filter to remove more noise while keeping the signal, but today's (and last decade's and the decade's before that) fast computers can do part of the averaging in software, which leads to seeing a digital signal come in as noise, and then a signal magically appears after processing. This can also be done with CDMA signals provided that you're locked onto the timing of the code, which is something analog electronics can't do.