Signal to noise in relationship with limit of detection and/or signal strength
It's a good question and there is a strong correlation between SNR and the ratio of errors /bit or BER and the steepness of the BER curve in dB per decade of BER.  This curve can also be used with different data patterns and be used to find an asymmetric error in the detector or ISI or harmonic, random and periodic sources of noise.

Normally (no pun intended) each communication standard may have a defined discriminator model and standard detector error value in dB and assume the resolution or quantization error is minimal.

So its not a simple 3 or 10 sigma value, but for a given type, the concept is similar but often expressed in dB for a BER of 1e-9 soft error rate and a few decades higher for hard errors that are uncorrectable.  The variation in standard deviation can be expressed for SNR in dB for a given BER then the slope of dB/ decade is a quality indicator of the discriminator and filters.

Electronic detectors are a little different than chemical detectors with a wide range for error probability.  They may be linear, non-linear, and multidimensional with phases, amplitudes frequencies, antenna diversion or coloured-space and time-multiplexed and even error corrected. 

Each detector must be characterized for Resolution, Jitter, SNR, ISI,  Intersymbol Interference, and any source of error than might be non-Gaussian like PS noise. The ISI might be minimized using a Raised Cosine Filter that is matched to the channel BW for a "Matched receiver response. Or it might not and just have a simple-might level comparator sampled once per bit. 

There may be other sources of error like adjacent channel interference or environmental stress.

It's usually best to use logarithmic values for thresholds and tie this into an overall Channel error budget combining Friis losses, detector errors from jitter and sub-optimal methods not integrating over the entire time interval, A/D errors. etc.  

So each source must be allocated an error budget in the design then verified.

For a very steep slope of BER vs SNR, we expect few surprises from unwanted error sources. When this slope flattens out or changes with data patterns then there is some non-Gaussian effects occurring like Riciian Fading from echoes off walls or trees.

The difference between no signal and no errors with FEC or ECC might be 10 to 20dB depending on the optimization of each block in the design.

With a lot more thought, I might be able to make a more concise answer for you. ;)